{ "cells": [ { "cell_type": "markdown", "id": "5894bc31", "metadata": { "id": "5894bc31" }, "source": [ "# Overview of BasicHullWhite\n", "\n", "The [Hull-White model](https://en.wikipedia.org/wiki/Hull%E2%80%93White_model) is a short rate model represented by the stochastic differential equiation:\n", "\n", " $$dr(t) = (\\theta(t) - a r(t))dt + \\sigma dW$$\n", "\n", "\n", "`BasicHullWhite` in the **economic** library is a simple implementation of the Hull-White model built using [modelx](https://github.com/fumitoh/modelx).\n", "\n", "`BasicHullWhite` preforms Monte-Carlo simulations and generates paths of the instantaneous short rate based on the Hull-White model. It also inclues formulas to calculate various properties of the Hull-White model.\n", "\n", "[Gouthaman Balaraman] presents some tests performed on a Hull-White model. He uses QuantLib to build his model, but the `BasicHullWhite` does not use QuantLib, and its Monte-Carlo simulations are generated from first principles using random numbers following the standard normal distribution.\n", "In addition, `BasicHullWhite` generates values of stochastic variable at each time step at once as a numpy array based on the vector modeling approach.\n", "\n", "This notebook aims to perform analyses similar to Balaraman's using `BasicHullWhite`. \n", "\n", "\n", "[Gouthaman Balaraman]: http://gouthamanbalaraman.com/blog/hull-white-simulation-quantlib-python.html\n", "\n", "\n", "
\n", " \n", "**References**\n", "\n", "* [Gouthaman Balaraman. Hull White Term Structure Simulations with QuantLib Python](http://gouthamanbalaraman.com/blog/hull-white-simulation-quantlib-python.html)\n", "* [Gouthaman Balaraman. On the Convergence of Hull White Monte Carlo Simulations](http://gouthamanbalaraman.com/blog/hull-white-simulation-monte-carlo-convergence.html) \n", "* [Damiano Brigo, Fabio Mercurio (2006). Interest Rate Models - Theory and Practice with Smile, Inflation and Credit, 2nd ed.](https://link.springer.com/book/10.1007/978-3-540-34604-3)\n", "* [Paul Glasserman (2003). Monte Carlo Methods in Financial Engineering](https://link.springer.com/book/10.1007/978-0-387-21617-1)\n", "\n", "\n", "
\n", "\n", "\n" ] }, { "cell_type": "markdown", "id": "f85e6abc", "metadata": { "id": "f85e6abc" }, "source": [ "Click the badge below to run this notebook online on Google Colab. You need a Google account and need to be logged in to it to run this notebook on Google Colab.\n", "[![Run on Google Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/lifelib-dev/lifelib/blob/current/lifelib/libraries/economic/hull-white-simulation.ipynb)\n", "\n", "\n", "The next code cell below is relevant only when you run this notebook on Google Colab. It installs lifelib and creates a copy of the library for this notebook." ] }, { "cell_type": "code", "execution_count": null, "id": "c306b268", "metadata": { "id": "c306b268" }, "outputs": [], "source": [ "import sys, os\n", "\n", "if 'google.colab' in sys.modules:\n", " lib = 'economic'; lib_dir = '/content/'+ lib\n", " if not os.path.exists(lib_dir):\n", " !pip install lifelib\n", " import lifelib; lifelib.create(lib, lib_dir)\n", "\n", " %cd $lib_dir" ] }, { "cell_type": "markdown", "id": "3e70ecf0", "metadata": { "id": "3e70ecf0" }, "source": [ "## Overview of the model\n", "\n", "`HullWiteModel` include only one space, which is named `HullWhite`, and all the definitions are in that space. The `HullWhite` space is assined to `HW` in this notebook." ] }, { "cell_type": "code", "execution_count": null, "id": "bd39830d", "metadata": { "id": "bd39830d" }, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "import modelx as mx\n", "\n", "model = mx.read_model('BasicHullWhite')\n", "HW = model.HullWhite" ] }, { "cell_type": "markdown", "id": "0856413a", "metadata": { "id": "0856413a" }, "source": [ "All the input parameters except for the initial curve are given as *References* (names starting with \"_\" are default names defined by modelx)." ] }, { "cell_type": "code", "execution_count": null, "id": "da0a349b", "metadata": { "id": "da0a349b", "outputId": "62ad2b91-8c48-4084-ec6a-97c33ce9ccab" }, "outputs": [ { "data": { "text/plain": [ "{__builtins__,\n", " _self,\n", " _space,\n", " np,\n", " step_size,\n", " time_len,\n", " a,\n", " sigma,\n", " seed1,\n", " seed2,\n", " scen_size}" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "HW.refs" ] }, { "cell_type": "markdown", "id": "80e9824f", "metadata": { "id": "80e9824f" }, "source": [ "The defalut values for the number of scenarios, length of time ($T$), number of steps, $a$, $\\sigma$ are set equal to the Balaraman's example." ] }, { "cell_type": "code", "execution_count": null, "id": "853a5fe1", "metadata": { "id": "853a5fe1", "outputId": "085d463d-0c5e-49f5-f8b8-7b7720d795d2" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of scenarios: 1000\n", "Length of time (in years): 30\n", "Number of steps: 360\n", "a: 0.1\n", "sigma: 0.1\n" ] } ], "source": [ "print(\"Number of scenarios:\", HW.scen_size)\n", "print(\"Length of time (in years):\", HW.time_len)\n", "print(\"Number of steps:\", HW.step_size)\n", "print(\"a:\", HW.a)\n", "print(\"sigma:\", HW.sigma)" ] }, { "cell_type": "markdown", "id": "c9db74dc", "metadata": { "id": "c9db74dc" }, "source": [ "Below is a list of cells defined in `HW`." ] }, { "cell_type": "code", "execution_count": null, "id": "5448ca15", "metadata": { "id": "5448ca15", "outputId": "8191b653-9b3c-4235-999b-012a6356e856" }, "outputs": [ { "data": { "text/plain": [ "{A_t_T,\n", " B_t_T,\n", " E_rt,\n", " E_rt_s,\n", " P_t_T,\n", " V_t_T,\n", " Var_rt,\n", " Var_rt_s,\n", " accum_short_rate,\n", " accum_short_rate2,\n", " alpha,\n", " disc_factor,\n", " disc_factor_paths,\n", " mean_disc_factor,\n", " mean_short_rate,\n", " mkt_fwd,\n", " mkt_zcb,\n", " short_rate,\n", " short_rate_paths,\n", " std_norm_rand,\n", " t_,\n", " var_short_rate}" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "HW.cells" ] }, { "cell_type": "markdown", "id": "c76bea80", "metadata": { "id": "c76bea80" }, "source": [ "Time-dependent functions are paremeterized with integer indexes instead of times themselves,\n", "i.e. $f(t)$ where $t=t_i, i=1, 2, 3, \\ldots$ in math expression is translated as `f(i)`, `i=1, 2, 3...` in modelx formula.\n", "Mapping $i$ to $t_i$ is done by `t_(i)`. By defalut, $t_i$s are evenly spaced, but the model should work even if the intervals are set uneven." ] }, { "cell_type": "code", "execution_count": null, "id": "66cfc15a", "metadata": { "id": "66cfc15a", "outputId": "a1bb2348-6467-4c65-b4a0-d15e67deb083" }, "outputs": [ { "data": { "text/plain": [ "lambda i: i * time_len / step_size" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "HW.t_.formula" ] }, { "cell_type": "markdown", "id": "5f688053", "metadata": { "id": "5f688053" }, "source": [ "By default, the instanteneous forward rates observed at time 0 ($f^M(0, t_i)$) are set to 0.05 in `mkt_fwd` to be consistent with the Balaraman's example. $P^M(0, t_i)$, the market prices of zero-coupon bonds by duration are calculated from $f^M(0, t_i)$ in `mkt_zcb`. These may be defined the other way around, i.e. $f^M(0, t_i)$ may be derived from $P^M(0, t_i)$ inputs. The forward rates don't have to be constant." ] }, { "cell_type": "code", "execution_count": null, "id": "d50e2889", "metadata": { "id": "d50e2889", "outputId": "498eeb05-3c74-4395-972d-c255fbf8ad04" }, "outputs": [ { "data": { "text/plain": [ "def mkt_fwd(i):\n", " \"\"\"The initial instantaneous forward rate for :attr:`t_(i)`.\n", "\n", " By default, returns 0.05 for all ``i``.\n", " \"\"\"\n", " return 0.05" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "HW.mkt_fwd.formula" ] }, { "cell_type": "code", "execution_count": null, "id": "fb61ea42", "metadata": { "id": "fb61ea42", "outputId": "99caafd9-c90a-46f6-e2dd-631aa260d984" }, "outputs": [ { "data": { "text/plain": [ "def mkt_zcb(i):\n", " \"\"\"The initial price of zero coupon bond\n", "\n", " The initial price of the unit zero coupon bond maturing at :attr:`t_(i)`.\n", "\n", " If ``i=0`` returns 1. Otherwise, defined as::\n", "\n", " mkt_zcb(i-1) * np.exp(-mkt_fwd(i-1)*dt)\n", "\n", " where ``dt = t_(i) - t_(i-1)``.\n", "\n", " .. seealso::\n", " * :attr:`t_`\n", " * :attr:`mkt_fwd`\n", " \"\"\"\n", " if i == 0:\n", " return 1.0\n", " else:\n", " dt = t_(i) - t_(i-1)\n", " return mkt_zcb(i-1) * np.exp(-mkt_fwd(i-1)*dt)" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "HW.mkt_zcb.formula" ] }, { "cell_type": "markdown", "id": "88ca3de3", "metadata": { "id": "88ca3de3" }, "source": [ "`short_rate` corresponds to $r(t_{i})$, and recursively calculates stochastic paths of the instantaneous short rate at each time step." ] }, { "cell_type": "code", "execution_count": null, "id": "f5d42e69", "metadata": { "id": "f5d42e69", "outputId": "ee78b200-6c98-415d-9fc5-26c2ea73b933" }, "outputs": [ { "data": { "text/plain": [ "def short_rate(i):\n", " r\"\"\"Stochastic short rates at :attr:`t_(i)`\n", "\n", " Returns, in a numpy array, simulated stochastic short rates at :attr:`t_(i)`\n", " for all scenarios.\n", "\n", " For ``i=0``, defined as :meth:`mkt_fwd(0)`.\n", "\n", " For ``i>0``, defined as\n", " :math:`r(t_i) = E\\{r(t_i) | \\mathcal{F}_{i-1}\\} + \\sqrt{Var\\{ r(t_i) | \\mathcal{F}_{i-1} \\}} * Z`,\n", "\n", " where :math:`E\\{r(t_i) | \\mathcal{F}_{i-1}\\}`, the expected value of\n", " :math:`r(t_i)` conditional on :math:`\\mathcal{F}_{i-1}` is calculated by :meth:`E_rt_s(i-1, i)`,\n", " :math:`Var\\{ r(t_i) | \\mathcal{F}_{i-1} \\}` the variance of :math:`r(t_i)` conditional on :math:`\\mathcal{F}_{i-1}`\n", " is calculated by :meth:`Var_rt_s(i-1, i)`,\n", " and :math:`Z`, a random number drawn from :math:`\\mathcal{N}(0, 1)`\n", " a standard normal distribution calculated by :meth:`std_norm_rand`.\n", "\n", " .. seealso::\n", " * :attr:`scen_size`\n", " * :meth:`mkt_fwd`\n", " * :meth:`E_rt_s`\n", " * :meth:`Var_rt_s`\n", " * :meth:`std_norm_rand`\n", " * :attr:`seed1`\n", " \"\"\"\n", " if i == 0:\n", " return np.full(scen_size, mkt_fwd(0))\n", " else:\n", " return E_rt_s(i-1, i) + Var_rt_s(i-1, i)**0.5 * std_norm_rand(seed1)[:, i-1]" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "HW.short_rate.formula" ] }, { "cell_type": "markdown", "id": "8b28f6f7", "metadata": { "id": "8b28f6f7" }, "source": [ "Note that the initial stochastic differential equation, $dr(t) = (\\theta(t) - a r(t))dt + \\sigma dW$ is not used in this model.\n", "Rather, the model uses the fact that the Hull-White model is a Gaussian process,\n", "and $r(t^i)$ conditional on $\\mathcal{F}_{t_{i-1}} $ is normally distributed. `short_rate(i)` corresponds to the following expression\n", "\n", "$$r(t_i) = E\\{r(t_i) | \\mathcal{F}_{t_{i-1}}\\} + \\sqrt{Var\\{ r(t_i) | \\mathcal{F}_{t_{i-1}} \\}} * Z$$\n", "\n", "where $Z$ represents random samples drawn from $\\mathcal{N}(0, 1)$, the strandard normal distribution." ] }, { "cell_type": "markdown", "id": "8651ebec", "metadata": { "id": "8651ebec" }, "source": [ "$E\\{r(t_j) | \\mathcal{F}_i\\}$, the mean of $r(t_j)$ conditional on $\\mathcal{F}_{t_i} $ is modeled as `E_rt_s(i, j)`. By replacing $t_{i}$ with $s$ and $t_{j}$ with $t$, the mean is expressed as:\n", "\n", "\n", "$$ E\\{r(t) | \\mathcal{F}_{s}\\} = r(s)e^{-a(t-s)} + \\alpha(t) - \\alpha(s)e^{-a(t-s)} $$\n", " where\n", " $$ \\alpha(t) = f^M(0, t) + \\frac{\\sigma^2} {2a^2}(1-e^{-at})^2$$" ] }, { "cell_type": "code", "execution_count": null, "id": "60fcf2f2", "metadata": { "id": "60fcf2f2", "outputId": "ab56b6df-9aac-4d3a-cde1-d1c2da2295fc" }, "outputs": [ { "data": { "text/plain": [ "def E_rt_s(i, j):\n", " r\"\"\"Conditional expected values of :math:`r(t_j)`\n", "\n", " Returns, in a numpy array,\n", " :math:`E\\{r(t_j) | \\mathcal{F}_{i}\\}`,\n", " the expected values of :math:`r(t_j)` conditional on :math:`\\mathcal{F}_{i}`\n", " for all scenarios.\n", " :math:`E\\{r(t) | \\mathcal{F}_{s}\\}` is calculated as:\n", "\n", " .. math::\n", "\n", " r(s)e^{-a(t-s)} + \\alpha(t) - \\alpha(s)e^{-a(t-s)}\n", "\n", " where :math:`\\alpha(t)` is calculated by :meth:`alpha`.\n", "\n", " .. seealso:\n", " * :meth:`short_rate`\n", " * :meth:`alpha`\n", " \"\"\"\n", " s, t = t_(i), t_(j)\n", " r_s = short_rate(i)\n", " return r_s * np.exp(-a * (t-s)) + alpha(j) - alpha(i) * np.exp(-a * (t-s))" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "HW.E_rt_s.formula" ] }, { "cell_type": "code", "execution_count": null, "id": "b26d1172", "metadata": { "id": "b26d1172", "outputId": "cf644f64-0265-416f-c5c2-705352bb272d" }, "outputs": [ { "data": { "text/plain": [ "def E_rt():\n", " \"\"\"The expected values of :math:`r(t_i)` at time 0 for all :math:`t_i`.\n", "\n", " Returns, in a numpy array, the expected values of\n", " :math:`r(t_i)` for all :math:`t_i`.\n", " Calculated as :math:`E\\{r(t_i) | \\mathcal{F}_{0}\\}`.\n", "\n", " .. seealso::\n", "\n", " * :meth:`E_rt_s`\n", "\n", " \"\"\"\n", " return np.array([E_rt_s(0, i)[0] for i in range(step_size + 1)])" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "HW.E_rt.formula" ] }, { "cell_type": "markdown", "id": "e048eb28", "metadata": { "id": "e048eb28" }, "source": [ "In the same way, $Var\\{r(t_{j}) | \\mathcal{F}_{t_i}\\}$, the variance of $r(t_j)$ conditional on $\\mathcal{F}_{t_i}$ is modeled as `Var_rt_s(i, j)`. With the same definitions for $s$, $t$, $\\alpha(t)$ as above, the variance is expressed as:\n", "\n", "$$ Var\\{ r(t) | \\mathcal{F}_s \\} = \\frac{\\sigma^2}{2a} (1 - e^{-2a(t-s)})$$\n" ] }, { "cell_type": "code", "execution_count": null, "id": "080f961d", "metadata": { "id": "080f961d", "outputId": "d4f549eb-bea5-4e46-b6c3-da8704048a33" }, "outputs": [ { "data": { "text/plain": [ "def Var_rt_s(i, j):\n", " r\"\"\"The variance of :math:`r(t_j)` conditional on :math:`\\mathcal{F}_{t_i}`\n", "\n", " :math:`Var\\{r(t_{j}) | \\mathcal{F}_{t_i}\\}`,\n", " the variance of :math:`r(t_j)` conditional on :math:`\\mathcal{F}_{t_i}`,\n", " calculated as:\n", "\n", " .. math::\n", "\n", " Var\\{ r(t) | \\mathcal{F}_s \\} = \\frac{\\sigma^2}{2a} (1 - e^{-2a(t-s)})\n", "\n", " .. seealso::\n", " * :attr:`a`\n", " * :attr:`sigma`\n", "\n", " \"\"\"\n", " s, t = t_(i), t_(j)\n", " return sigma**2 / (2*a) * (1 - np.exp(-2 * a * (t-s)))" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "HW.Var_rt_s.formula" ] }, { "cell_type": "markdown", "id": "1bc419f2", "metadata": { "id": "1bc419f2" }, "source": [ "Note that for each `i`, `short_rate(i)` returns a 1-dimensional numpy array having `scen_size` elements,\n", "and for each pair of `i` and `j`, both `E_rt_s(i, j)` and `Var_rt_s(i, j)` also return an array with `scen_size` elements." ] }, { "cell_type": "markdown", "id": "dca46262", "metadata": { "id": "dca46262" }, "source": [ "$\\alpha(t_{i})$ is modeled as `alpha(i)`. `alpha(i)` doesn't vary by scenario, so it returns a single value for each `i`." ] }, { "cell_type": "code", "execution_count": null, "id": "80339d01", "metadata": { "id": "80339d01", "outputId": "ba386c04-7944-4b72-e4a7-b1ca330dd0bc" }, "outputs": [ { "data": { "text/plain": [ "def alpha(i):\n", " r\"\"\":math:`\\alpha(t_i)`\n", "\n", " Returns, in a numpy array, :math:`\\alpha(t_i)` for all scenarios.\n", " :math:`\\alpha` appears in the expression of\n", " :math:`E\\{r(t) | \\mathcal{F}_{s}\\}` and is defined as:\n", "\n", " .. math::\n", "\n", " \\alpha(t) = f^M(0, t) + \\frac{\\sigma^2} {2a^2}(1-e^{-at})^2\n", "\n", " .. seealso::\n", " * :meth:`E_rt_s`\n", "\n", " \"\"\"\n", " t = t_(i)\n", " return mkt_fwd(i) + 0.5 * sigma**2 / a**2 * (1 - np.exp(-a*t))**2" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "HW.alpha.formula" ] }, { "cell_type": "markdown", "id": "4a5a37b8", "metadata": { "id": "4a5a37b8" }, "source": [ "## Simulating $r(t_i)$\n", "\n", "The chart below shows the first 10 paths of $r(t_i)$.\n", "`short_rate_paths()` is defined to return $r(t_i)$ for all the scenarios and all the tim steps in a 2-dimensional array." ] }, { "cell_type": "code", "execution_count": null, "id": "8a28a393", "metadata": { "id": "8a28a393", "outputId": "53525671-0151-4224-abe7-479796f14879" }, "outputs": [ { "data": { "text/plain": [ "def short_rate_paths():\n", " \"\"\"Short rate paths.\n", "\n", " Returns, as a 2D numpy array, the simulated short rate paths\n", " for all scenarios.\n", "\n", " .. seealso::\n", " * :meth:`short_rate`\n", " \"\"\"\n", " return np.array([short_rate(i) for i in range(step_size + 1)]).transpose()" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "HW.short_rate_paths.formula" ] }, { "cell_type": "code", "execution_count": null, "id": "824f6ee1", "metadata": { "id": "824f6ee1", "outputId": "3eb943ca-5fa6-451c-c8d8-5ec3d3d37579" }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for i in range(10):\n", " plt.plot(range(HW.step_size+1), HW.short_rate_paths()[i])" ] }, { "cell_type": "markdown", "id": "75a7a999", "metadata": { "id": "75a7a999" }, "source": [ "For each $t_i$, the mean of $r(t_i)$ should converge to $E\\{r(t_i) | \\mathcal{F}_{0}\\}$. For convenience, `mean_short_rate` and `E_rt` are defined to represent the mean of $r(t_i)$ and $E\\{r(t_i) | \\mathcal{F}_{0}\\}$ respectively." ] }, { "cell_type": "code", "execution_count": null, "id": "50153c02", "metadata": { "id": "50153c02", "outputId": "9021e1c3-55de-41cf-b975-e27b323a2d10" }, "outputs": [ { "data": { "text/plain": [ "def mean_short_rate():\n", " \"\"\"The means of generated short rates\n", "\n", " Returns, as a numpy array, the means of short rates of all scenarios\n", " for all :math:`t_i`.\n", " This should converge to the theoretical variances\n", " calculated by :meth:`E_rt`.\n", "\n", " .. seealso::\n", " * :meth:`short_rate`\n", " * :meth:`E_rt`\n", " \"\"\"\n", " return np.array([np.mean(short_rate(i)) for i in range(step_size + 1)])" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "HW.mean_short_rate.formula" ] }, { "cell_type": "code", "execution_count": null, "id": "1beaed66", "metadata": { "id": "1beaed66", "outputId": "178e19b2-cbd1-41ae-c15e-8821751075bc" }, "outputs": [ { "data": { "text/plain": [ "def E_rt():\n", " \"\"\"The expected values of :math:`r(t_i)` at time 0 for all :math:`t_i`.\n", "\n", " Returns, in a numpy array, the expected values of\n", " :math:`r(t_i)` for all :math:`t_i`.\n", " Calculated as :math:`E\\{r(t_i) | \\mathcal{F}_{0}\\}`.\n", "\n", " .. seealso::\n", "\n", " * :meth:`E_rt_s`\n", "\n", " \"\"\"\n", " return np.array([E_rt_s(0, i)[0] for i in range(step_size + 1)])" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "HW.E_rt.formula" ] }, { "cell_type": "markdown", "id": "dbde5f1c", "metadata": { "id": "dbde5f1c" }, "source": [ "The chart below compares the mean of $r(t_i)$ against $E\\{r(t_i) | \\mathcal{F}_{0}\\}$ with 1000 scenarios. The chart looks similar to Balaraman's analysis. The mean converges pretty well during the first 20 years (240 steps), but diverges from the expectation around the 300th step." ] }, { "cell_type": "code", "execution_count": null, "id": "bab42dc4", "metadata": { "id": "bab42dc4", "outputId": "126311d4-8480-4581-b437-b1b03163868e" }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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Y1OMT7JOnUHbLUjzLaLEQsYZ6RkREXJhhwHffwSuvwC+/wJ2sZxSvmvveeY/GL/SxuEIRhREREZf1ww8wZAisX28+9/eHiJeakZYyAu9iRSjywrPWFihygcKIiIiL2bULXnoJFi0ynzfw/pW+Dx6iwyfhlC4N8LqV5YlcRmFERMRFHDsGI0bAJ59AZibU8PiD+cFPU/PgSthyM5T+y+oSRa5IE1hFRJzc+fPw9ttQtSpMmGAGkaGNV/Jr8cZmEClSBKpVMw8UcUDqGRERcVJ2O8yebc4L2bcPwODpqrG8XvELglbNNA9q1AhmzTKXVhVxUAojIiJOaMMGGDwYfvrJfH7TTTDh6d9oN/Q++PPCQX36wNixUKyYZXWK5ITCiIiIE4mPh+efhzlzzOeV/I7Ra0gZnn0WihWrDYf6m9fzdu8Od9xhbbEiOaQwIiLiBM6dg3ffhTFjzK89PODFx/Yzaml9PB7+AYrVMA/8+GNrCxXJA01gFRFxYIYB8+aZK6cOG2YGkebNIS4ORme8gMepk2ZCEXFi6hkREXFQO3bAM8/AqlXm8woV4L33oGOdndgGDjB3eHhAVJSldYpcL/WMiIg4mFOnYNAgqFfPzBs+PvDaa7BzJ3SqugVb87suBZERI6B+fatLFrku6hkREXEQhgFffgkvvADHj5vbHnoI3n8fKlfG3DFunLmQSGioOX4TEmJpzSL5QT0jIiIOYMcOcy7IE0+A1/FDzAt4kmMN72d+x5lmEAEoW9YMIg89BCtWKIiIy1AYERGx0Nmz8PLL5khL4vpf+MazHXu9q9Mh8XMCf14Ga9ZcOvjiwiLz50OJEhZVLJL/NEwjImKRxYvNCaqV9q1hCOt4uch7FMs4A5mYwzBdu2bv/bDZoGFDy+oVKSgKIyIihSw+3gwhixaBDTvRxT6mdco8yABatIB33jHDiIc6r8U9KIyIiBSSjAxz/unw4ZCSAl6edgY/70Hz1+bCpLHmAc88A76+VpcqUqgURkRECsHWrdCzJ+zakowHBpNDxtOmkx9lxww2Dxg82NL6RKykMCIiUoDOnYORI82l3IMyD/KXLZQytuN47MuEnW0h4xkool/F4t70P0BEpICsWwe9esHu3ebckCVBTxJ05AgYFw5o1kxBRASFERGRfJeYCC+9BJMmmc9rlT3JlpTq+Bw5bs4HWbDAvDS3cWNL6xRxFAojIiL5aPFiiOqXitehvUB1eveGcdW/xue54+DnB5Mnw/33W12miEPJ03Vj0dHRVK5cGV9fX0JDQ1m/fn2OXvfDDz9QpEgR6us+CiLiYk6cgMceg0Ht9hBzqA0LvTuxekUmkyZBsea3wwcfmMusPvqo1aWKOJxch5HZs2cTFRXF0KFDiYuLo1mzZkRERBAfH3/N1yUmJtKtWzfuueeePBcrIuKIFi+G2rWhxaw+7OFm7mUlNbz+okXlfeYBoaHmJbtavl3kinIdRsaOHUvPnj3p1asXNWvWZPz48VSoUIGJEyde83V9+vShc+fOhIWF5blYERFHcvo09OgB7dpBzSOr6UMMhs0Gd92Fbc0auPlmiysUcQ65CiNpaWls3ryZ8PDwbNvDw8PZuHHjVV/3+eef89dffzFs2LAcfZ/U1FSSkpKyPUREHMmyZVCnjnmXXV/OMy3oeQBsTz8Na9dq2XaRXMhVGDl+/DiZmZkEBQVl2x4UFMThw4ev+Jrdu3fz8ssvM2PGDIrk8BK20aNHExAQkPWoUKFCbsoUESkwZ85A797mHNSDB6H2zec4dEc7yh/ZAv7+8PrrVpco4nTyNIHVZrNle24YxmXbADIzM+ncuTMjRoygWrVqOX7/IUOGkJiYmPXYv39/XsoUEclXq1dD3brw6afm82eegR+3elPy5lLmlTILF8KNN1pao4gzytWlvYGBgXh6el7WC3L06NHLeksAzpw5w88//0xcXBwDBgwAwG63YxgGRYoUYfny5bRs2fKy1/n4+ODj45Ob0kRECsz58zBkCIwfb9CapdQLvpEXPyxP00eCAU+YOhV27TLHbUQk13IVRry9vQkNDSU2NpaHHnooa3tsbCzt2rW77Hh/f3+2b9+ebVt0dDSrVq1i7ty5VK5cOY9li4gUju3boXNn+PVXeIm3GcMQSACG1YKIH80eES8vBRGR65DrRc8GDx5M165dadiwIWFhYcTExBAfH0/fvn0Bc4jl4MGDTJ06FQ8PD+r86z/ojTfeiK+v72XbRUQcid0OH30En77wB+fSPWlZMolRycMhHbDZ4ORJ2LcPatWyulQRp5frMBIZGcmJEycYOXIkCQkJ1KlTh6VLlxJy4fr5hISE/1xzRETEkSUkmJfsLl8O7xLD87yPkeiBzW6HiAiYPh18fMxeERG5bjbDMIz/PsxaSUlJBAQEkJiYiL+/v9XliIgLW7jQvLndiRPmbWQ+HnmSJ9+uhu3ECWjbFj77TJNURXIop5/fujeNiAhwNtlg1gMzKLZmCSv5jberTeG1haHUrFkKumyHlBSoUsXqMkVcksKIiLi9LVtgdusvefvIE1nbvnx+O141Q80nwcEWVSbiHhRGRMRtGXaD+VHrODXhK163TwfgUOuelOvXHq877rC4OhH3oTAiIm7p1ClY2GwsT+x4PmtbeotWlFs8CTw9LaxMxP3kaQVWERGnlJwMycls2gS33QZf7gjlHL782qQ3xvwFeC1foiAiYgH1jIiI67PbISUFo00b/jxegua75pOW6YnvzU35fcoRbmuuq/RErKQwIiKu7f/+Dzp1gvh4bMCN+FOevdweWYWYGC/8/b2srlDE7WmYRkRc1zffwN13w4WFGFMoyiPei3k5pgozZ5o32RUR66lnRERc04wZGN26YbPb+Y4I+hFNcDV/YuaWom5dq4sTkX9Sz4iIuKTU/23BZrfzOT14kEW06F6JFVsUREQckXpGRMTlbNsGDy97n1u4h1Ve9xM9wYNevcz724mI41EYERGXMm0a9OkD585BekhrNsyFhg2trkpErkXDNCLiElIPHuf/qnWhdLfWlD33N/fdB5s3K4iIOAP1jIiI04uPhz/qP829p+YAsLxKPyp/+z2eRTQuI+IM1DMiIk4tNhZG1P6ae0/NIRMPNo/4lqq/L1EQEXEiCiMi4pSMTDuz+q3FFn4vnyVHAnC2e39CX28DRdTpK+JM9D9WRJzOuXPwVC8b4796mEBOkO7hja1fP/zfHW11aSKSBwojIuJU4uPhoYdgyxYb99laE9rIi5ozX8dWKcTq0kQkjxRGRMRp/D5sJqM+uIEtiQ8QGAgV5kylVgurqxKR66UwIiJOYfpb8Twy8gk+pChHav3Kp0tvIkSdISIuQRNYRcShpaVB376QPnQYvqRyJLAOC/8vWEFExIWoZ0REHNaRI/DII3Byww4mMBWA6t+8h+0G/R0l4koURkTEIW3bBg88YE5YXVLkFTwz7PDww9gaN7K6NBHJZ/rzQkQcztKl0LQp7I+3M7zMBFpnLAZPTxg1yurSRKQAKIyIiMMwDPjwQ7NHJDkZBtdbxevHB5o7n34aqle3tkARKRAaphERh5CeDoMGwcSJ5vOePeGt6HuxLZgJhw/DgAHWFigiBUZhREQsd/o0dOpk3mfGZoN334XBg82viYy0ujwRKWAaphERS/39NzRpYgaRYsXg+0/28tyOJ7H9udvq0kSkkKhnREQss2EDtG8P508kE33DSHr5Tser3xGw22HFCvjrL/DysrpMESlgCiMiYomvvoInngDftES2Fr2Tqsm/QvKFnS1bwkcfKYiIuAkN04hIoTIMGDMGHn8cMtMyWHNjJFXP/Qply8L8+ZCQACtXQq1aVpcqIoVEPSMiUmgyM2HgwEtXzHzQ8Qfqz4uFokVhyRJo0MDaAkXEEgojIlIoUlLgscdg8WLzKplx46D/oObw/RI4d05BRMSNKYyISIE7etRcyOzHH8HXF6ZPh4cfvrDz/vstrU1ErKc5IyJSoHbvNi/d/fFHqFziFNsHfcrDszvBn39aXZqIOAiFEREpMJs2mUEk/q80xpYYyZ+p5an6dm+YM8ccltm3z+oSRcQBaJhGRArEokXw6KOQet7O9yW7EX5qtrmjTh3o0sWcQFKxorVFiohDUBgRkXwXEwP9+kE3++cM9f+IqqfioEgR+OIL6Nz5wjrvIiImDdOISL4xDBg1Cvr0MRdRrdm2KlWCU8DTEyZPNhcXURARkX9Rz4iI5Au73by53QcfmM+HDoUX3miGLX4ZeHhAhQrWFigiDkthRESuW3q6ubT7jBkQySyeaf0XTd4cau4MCbG2OBFxeAojInJdzp6Fjh1h43en+dA2jIHGh7C8COzuBLfcYnV5IuIEFEZEJM9OnoS2bQxqbPqcP3iZG41j5o6oKLj5ZktrExHnoTAiInly8CA82Oocz+3sSWdmmhtr1IDx4+G++yytTUSci66mEZFc++MPaNoUuu18mc7MxChSBN5+G7ZtUxARkVxTz4iI5Movv0CrVnDsGNhLl8Ge7IvHnK/Nm8+IiOSBwoiI5Nj//Z95X7vTp+G22+Dx71/Fg95w441WlyYiTkxhRERyZO1aaNsW0pPP07yxjUXf+xAQAKAgIiLXR3NGROQ/ff+92SOSnAwf3zyOVYeqE7BqgdVliYiLUBgRkWtasAAefBDOn4fu9xyg58l38IjfBykpVpcmIi5CYURErmr6dHNBs/R06Nv2AJ/vaY7t9Gm49VbzlrwiIvlAYURErigmBrp1g8xM6NEDJvgOxvb33+ZiZt98Y978TkQkH2gCq4hcZtw486Z3AAMGwAcdN+DRfI55x90FC6BiRWsLFBGXojAiItmMGgWvvmp+/dJLMPrNTGyBbc0Njz9uDtGIiOQjhRERyTJiBAwfbn79xhswdCjYbJ7w0EPw668wZoyl9YmIa1IYEREMA4YNMwMIwAdvJPHM0xlgK2VumDgRfH2tK1BEXJomsIq4OcMwh2UuBpGpg7fyzPQ7zCVWN20yNyqIiEgBUs+IiBszDBgyxLzHHcCcp1fzSMyD5upm5crpihkRKRTqGRFxU4ZhTlA1g4jB+vbv80hMuBlEWrQw78B7++0WVyki7kBhRMQNGQY8/zy8+675fHP4K9y58HnIyIDISPjuOyhd2toiRcRtKIyIuBnDgGefhbFjzedLn/6WBssvXCUzdizMnKk5IiJSqDRnRMSNGAYMGgQffWQ+j4mBiO7hsKwK9O9vphQRkUKmMCLiJv4ZRGw2mDwZnnwSwBu2b4eiRa0uUUTcVJ6GaaKjo6lcuTK+vr6Ehoayfv36qx67YcMGmjZtSunSpSlatCg1atRg3LhxeS5YRHLv4hyRi0Fk/ojtPHnwjUt33lUQEREL5bpnZPbs2URFRREdHU3Tpk2ZNGkSERER/Pbbb1S8wv0q/Pz8GDBgALfeeit+fn5s2LCBPn364OfnR+/evfOlESJydYYBr7xyaY7Il2NP0P6bKFi1Cg4ehE8+sbQ+ERGbYRhGbl7QqFEjGjRowMSJE7O21axZk/bt2zN69OgcvUeHDh3w8/Nj2rRpOTo+KSmJgIAAEhMT8ff3z025Im5v+HBYO2I1NdnJgKZx1Nr4mZlQvL1h507zLrwiIgUgp5/fuRqmSUtLY/PmzYSHh2fbHh4ezsaNG3P0HnFxcWzcuJHmzZvn5luLSB6MGgVfjfiDWFoRTX9q/TDZDCLVqsHnnyuIiIhDyNUwzfHjx8nMzCQoKCjb9qCgIA4fPnzN15YvX55jx46RkZHB8OHD6dWr11WPTU1NJTU1Net5UlJSbsoUEcw1RF59FZpylORSFSlxcg9ERJhjNnfeaXV5IiJZ8nQ1jc1my/bcMIzLtv3b+vXrSU5OZtOmTbz88stUrVqVxx577IrHjh49mhEjRuSlNBEBpg7ZyU9jtgOdiHjzTkq8uAtOn4YyZawuTUTkMrkKI4GBgXh6el7WC3L06NHLekv+rXLlygDUrVuXI0eOMHz48KuGkSFDhjB48OCs50lJSVSoUCE3pYq4rUnjz9F6TDi3UJ6ar3di6FAALwUREXFYuZoz4u3tTWhoKLGxsdm2x8bG0qRJkxy/j2EY2YZh/s3Hxwd/f/9sDxH5b5Mnw9/PfkgFDnBr0d0MH5pudUkiIv8p18M0gwcPpmvXrjRs2JCwsDBiYmKIj4+nb9++gNmrcfDgQaZOnQrAhAkTqFixIjVq1ADMdUfee+89Bg4cmI/NEJHp02HhU0uYxRsAFPtkHDZvL4urEhH5b7kOI5GRkZw4cYKRI0eSkJBAnTp1WLp0KSEhIQAkJCQQHx+fdbzdbmfIkCHs2bOHIkWKUKVKFcaMGUOfPn3yrxUibm7hQpjWfQVLeRBP7Bjh4di6PG51WSIiOZLrdUasoHVGRK4uNhai2uxmZXozynIE49HHsE39ErzUKyIi1iqQdUZExLH88AO0bw9V0neaQeSWW7BN/lRBREScisKIiDP6+29Otu5Cx4hkUlLAt2VT7Hffg23BAvDzs7o6EZFc0V17RZxJZiZMmULm4OcplZzEGSbSrBl88U1pPIqtsLo6EZE8URgRcRZJSfDww7BiBZ7AJhpx2202vv0WihWzujgRkbxTGBFxBkePmku5b9nCWZsfrxijWFOrP6tii6A53SLi7BRGRBzd0aPmvWR27+aEZxnCM78jsUoo61dA6dJWFycicv0URkQc3Zw5sHs3h7xDaJG2nJSbqrFhBQQHW12YiEj+UBgRcXCpvfozMiaEJdvKcyqwGutXQKVKVlclIpJ/FEZEHFhmJnTpAnO3teWGG2DN93DhzgoiIi5D64yIOKLff8eIiODNzr8xdy54e8OiRRAaanVhIiL5Tz0jIo4mMxMGDsS2YgX18MFmW8iMGdCypdWFiYgUDPWMiDiSzEzo0QNWrCAVb57nPaKj4ZFHrC5MRKTgKIyIOJJnn4Xp00mnCI8zg24jqtK3r9VFiYgULIUREUfx7rvw0UcAdGE6Zfs/wmuvWVyTiEghUBgRcQSTJsGLLwLwAu9gi4zkww/BZrO4LhGRQqAJrCIOYHfNBznkNYc16U35pdULfDsVPPSngoi4CYUREYsdOAD3dg1mf/pyGja0sXKeeSmviIi70N9eIlZJTSV5xiLuvx/i46FadQ+WLLVRvLjVhYmIFC6FERGLZLw5hhu6tOeRHcMpVw6WLYMyZayuSkSk8CmMiFjA/sef2N8aDcC+ojX5/nsICbG4KBERiyiMiBS206c53LQD3vZUltvC6fpNJ+rWtbooERHrKIyIFCa7nX2NIyl3fDsJlCVlXAwt79H1uyLi3hRGRApR3FMTCNm1nBSKsmzQd7QfpLEZERGFEZFC8sOyZEKmDAPg27vepfu4+tYWJCLiIBRGRArBzp3wwGM30IdJrL/pUR5e0U+rq4qIXKAwIlLADh00uP9+OHUKDoZ1pOEfX+Hppf96IiIX6TeiSAFK3rCVs1VvpXr8cqpVg8WLoWgxdYmIiPyTwohIQTAMMt94i4yW4dxy/lee9pnCd99BYKDVhYmIOB7dm0akABifTMLz9aGUAPbYKlN57rvcfLPVVYmIOCb1jIjkpwMH4KmnyHjmWQCG2Uaya9Eu6rWtYHFhIiKOSz0jIvklIwMefBDi4vACvqEtN0UP5f4HlPlFRK5FvyVF8ounJzsffIk/qEYES/nh+YX07qv/YiIi/0W/KUXyyR+7bdz5USQ1+Q2/hyN4621Pq0sSEXEKCiMi1yszk+PxKbRpAydPwu2NPJk2DTz0v0tEJEf061LkOqV9Ph2qVqXxn9OoVAkWLYKiRa2uSkTEeSiMiFwH43wqiVHDCExPoJLvYZYsgaAgq6sSEXEuCiMieZWWxo4GXSlzdh+HCKbl3P7UqmV1USIizkdhRCQvtm3jRLUw6uycQyre/PrMp9zdppjVVYmIOCWtMyKSWwkJpN11D6UTj3OKEix8dBZPfHCf1VWJiDgthRGRXDo25jPKJB5nK/WY2G4ZE2dokoiIyPVQGBHJhWPHoNHiobSiDGfq38WUWUG6hFdE5DopjIjk0Llz0K4d7NlrY8XNfdi0HHx9ra5KRMT56W86kRww0tJZcscI9vwvgRIlYMkSKFPG6qpERFyDwohIDnzz6Awe+XU4/yOM+XPt1KhhdUUiIq5DYUTkP8yba1BxwXgAjjzUj7vv0X8bEZH8pN+qItewZQtMeHwj9fmFNE9fGk1+yuqSRERcjsKIyFUcOgQPPgi90iYAUKRrZyhVyuKqRERcj8KIyBWkpJhXzmQcPExH5gLgMbC/xVWJiLgmhRGRfzEMeOIJ+PlnGFT0U7xIh8aNoUEDq0sTEXFJCiMi/zJyJHz9NXh5QedOGVCsGPRXr4iISEFRGBH5h6+/huHDza8nToSQL0aYk0c6drS0LhERV6YVWEUu+Okn6N7d/Pq556Bnzws7AgIsq0lExB2oZ0QEOHjQnLB6/jx0DE/k3VUNYNw4SE+3ujQREZenMCJuLyXFvIQ3IQFq14apLaZgi4uDzz6DIuo8FBEpaPpNK27NbjeHZrZsgcBAWBpzAN+I4ebOZ54Bm83S+kRE3IF6RsStDR8Oc+eaV84smG9Q8c3ekJRkXsqbNWlEREQKksKIuK2ZM+GNN8yvY2Lgzr++hO++Ax8fmDIFPD2tLVBExE1omEbc0s8/w5NPml+/+CL0aHUQakeZG0aOhJo1LatNRMTdqGdE3E5CArRvb14507YtvPUWsHIlnDkDd9wBgwdbXaKIiFtRz4i4ldRUePhh81LemjVhxowLozHdukH16uDvrytoREQKmX7ritswDOjXD/73PyhRAr4b8wv+uzMgNNQ8oFEjS+sTEXFXCiPiNj78ED7/HDw8YMEnRwjpfR9kZsLGjXDLLVaXJyLitjRnRNzCihXmEu8A771jp8WUbnDkCJQtC2XKWFuciIibUxgRl/fnn9Cpk9kJ0r07RGW+D8uXQ9GiMHu2OWYjIiKWyVMYiY6OpnLlyvj6+hIaGsr69euveuz8+fNp1aoVZcqUwd/fn7CwMJYtW5bngkVyIynJvOfMqVPwSL3dfJbRHdvQV8ydH3wAtWpZW6CIiOQ+jMyePZuoqCiGDh1KXFwczZo1IyIigvj4+Csev27dOlq1asXSpUvZvHkzd999Nw888ABxcXHXXbzItdjt0KUL/PYb1C57gllH78ZzxlTIyIDOnaFXL6tLFBERwGYYhpGbFzRq1IgGDRowceLErG01a9akffv2jB49OkfvUbt2bSIjI3n99ddzdHxSUhIBAQEkJibi7++fm3LFjb36KowaZS6oun6dwe1LR8DXX8OECdC8uTmTVURECkxOP79z9ds4LS2NzZs3Ex4enm17eHg4GzduzNF72O12zpw5Q6lSpa56TGpqKklJSdkeIrnx9dcwZlQGFYhn8mS4/Q6beSOan3+Gu+9WEBERcSC5+o18/PhxMjMzCQoKyrY9KCiIw4cP5+g93n//fc6ePUunTp2ueszo0aMJCAjIelSoUCE3ZYqbi4uDHj3gdUays2gDulRcd2lnsWKW1SUiIleWpz8Pbf+6rbphGJdtu5KZM2cyfPhwZs+ezY033njV44YMGUJiYmLWY//+/XkpU9zQkSPQ/kE7Lc99y1DbW/idO2Gu/y4iIg4rV4ueBQYG4unpeVkvyNGjRy/rLfm32bNn07NnT+bMmcO99957zWN9fHzw8fHJTWkipKXBwNZ/Me9AJA3ZDAbmNb2RkVaXJiIi15CrnhFvb29CQ0OJjY3Ntj02NpYmTZpc9XUzZ86kR48efPXVV7Rp0yZvlYpcg2HAmMe2ErMllIZsJtOvOPTpAzExVpcmIiL/IdfLwQ8ePJiuXbvSsGFDwsLCiImJIT4+nr59+wLmEMvBgweZOnUqYAaRbt268cEHH9C4ceOsXpWiRYsSEBCQj00Rd/blqAM8NT+CEiRyunojSqyYC+XLW12WiIjkQK7njERGRjJ+/HhGjhxJ/fr1WbduHUuXLiUkJASAhISEbGuOTJo0iYyMDPr3709wcHDWY9CgQfnXCnFrq1dDv2E3MpleHClXnxKbvlcQERFxIrleZ8QKWmdErmbPHrj9djhxwlzgbOqUDGxeuv+jiIgjKJB1RkQcSXIyPN42kVMnMmnY0JweoiAiIuJ89JtbnJLdDk92SePV3x6jfJEjBL31OUWL3mp1WSIikgcKI+KUPnxuHz0X9eY+lmPHC4+y/73OjYiIOCaFEXE6Pz87g77je+JLKunexfBaOBfq1rW6LBERySPNGRGncmjEpzQc3wVfUtl9U3O8fvofRERYXZaIiFwHhRFxGonrtxE4fAAAc8tHUemvVXCr5omIiDg7DdOIU8jIgEFDitGfW0kqWpYWW8bi5aN5IiIirkBhRJzCyy/Dlz9UZUHRjWxYdpbAMgoiIiKuQsM04thOnWJj36m8/775dPKXXtRtVsLSkkREJH+pZ0QcV2Ymia0fo8mmZfQkjaBXetGxo9VFiYhIflPPiDis5BdHErBpGSkUxa9ZKG+8YXVFIiJSEBRGxCGl//AjRce+CcDrwZMZ+c1teOhfq4iIS9Kvd3E8p05xok1XPLEzp8hjPLW6MwEBVhclIiIFRWFEHEtGBgcbP0zZxD/YT3lKTPuI6tWtLkpERAqSwog4lN/e+Zab/ljNGW4g9plvafVoaatLEhGRAqaracRhxMdDi3HtuI3vaR12imfG17O6JBERKQQKI+IQUlLgoYfg2HEbR+vfR69YsGldMxERt6BhGrGcYcAP9ftj2/IzgYGwcCH4+VldlYiIFBb1jIjlvu6zksjd0VTnG/bO/JOQEG+rSxIRkUKknhGx1Mr5iTT8tDcAp+9qx133KoiIiLgbhRGxzO5ddlIefYIq/M0Jv4rUXTzK6pJERMQCCiNiiaTTdrY0fpoH0heQZvOm+LK52AL8rS5LREQsoDAihc5uh4VN3iby9CTs2Dj70RS8m95udVkiImIRhREpdMOHGdy4cy0A+17+hJL9H7e4IhERsZKuppFCNX8+vPGmDRtLWRG1hJZvtbW6JBERsZjCiBSa7duhWzfz60FRHrQc94C1BYmIiEPQMI0UihMn4LX7f+KVs6/wyJ2HefddqysSERFHoZ4RKXAZGRAZCX0Pvc0jzON8xcMUKTLF6rJERMRBqGdECtzzz8OJlXF0YD4AvkMGW1yRiIg4EvWMSIH67DOI+SCFn3kcDwzo2BHq1LG6LBERcSAKI1JgNmyAfv1gLC9Si50QHAzR0VaXJSIiDkbDNFIg9u6FDh2gbfp8BjDB3PjFFxAYaGVZIiLigBRGJN8lJ0O7dnDsmMFLN1zoCYmKgvBwS+sSERHHpGEayVd2O3TtCtu2QVCQjfJLZ8D0t2H0aKtLExERB6UwIvlq2DBYtTARb+8AFiyAmxoEQYOxVpclIiIOTMM0km9mz4Zpb+5lJzX5of27hIVZXZGIiDgDhRHJF5s3w5PdM5lGV8qRQMOd0+DcOavLEhERJ6AwItctIcGcsDow9V2asQHjhhtg8WIoWtTq0kRExAkojMh1OX8eHnoIWh6cyhiGAGAbOxYqVbK2MBERcRoKI5JnhgG9e0P5/5vLFJ40N0ZFQa9eltYlIiLORVfTSJ69+y5Mmwa/M5QiZEKPHvD++2CzWV2aiIg4EYURyZMlS+Dlly88uf0OqBUGn34KHupsExGR3FEYkVzbtg0efdQcpunTB6pN+BI8FUJERCRvFEYkVxISoEObVD5PfpxTVW6n+5v9sHn6W12WiIg4MYURybGUFHjkgVRGHejGI8zDOLIc2+mHIVBhRERE8k5hRHLEbofej53hvc3hhLEJo0gRbPPnQdWqVpcmIiJOTgP9kiOvvgoNF79GGJtIL14S25Il0KqV1WWJiIgLUM+I/KcvvoDvR2/hJz4CwGvebAURERHJNwojck1r15oLm81hBJ7YzctoFERERCQfKYzIVf3xh7nUe3q6wcnb7sU4vR3b8OFWlyUiIi5GYUSu6ORJaNsWTp2CRo1sPLp6IDaf/lrUTERE8p0+WeQyaWnQoQPs3g31yp9g0aILN+BVEBERkQKgTxfJxjDgqafMuSJ3F/s/Np++maBNi6wuS0REXJjCiGTz+uswdSqU9EhkcekeeCYnwZw5VpclIiIuTGFEssTEwJtvQk1+48/gZtyw/3cIDoYPP7S6NBERcWGawCoALJt7hv19P2Qty7jT9gMeB+1Qtqx5e95SpawuT0REXJjCiPDzz9CtG/xmjKU0J8HAvKZ3/HioWNHq8kRExMUpjLi5PXugTRs4eq44X9R+l0EDMilyTwu45RarSxMRETehMOKuDIPzvQbw1rK2HD0aQf368NTaJymiG/CKiEgh0wRWN5U+/E18p0Qz5mAXapY/w5Il4K8gIiIiFlAYcUOZK9fgNfJ1AEYVHcWc74tTrpzFRYmIiNtSGHEzxulETj30BACfeTxFu+/6Uru2xUWJiIhbUxhxJ+np/NXgEQLP7GUPlSj9xfs0b251USIi4u7yFEaio6OpXLkyvr6+hIaGsn79+qsem5CQQOfOnalevToeHh5ERUXltVa5HqmpHKx5D1X3rCAZP7a8Mo/2XYtbXZWIiEjuw8js2bOJiopi6NChxMXF0axZMyIiIoiPj7/i8ampqZQpU4ahQ4dSr1696y5Y8mbGXB8W/VWHJIqzuNtcHh7VwOqSREREALAZhmHk5gWNGjWiQYMGTJw4MWtbzZo1ad++PaNHj77ma1u0aEH9+vUZP358ropMSkoiICCAxMRE/HXJR84ZBsTFsfRwA9q1A6+MFF7qfoTXP6+MzWZ1cSIi4upy+vmdq56RtLQ0Nm/eTHh4eLbt4eHhbNy4MW+VXkFqaipJSUnZHpJLGRnw9NNkNrmTLg+fIyMDOjxejNemKIiIiIhjyVUYOX78OJmZmQQFBWXbHhQUxOHDh/OtqNGjRxMQEJD1qFChQr69t1swDHj6afjkE2yp56l4fhetW8Pnn4OHpiyLiIiDydNHk+1ff1obhnHZtusxZMgQEhMTsx779+/Pt/d2C9HR8Omn2LERyWz8mtRnzhzw8rK6MBERkcvlajn4wMBAPD09L+sFOXr06GW9JdfDx8cHHx+ffHs/t7JqFcagQdiAF3mHvxt0ZOUSKFbM6sJERESuLFc9I97e3oSGhhIbG5tte2xsLE2aNMnXwiQPvv0We7uHsGVmMo0uLK/zHMuXQ4kSVhcmIiJydbm+Ud7gwYPp2rUrDRs2JCwsjJiYGOLj4+nbty9gDrEcPHiQqVOnZr1m69atACQnJ3Ps2DG2bt2Kt7c3tWrVyp9WCBw7RmbPp/BMTmINzXmv2qfErrBRurTVhYmIiFxbrsNIZGQkJ06cYOTIkSQkJFCnTh2WLl1KSEgIYC5y9u81R2677basrzdv3sxXX31FSEgIe/fuvb7qJcvhzDJE+O/m1qPz+PHmx1i52pt8HDkTEREpMLleZ8QKWmfk2o4fhxYtYMcOqFgR1q2DC9lQRETEMgWyzog4nsToGSyr/gw7dhiUKwerVimIiIiIc8n1MI04jmOrf8V/QE8eN1JZWbIlL65sT5UqVlclIiKSO+oZcVKHfk/i5P2P4WOkstK3NUM2taNGDaurEhERyT2FEWdjGByZtZoDtz1A9bRfOeoRRNW1U7ilmtZ4FxER56RhGmdit3PmkR4ELZhGEHDGVpzMxUsJuUOXzYiIiPNSz4gT2bXqICmLYsnAkwXFu3L22zUEt2lgdVkiIiLXRT0jTmLjRmjTsQKl7et5oMIvvLDpYcqWs7oqERGR66eeESewcsZh7r0XTp+GoCZVeW3rw5RTEBERERehMOLIMjPZ3uF1GnepQotzS4mIgOXLoVQpqwsTERHJPxqmcVDGiZPsvbMLdX//DoDetTfSZlFrvLwsLkxERCSfKYw4oPQTSRypdjeVT24jhaLMbRVDl++74KF+LBERcUH6eHMwiScz+aV6J8qf3EYCZZn/3Ea6LlMQERER16WPOAeydy9MrfEWDU8s4yzF2PXet3R5rz42rWcmIiIuTGHEQWzcCI3uMCh9bCcAx0Z+QovnQi2uSkREpOApjFjMMGDCBGjRAo4es/FuvRkcm7WSSq91tbo0ERGRQqEJrBY6dw769oWpU83nHTvClCk2brihpbWFiYiIFCKFESucO8exUTH8/cFiOiX70oV0qtQoQuW3o7HdUMnq6kRERAqVwkghM+wGB5pEUmHrN5T5547fgXfehokTLapMRETEGpozUogSE+G1iJ8psvUnzuPDx1XGcWpUtDlhpF49ePVVq0sUEREpdDbDMAyri/gvSUlJBAQEkJiYiL+/v9Xl5J5hsHKVjV69IH5vJqcoyf/ajOLeRQPx9LS6OBERkYKR089v9YwUsMT9SfxRrjmj713B3r1Qs2IKh9+YzH3fDFAQERERQWGkwBgGLJ6XTtwtnah2eD1TeJJBfc7zv1+LU+3VTmglMxEREZPCSAH47Te4/z6Dw4/0p0XqMlJsxTg+aT7jP/GleHGrqxMREXEsCiP56MQJiIqC0LpphMWOoDefYseG5+yZNOjd0OryREREHJIu7c0HJ07A2LHw4Ydwe/Iq9tCZshwBwOOD8fh0fNDiCkVERByXwkhO/fkn7N4NDRrA1q3w66+cLFae7VPjWBAXwgep/QBoXW4rZQ8dgbJl4cUX4ZlnrK1bRETEwSmM5NSoUfDFFxgeHtjsdgBKAc0Bg+asrd+P4cPhwQeehemB0KkT+PpaWbGIiIhTUBj5t6NHYelS2LED+vSBqlUxDDhQuj5FS1Yl8NSfpOLNCu4liCMklL2Nmx4OY8tHFy+QsUG3bla3QkRExGkojBgG7NoFJUvCuHHwwQdw/jwAP+8OYPwNr7JyJRw+PAgYRFV2Y/fzJ6JHEH37wgN1rC1fRETE2bl1GJn2eQZhr95D1UPrsm2P4zb+jzuYv+gOYi9sK1YMWreGjh1voU0b8PMr/HpFRERckVuHkaXLi5ByqAaV+IEiZHKMQHoTw0LaU6qUjQYNYGgjaNUKGjcGHx+rKxYREXE9bn1vmtmz4a9Nxyjum45vURvFQ0pRvooPlSrBTTdpkVQREZHrkdPPb7fuGYmMBCLLWF2GiIiIW9MKrCIiImIphRERERGxlMKIiIiIWEphRERERCylMCIiIiKWUhgRERERSymMiIiIiKUURkRERMRSCiMiIiJiKYURERERsZTCiIiIiFhKYUREREQspTAiIiIilnKKu/YahgGYtyIWERER53Dxc/vi5/jVOEUYOXPmDAAVKlSwuBIRERHJrTNnzhAQEHDV/Tbjv+KKA7Db7Rw6dIjixYtjs9ny7X2TkpKoUKEC+/fvx9/fP9/e1xmo7e7XdndtN6jt7th2d203OFbbDcPgzJkzlCtXDg+Pq88McYqeEQ8PD8qXL19g7+/v72/5CbOK2u5+bXfXdoPa7o5td9d2g+O0/Vo9IhdpAquIiIhYSmFERERELOXWYcTHx4dhw4bh4+NjdSmFTm13v7a7a7tBbXfHtrtru8E52+4UE1hFRETEdbl1z4iIiIhYT2FERERELKUwIiIiIpZSGBERERFLuXUYiY6OpnLlyvj6+hIaGsr69eutLilfDR8+HJvNlu1RtmzZrP2GYTB8+HDKlStH0aJFadGiBTt27LCw4rxbt24dDzzwAOXKlcNms7Fw4cJs+3PS1tTUVAYOHEhgYCB+fn48+OCDHDhwoBBbkTf/1fYePXpc9u+gcePG2Y5xxraPHj2a22+/neLFi3PjjTfSvn17du3ale0YVzzvOWm3q57ziRMncuutt2Yt5hUWFsZ3332Xtd8Vz/dF/9V2Zz/nbhtGZs+eTVRUFEOHDiUuLo5mzZoRERFBfHy81aXlq9q1a5OQkJD12L59e9a+d955h7Fjx/Lxxx/z008/UbZsWVq1apV1LyBncvbsWerVq8fHH398xf05aWtUVBQLFixg1qxZbNiwgeTkZNq2bUtmZmZhNSNP/qvtAPfff3+2fwdLly7Ntt8Z27527Vr69+/Ppk2biI2NJSMjg/DwcM6ePZt1jCue95y0G1zznJcvX54xY8bw888/8/PPP9OyZUvatWuXFThc8Xxf9F9tByc/54abuuOOO4y+fftm21ajRg3j5Zdftqii/Dds2DCjXr16V9xnt9uNsmXLGmPGjMnadv78eSMgIMD45JNPCqnCggEYCxYsyHqek7aePn3a8PLyMmbNmpV1zMGDBw0PDw/j+++/L7Tar9e/224YhtG9e3ejXbt2V32Nq7T96NGjBmCsXbvWMAz3Oe//brdhuM85NwzDKFmypDF58mS3Od//dLHthuH859wte0bS0tLYvHkz4eHh2baHh4ezceNGi6oqGLt376ZcuXJUrlyZRx99lL///huAPXv2cPjw4Ww/Ax8fH5o3b+5yP4OctHXz5s2kp6dnO6ZcuXLUqVPHJX4ea9as4cYbb6RatWo89dRTHD16NGufq7Q9MTERgFKlSgHuc97/3e6LXP2cZ2ZmMmvWLM6ePUtYWJjbnG+4vO0XOfM5d4ob5eW348ePk5mZSVBQULbtQUFBHD582KKq8l+jRo2YOnUq1apV48iRI7z55ps0adKEHTt2ZLXzSj+Dffv2WVFugclJWw8fPoy3tzclS5a87Bhn/zcRERFBx44dCQkJYc+ePbz22mu0bNmSzZs34+Pj4xJtNwyDwYMHc+edd1KnTh3APc77ldoNrn3Ot2/fTlhYGOfPn+eGG25gwYIF1KpVK+sD1ZXP99XaDs5/zt0yjFxks9myPTcM47JtziwiIiLr67p16xIWFkaVKlX48ssvsyY2ufrP4J/y0lZX+HlERkZmfV2nTh0aNmxISEgIS5YsoUOHDld9nTO1fcCAAWzbto0NGzZcts+Vz/vV2u3K57x69eps3bqV06dPM2/ePLp3787atWuz9rvy+b5a22vVquX059wth2kCAwPx9PS8LA0ePXr0slTtSvz8/Khbty67d+/OuqrGHX4GOWlr2bJlSUtL49SpU1c9xlUEBwcTEhLC7t27Aedv+8CBA1m8eDGrV6+mfPnyWdtd/bxfrd1X4krn3Nvbm6pVq9KwYUNGjx5NvXr1+OCDD1z+fMPV234lznbO3TKMeHt7ExoaSmxsbLbtsbGxNGnSxKKqCl5qaio7d+4kODiYypUrU7Zs2Ww/g7S0NNauXetyP4OctDU0NBQvL69sxyQkJPDrr7+63M/jxIkT7N+/n+DgYMB5224YBgMGDGD+/PmsWrWKypUrZ9vvquf9v9p9Ja5yzq/EMAxSU1Nd9nxfy8W2X4nTnfNCnzLrIGbNmmV4eXkZn332mfHbb78ZUVFRhp+fn7F3716rS8s3zz33nLFmzRrj77//NjZt2mS0bdvWKF68eFYbx4wZYwQEBBjz5883tm/fbjz22GNGcHCwkZSUZHHluXfmzBkjLi7OiIuLMwBj7NixRlxcnLFv3z7DMHLW1r59+xrly5c3VqxYYWzZssVo2bKlUa9ePSMjI8OqZuXItdp+5swZ47nnnjM2btxo7Nmzx1i9erURFhZm3HTTTU7f9n79+hkBAQHGmjVrjISEhKxHSkpK1jGueN7/q92ufM6HDBlirFu3ztizZ4+xbds245VXXjE8PDyM5cuXG4bhmuf7omu13RXOuduGEcMwjAkTJhghISGGt7e30aBBg2yXxrmCyMhIIzg42PDy8jLKlStndOjQwdixY0fWfrvdbgwbNswoW7as4ePjY9x1113G9u3bLaw471avXm0Alz26d+9uGEbO2nru3DljwIABRqlSpYyiRYsabdu2NeLj4y1oTe5cq+0pKSlGeHi4UaZMGcPLy8uoWLGi0b1798va5Yxtv1KbAePzzz/POsYVz/t/tduVz/mTTz6Z9Tu7TJkyxj333JMVRAzDNc/3Rddquyucc5thGEbh9cOIiIiIZOeWc0ZERETEcSiMiIiIiKUURkRERMRSCiMiIiJiKYURERERsZTCiIiIiFhKYUREREQspTAiIiIillIYEREREUspjIiIiIilFEZERETEUgojIiIiYqn/B5xmK0F6Ty1PAAAAAElFTkSuQmCC", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "HW.scen_size = 1000\n", "plt.plot(range(HW.step_size + 1), HW.E_rt(), \"b-\")\n", "plt.plot(range(HW.step_size + 1), HW.mean_short_rate(), \"r--\")" ] }, { "cell_type": "markdown", "id": "50adfb01", "metadata": { "id": "50adfb01" }, "source": [ "The chart below is with 10,000 scenarios. The divergence dissapears and the mean fits the expectation much better." ] }, { "cell_type": "code", "execution_count": null, "id": "871056b7", "metadata": { "id": "871056b7", "outputId": "255fa861-22bc-4f5a-d049-e4e4d4589599" }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "HW.scen_size = 10000\n", "HW.a = 0.1\n", "HW.sigma = 0.1\n", "plt.plot(range(HW.step_size + 1), HW.E_rt(), \"b-\")\n", "plt.plot(range(HW.step_size + 1), HW.mean_short_rate(), \"r--\")" ] }, { "cell_type": "markdown", "id": "1c975725", "metadata": { "id": "1c975725" }, "source": [ "In the same manner as the mean, for each $t_i$, the variance of $r(t_i)$ should converge to $Var\\{r(t_i) | \\mathcal{F}_{0}\\}$. For convenience, `var_short_rate` and `Var_rt` are defined to represent the variance of $r(t_i)$ and $Var\\{r(t_i) | \\mathcal{F}_{0}\\}$ respectively." ] }, { "cell_type": "code", "execution_count": null, "id": "7aebb20c", "metadata": { "id": "7aebb20c", "outputId": "e58b8e29-c136-416a-e802-221789145b27" }, "outputs": [ { "data": { "text/plain": [ "def var_short_rate():\n", " \"\"\"Variance of generated short rates\n", "\n", " Returns, as a vector in a numpy array, the variances of\n", " the generated short rates for all :math:`t_i`.\n", " This should converge to the theoretical variances\n", " calculated by :meth:`Var_rt`.\n", "\n", " .. seealso::\n", " * :meth:`short_rate`\n", " * :meth:`Var_rt`\n", "\n", " \"\"\"\n", " return np.array([np.var(short_rate(i)) for i in range(step_size + 1)])" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "HW.var_short_rate.formula" ] }, { "cell_type": "code", "execution_count": null, "id": "975d0644", "metadata": { "id": "975d0644", "outputId": "71b82dbe-9933-4e57-c864-6cb39d7a42fe" }, "outputs": [ { "data": { "text/plain": [ "def Var_rt():\n", " r\"\"\"The variance of :math:`r(t_i)` at time 0 for all :math:`t_i`.\n", "\n", " Returns, in a numpy array, the variance of\n", " :math:`r(t_i)` for all :math:`t_i`.\n", " Calculated as :math:`Var\\{r(t_i) | \\mathcal{F}_{0}\\}`.\n", "\n", " .. seealso::\n", " * :meth:`Var_rt_s`\n", " \"\"\"\n", " return np.array([Var_rt_s(0, i) for i in range(step_size + 1)])" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "HW.Var_rt.formula" ] }, { "cell_type": "code", "execution_count": null, "id": "423dcd7a", "metadata": { "id": "423dcd7a", "outputId": "a217034a-9741-4b61-de2c-b4733f514928" }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "HW.scen_size = 1000\n", "plt.plot(range(HW.step_size + 1), HW.Var_rt(), \"b-\")\n", "plt.plot(range(HW.step_size + 1), HW.var_short_rate(), \"r--\")" ] }, { "cell_type": "code", "execution_count": null, "id": "0ff67c94", "metadata": { "id": "0ff67c94", "outputId": "e4707807-5116-4985-eba3-d10bbf078c99" }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "HW.scen_size = 10000\n", "plt.plot(range(HW.step_size + 1), HW.Var_rt(), \"b-\")\n", "plt.plot(range(HW.step_size + 1), HW.var_short_rate(), \"r--\")" ] }, { "cell_type": "markdown", "id": "d4f88b73", "metadata": { "id": "d4f88b73" }, "source": [ "## Simulating the discount factor" ] }, { "cell_type": "markdown", "id": "950401f4", "metadata": { "id": "950401f4" }, "source": [ "Along with $r(t_{i})$, the discount factor needs to be simulated. The discount factor is defined as $e^{-Y(t_i)}$ where\n", "\n", "$$Y(t_i)=\\int_0^{t_i}r(t)dt$$\n", "\n", "For simplicity, we model $Y(t_i)$ as a descrete approximation to the integral:\n", "\n", "$$\\sum_{j=1}^{i}r(t_{j-1})(t_j-t_{j-1})$$" ] }, { "cell_type": "code", "execution_count": null, "id": "63c8f842", "metadata": { "id": "63c8f842", "outputId": "a1db734b-526b-4f07-c4da-4380e031b821" }, "outputs": [ { "data": { "text/plain": [ "def accum_short_rate(i):\n", " r\"\"\"Accumulated short rates.\n", "\n", " a descrete approximation to the integral :math:`\\int_0^{t_i}r(t)dt`,\n", " calculated as :math:`\\sum_{j=1}^{i}r(t_{j-1})(t_j-t_{j-1})`\n", "\n", " .. seealso::\n", " * :meth:`disc_factor`\n", " \"\"\"\n", " if i == 0:\n", " return np.full(scen_size, 0.0)\n", " else:\n", " dt = t_(i) - t_(i-1)\n", " return accum_short_rate(i-1) + short_rate(i-1) * dt" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "HW.accum_short_rate.formula" ] }, { "cell_type": "markdown", "id": "c79984f0", "metadata": { "id": "c79984f0" }, "source": [ "There is an alternative approach to simulate $Y(t_i)$ by using the fact that $Y(t_i)$ follows a normal distribution, and by simulating the joint distribution of $(r(t_i), Y(t_i))$ as suggested in [Monte Carlo Methods in Financial Engineering](https://link.springer.com/book/10.1007/978-0-387-21617-1). `accum_short_rate2` implements this alternative approach, althogh it does not have material impact on the discussion below. " ] }, { "cell_type": "code", "execution_count": null, "id": "132cdae9", "metadata": { "id": "132cdae9", "outputId": "d1ac46dc-c4e1-4458-fefa-87e1f171bf69" }, "outputs": [ { "data": { "text/plain": [ "def accum_short_rate2(i):\n", " r\"\"\"Alternative implementation of accumulated short rates.\n", "\n", " An alternative approach to simulate :math:`Y(t_i)=\\int_0^{t_i}r(t)dt`\n", " by using the fact that :math:`Y(t_i)` follows a normal distribution,\n", " and by simulating the joint distribution of :math:`(r(t_i), Y(t_i))`,\n", " as suggested in Glasserman (2003).\n", "\n", " .. seealso::\n", " * :meth:`accum_short_rate`\n", " * :attr:`seed2`\n", " * Paul Glasserman (2003). Monte Carlo Methods in Financial Engineering\n", " \"\"\"\n", " if i == 0:\n", " return np.full(scen_size, 0.0)\n", " else:\n", " t, T = t_(i-1), t_(i)\n", " dt = T - t\n", " cov = sigma**2/(2*a**2)*(1 + np.exp(-2*a*dt) -2 * np.exp(-a*dt))\n", " z1 = std_norm_rand(seed1)[:, i-1]\n", " z2 = std_norm_rand(seed2)[:, i-1]\n", "\n", " rho = cov / (Var_rt_s(i-1, i)**0.5 * V_t_T(i-1, i)**0.5)\n", "\n", " mean = B_t_T(i-1, i) * (short_rate(i-1) - alpha(i-1)) + np.log(mkt_zcb(i-1)/mkt_zcb(i)) + 0.5*(V_t_T(0, i)-V_t_T(0, i-1))\n", " return accum_short_rate2(i-1) + mean + V_t_T(i-1, i)**0.5 * (rho*z1 + (1-rho**2)**0.5*z2)" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "HW.accum_short_rate2.formula" ] }, { "cell_type": "markdown", "id": "85d20beb", "metadata": { "id": "85d20beb" }, "source": [ "`discount_factor` and `mean_disc_factor` are defined as follows." ] }, { "cell_type": "code", "execution_count": null, "id": "d3a94e25", "metadata": { "id": "d3a94e25", "outputId": "9c96101e-f148-437d-d9f4-2325554ead7c" }, "outputs": [ { "data": { "text/plain": [ "def disc_factor(i):\n", " \"\"\"Discount factors\n", "\n", " Returns, in a numpy array, the discount factors for\n", " cashflows at :math:`t_i` for all scenarios.\n", " Defined as::\n", "\n", " np.exp(-accum_short_rate(i))\n", "\n", " .. seealso::\n", " * accum_short_rate\n", "\n", " \"\"\"\n", " return np.exp(-accum_short_rate(i))" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "HW.disc_factor.formula" ] }, { "cell_type": "code", "execution_count": null, "id": "511e1583", "metadata": { "id": "511e1583", "outputId": "4387829c-ba0c-44a2-8e33-b09c1eee20df" }, "outputs": [ { "data": { "text/plain": [ "def mean_disc_factor():\n", " \"\"\"Discount factor means\n", "\n", " Returns, as a numpy array, the mean of discount factors of all scenarios\n", " for each :math:`t_i`.\n", "\n", " .. seealso::\n", " * :meth:`disc_factor`\n", " \"\"\"\n", " return np.array([np.mean(disc_factor(i)) for i in range(step_size + 1)])" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "HW.mean_disc_factor.formula" ] }, { "cell_type": "markdown", "id": "54082cfa", "metadata": { "id": "54082cfa" }, "source": [ "The chart below compares the mean of the simulated discount factors against $P^M(0, t_i)$ with 1000 scenarios. The mean diverges from the expectation significantly after the 150th step." ] }, { "cell_type": "code", "execution_count": null, "id": "a5430a48", "metadata": { "scrolled": false, "id": "a5430a48", "outputId": "d959562d-c9af-470e-bc4e-7cce5256492f" }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "HW.scen_size = 1000\n", "plt.plot(range(HW.step_size+1), [HW.mkt_zcb(i) for i in range(HW.step_size+1)], \"b-\")\n", "plt.plot(range(HW.step_size+1), HW.mean_disc_factor(), \"r--\")" ] }, { "cell_type": "markdown", "id": "797cddbb", "metadata": { "id": "797cddbb" }, "source": [ "The chart shows the case of 10,000 scenarios. The stochastic mean does not converge well. Even with 100,000 scenarios, the convergence is still poor." ] }, { "cell_type": "code", "execution_count": null, "id": "527baff8", "metadata": { "id": "527baff8", "outputId": "710c5bb7-eb1b-4be2-9dd7-2198b0c1232e" }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "HW.scen_size = 10000\n", "plt.plot(range(HW.step_size+1), [HW.mkt_zcb(i) for i in range(HW.step_size+1)], \"b-\")\n", "plt.plot(range(HW.step_size+1), HW.mean_disc_factor(), \"r--\")" ] }, { "cell_type": "markdown", "id": "19df009a", "metadata": { "id": "19df009a" }, "source": [ "The charts below examine the convergence of the discount factor for various combinations of $\\sigma$ and $a$, first by changing $\\sigma$ and secondly by changing $a$.\n", "As Balaraman's study shows, the convergence gets worse as $\\sigma/a$ gets larger than 1, and gets better as $\\sigma/a$ gets smaller than 1." ] }, { "cell_type": "code", "execution_count": null, "id": "8e446619", "metadata": { "id": "8e446619", "outputId": "47405795-a5dc-4f16-80b9-a1b212243a70" }, "outputs": [ { "data": { "image/png": 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5s+qrxN+Lz5T4hRDWISPlBsDcbxIY8PcQmrxTg5Bp27I4SiFEarJl9KKHW9EmThScVuvakSNHEhkZmbScP3/+sccoXx6mjoukADdocGEFO7wHoRJkQmIhcouMlBsAEz9W1C9xDidiKDfkeY4vP5TFkQohHpblyUjx4sWJiIhItu7y5cvY2dlRuHDhVPdxdHRM6o5nTrc873dbsH/QDyRgoumRr/mt1cQnjl8IYR0yWm7YOdridXQxB10a40oUBbo9R1jw2awNVgiRTJYnIw0aNCAoKCjZul9++QUfHx/s7e0z/3jT/Nnx0pcANN/yPltfmZvpxxBC5CxOBfNQ9tBPnHKqRvGEcOJatuby0X+NDkuIXMPsZOTmzZscOHCAAwcOALrr7oEDBwgLCwN0VWmPHj2Stu/fvz/nzp1j6NChhIaGEhAQwLx58xg2bFjmnEEqmqx4h22NRgHQeFE/dr33Y5YdSwiRM7iWKYDLzo38Y1uacrEnuVS3HVEXbxodlhC5gtnJyL59+6hVqxa1atUCYOjQodSqVYsxY8YAEB4enpSYAHh4eBAYGMjWrVvx8vLiww8/5Kuvvsr0br0PaxL8ETsq9caWBGI++5Lftkj7ESHEo7nVLknsuk1cNRWm6u29fOK3lRjpnCdEljOpxNakFiwqKgpXV1ciIyPNGtY5PiaOpbU/5Y1jg7DNn4+tW6F27ayLU4icKqP3oJGeJObQBX/wUf8LLL7biU6dYOlSsLOKyTOEsCzpvQ+tYy7wDLJ1tKPT/lHUaZqP6Gjw9YVje28ZHZYQwsJ5vlaPPus74eAAq1bB271uk5BgdFRC5Fw5OhkBcHKCn34CH2/FgKvjcGjgzd97Uh/fRAghEjVvrmtEytqEMXihN2sbT8Hy65GFsE45PhkBcHGBX5Zdp599AE/Hn+DWM605f/i60WEJISxcx46w/NWf8eQ4L+4axrL2P0hCIkQWyBXJCEDB8oWw3/ILV22LUj32T67Xac2lk5FGhyWEsHB1vnuLwy2HANB5fU/W+i8xOCIhcp5ck4wAFHmmMrEbNnPNpjA1YvYS4fUc186mb/4KIUQuZTJRfdPnHK7fF1sSeH7FK6zvsdToqITIUXJVMgJQvFV1bq39leumgtS88zth1doQ+Y+MJSCEeAQbG6rvnMOB2nq4gOd+eJlfX19mdFRC5Bi5LhkBKNXei+vLf+WGqQBet3YyufkvpHOCTyFEbmVjQ80937Kvei9sScB97ngWzE195nEhhHlyZTICUO6l2lz6/hcG5p3L5JMv4ueHJCRCiEcy2drgHTKXjT7v05Jf6fWGPfPnGx2VENYv1yYjAJVeqUPP7X0oWBB27YIuLa8Rdfmu0WEJISyYydaG1ns+pONb7igFvXvD8qn/GB2WEFYtVycjoEdk/fVXKO96hcl7m3O0Ukeir8j4z0KItJlMMGMGvPUWdFOLeGFoOX57e6XRYQlhtXJ9MgI6IVk/7RQVOUmDGxs5UqED0ZfvGB2WEMKCJSYkAypvxpF7NJ7Zld8GrDI6LCGskiQj/6nUswEXZq3jNnlocGMjxyu2JzpCho4XQqTNZIL6h7/lj4qvYkc8z3zdlS3vrDE6LCGsjiQjD6jYvzkXvt1INM7UidzM6Up+RF+MNjosIYQFM9nZUvfod+yp+Ar2xNF4Rhe2DFxrdFhCWBVJRh5SsW8TLn73C1G44BW1nbOVfLlx9obRYQkhLJjJzpY6R+ezp8LLOiGZ3plN/aWGRIj0kmQkFZV6NuCfhVu4biqI681/6NYmksuXjY5KCGHJTHa21Dm2gH0Vu2NPHAfm/M6UKUZHJYR1kGQkDZ4ve3NlxVa6FtnMxtAyNGkCFy4YHZUQwpKZ7GzxPvo9y9t9zwgmM2wYjB+PTK4nxGNIMvIIFTrVYMGuCpQqBSdOwGjvjZzbfdHosIQQFsxkZ0uXn1/l449NAEwad5eF7ZdJQiLEI0gy8hgVKsCOHdDT/Re+vfw8CY2bcGpzmNFhCSEs3KhR8OUX8SzDn1fXd2WDzwckxEtGIkRqJBlJh9Kl4ZPVFbhk/xQe8afJ69uI0NWhRoclhLBwA4fY4v5iAwDa/PkRm6sOJO5egsFRCWF5JBlJp2L1PHDeH8wZp8qUTLhAsZcac+DbvUaHJYSwcHVWjWBfzxkAtDoxgz/KdeNupIzyLMSDMpSMzJw5Ew8PD5ycnPD29mb79u2P3H7RokXUrFmTvHnzUqJECXr16sXVq1czFLCRClZ/isJHt3PMuQ6F1VWefqMZuyb8anRYQggL5/Pd2+z73xLuYU+jf5ZzrIwfN85FGh2WEBbD7GRk2bJlDB48mNGjRxMSEkLjxo3x8/MjLCz1dhQ7duygR48e9OnTh6NHj7JixQr27t1L3759nzh4I7iUK0LZvzYTUqQlztzCZ2wb1ow9YHRYQggL5/N5V459voEo8lM78jeOV+3ERWkPLwSQgWTkiy++oE+fPvTt2xdPT0+mTZtGqVKlmDVrVqrb//7775QtW5aBAwfi4eHBM888Q79+/di3b98TB2+UvG75qX52HXvLdmYJ3eg0oQYTJ0r3PSHEo3n9rwURS7dx1rYcg299RMOGcPKk0VEJYTyzkpF79+6xf/9+fH19k6339fVl165dqe7TsGFDLly4QGBgIEopLl26xMqVK2nbtm2ax4mJiSEqKirZYmns8jnic2oJp96bh8KG0aNh2Nt3SIiNNzo0IXIlayg3ACr610IdO87Vp+tz7hw0agR/bpRRFUXuZlYycuXKFeLj43Fzc0u23s3NjYiIiFT3adiwIYsWLcLf3x8HBweKFy9OgQIFmD59eprHmTRpEq6urklLqVKlzAkz25jsbPlosh3TpoGJBJ6Z1Z2QMh2IuSLz2QiR3ayl3ADwqGjPzp3g4wNPXQmhgl95TvX4EBKkp43InTLUgNVkMiX7WymVYl2iY8eOMXDgQMaMGcP+/fvZuHEjZ86coX///ml+/8iRI4mMjExazp8/n5Ews82gQRA4+TDPsRHv8HVc8HiGqCMyFokQ2cnayo1ixWDLFhha7kfyc5MKP4zhYk0/+Pdfo0MTItuZlYwUKVIEW1vbFLUgly9fTlFbkmjSpEk0atSI4cOHU6NGDVq3bs3MmTMJCAggPDw81X0cHR1xcXFJtli6596ryeHp27hkcqP8zUPEevkQsWyb0WEJkWtYY7mRPz/4h45jVr353CYP7kd+Iap8LdSOnUaHJkS2MisZcXBwwNvbm6CgoGTrg4KCaNiwYar73L59Gxub5IextbUFdI1KTlJ3QF3+XbeHI3ZeFI7/l8JdW3Ju2HRp2SqESJODA/Tb9Rpzeu/hOJVwif6HhCZNiZv8uZQdItcw+zXN0KFDmTt3LgEBAYSGhjJkyBDCwsKSXruMHDmSHj16JG3fvn17Vq9ezaxZs/j777/ZuXMnAwcOpG7duri7u2femViIam1KU/DYTtYX0DN3lpkykFMvvmd0WEIIC2ZjA0PmVWP3V/tYYuqGrYrHbuRwbn6z2OjQhMgWZicj/v7+TJs2jQkTJuDl5UVwcDCBgYGUKVMGgPDw8GRjjvTs2ZMvvviCGTNmUK1aNTp37kylSpVYvXp15p2FhSlZIS9Nzi3km0pTuEVeXln7ElOnykOOEOLRer3jTOENixjkOJufaUfdL7py+rTRUQmR9UzKCt6VREVF4erqSmRkpFW8B04UFwej+l7mswXFAHj7bZj2wVXs3AobHJkQ5rHGe9AaY050+DC0baM4f8FEkSLw87Lb1A/9Dvr3h/9ecwthDdJ7H8rcNFnIzg4++a4YU6aAyQQ7vw7hXkkP7kyaJtUkQog0Va8Of+wx4e0NV67AwVbDYMAAaN4cLLyXkBAZIclIFjOZYOhQWLkSXrFbSt74aPKMGkJUhx5w547R4QkhLFSJErBtG7zwAuxMqE80zhAcjKpZE5YskQcakaNIMpJNXnwRnt09mbGu04jDFpefFhJVoxGcOWN0aEIIC5UvH6xaBe7v9aAWIeyhDqbr16F7d/D319UmQuQAkoxkI28fE28eH8SgKr/yL0Vw+SuEmCq1UKvXGB2aEMJC2drC5MkwfuHTtHDcyVjGEYsdrFgBVavCThmTRFg/SUayWfHi8MWfzzL5pf3sogGOdyMxdXqRe+s2GR2aEMKCvfwybNluz1z3sdTnd47bVCH2Tix4eBgdmhBPTJIRAzg6wufLS7Pv8218yrts4DmafdyKNKb3EUIIAOrUgX37wL6eN14J+2l461e+Wul+v/mIFc+GLnI3SUYMYjLBwP/Z47XpE151/Zldv9vg7Q2/b7kNgYFGhyeEsFAlSsDWreDfw4l9CbUZNAh69oSYlT/rbKVrV5nfRlgdSUYM5usLu/fa4ekJFy/C0ZaDoG1b1Bv94NYto8MTQlggJyeYPx+mTNGjt37/PcwYeAJlawvLloGnJyxeLD1uhNWQZMQCVKgAe/aAf+cE/lWFScCE6dtvSKhVG/bvNzo8IYQFShw2YPNmPQPwsPBhPJvnDyLL1oCrV3Ujk+efhwsXjA5ViMeSZMRCODvDkmU2OE2dTGubX7lASWxOnUTVr6+b0sfHGx2iEMICPfss/PknNGgAwTe9KXp2L782/RDl4ADr1ukeN0uWGB2mEI8kyYgFMZlg8GAYs7U5rYodYiWdMMXFwciR0KIF/POP0SEKISxQyZK6Hck770AsDrTa9j6ve4cQ610PoqLAyobDF7mPJCMWqHFj2HKgEF82WkEvArhJPm7tOUJsvPxcQojUOTjAV1/BokWQNy/M212FCpd2EvrZOmjb9v6GBw5AbKxhcQqRGvl/NwtVogRs+c1EwSG98OIA7e6soHGXEpw9+98GMpS8ECIV3bvD77/rtmjnLthSfURbPvkEEhKA8HD9XsfHB/74w+hQhUgiyYgFs7eHL76AT1c9zYECzfjjD/Dygt3DV0OlSrBli9EhCiEsUPXqesiRrl11c7MRI6BNG7j++wk9g+ehQ7qRydCh8mAjLIIkI1bgxRchJATq14fISAWff6Zn7mzRAoYMkcJECJGCi4vu3fvtt5AnD2zaBFXeepbt3x6HV1/V3X6nToVatXR3PiEMJMmIlShbFoKD4d13TbQiiNn00x9Mmwbe3ro5vRBCPMBkgr59da5RpQpEREDTTkUYU/Z74n9cp98HnzgBzzwDM2fKuCTCMJKMWBF7e/jkE1i5wZkxRWfThvVEmIpDaCiqXj346COIizM6TCGEhalWDfbuhT59dL7x4YfQfEpb/vnlKLz0km7QevCgzl6EMIAkI1boued0g/g7z7ahmjrMCl7SXYA/+EBm8BRCpCpvXpg7V/e2cXbWNa3VGhdk+UvLYcEC3RVHCINIMmKl3N3h119h8IdF6GaznFf4gdnOw9gS39To0IQQFqx7d/1W18cHbtwA/64mXg3qQeRdR71BfDx06QLr1xsap8hdJBmxYra28P77sGu3iT0VXuHNm5/RooVuIH/31Hnw99cT3gghxAMqVIBdu3Rlqo0NLFwINWro2hLmzIEVK6BdOxg37r8+wUJkrQwlIzNnzsTDwwMnJye8vb3Zvn37I7ePiYlh9OjRlClTBkdHR8qXL09AQECGAhYp1a2re9v076//njoVfvd+C5Yv1y+Lly83NkAhhMWxt4cJE2D7dihXDsLC9BAko/7uS3z/t/VG48frpOTaNUNjFTmf2cnIsmXLGDx4MKNHjyYkJITGjRvj5+dHWFhYmvt06dKFzZs3M2/ePE6cOMGSJUuoXLnyEwUuksuXD2bNgp9/1pNmvRn9KftN3nD9uq4h6d5d/1sIIR7QsKFug9a7t27cOmmKAz6/z+DCxwv09MAbNuh3OiEhRocqcjJlprp166r+/fsnW1e5cmU1YsSIVLffsGGDcnV1VVevXjX3UEkiIyMVoCIjIzP8HbnJpUtKtW+vlB331DjGqFhslQKlSpZUatMmo8MTVsga70FrjNloa9YoVbiwLi4cHZUKGBiiEsqV0yucnJRaudLoEIWVSe99aFbNyL1799i/fz++vr7J1vv6+rJr165U9/npp5/w8fHh008/pWTJklSsWJFhw4Zx5xEDdcXExBAVFZVsEelXrBj8+CPM/Maez53H04idnDRV1BPttW4Nq1YZHaIQmU7KjSfXoQMcOaJHa42Jgd5fedHSdR/Rjdvobr8VKhgdosihzEpGrly5Qnx8PG5ubsnWu7m5ERERkeo+f//9Nzt27ODIkSOsWbOGadOmsXLlSt5+++00jzNp0iRcXV2TllKlSpkTpkCXG6+/DocPQ/4W9fBSIUxnAGfyVOHk022MDk+ITCflRuYoXhzWrYP588HVFbaEFKTo7z8zr+9u4qrUuL/hjRtGhShyoAw1YDU9NDCOUirFukQJCQmYTCYWLVpE3bp1adOmDV988QXz589Ps3Zk5MiRREZGJi3nz5/PSJgCPXJrUBBMm5OX0fmnU+3OHmrWz8OUKRAfEwdTpsCtW0aHKcQTk3Ij85hM8NprcPSobr8aE2tD3+k1qV9fP+CwezeULq173siorSITmJWMFClSBFtb2xS1IJcvX05RW5KoRIkSlCxZEldX16R1np6eKKW4cOFCqvs4Ojri4uKSbBEZZzLBG2/o6tdGrfJx9y4MGwZfV/xS/6N6dT1oiRBWTMqNzFeyJPz0E3z/PRQoAPv3/zf7xMDvIDpad+Hr1AmuXjU6VGHlzEpGHBwc8Pb2JigoKNn6oKAgGjZsmOo+jRo14uLFi9y8eTNp3cmTJ7GxseGpp57KQMgio0qX1pNlffst5M8P68Kqc47ScOYMtGqlx4qWqlchxANMJj2v3rFj8PzzeuR4n32z+az4FBLs7GHNGqhZE377zehQhRUz+zXN0KFDmTt3LgEBAYSGhjJkyBDCwsLo/98gFyNHjqRHjx5J23fv3p3ChQvTq1cvjh07RnBwMMOHD6d3797kyZMn885EpEvixFlHj4J9G1+qcYTpDNAfBgTo2bTWrjU0RiGE5SlRQhcNCxdC4SI2vBsxFJ+4P4goUEk3jm/RAkaNgnv3jA5VWCGzkxF/f3+mTZvGhAkT8PLyIjg4mMDAQMqUKQNAeHh4sjFHnJ2dCQoK4saNG/j4+PDyyy/Tvn17vpJ5EAxVqpRupDZ3aX4+dpvOM2znOJUgPBw6dtSDHQkhxANMJnj5ZQgN1W1KQqhF+Rv7WZznvxn4Jk3SNSVCmMmklOW3PoqKisLV1ZXIyEh5D5wFrl+HESNgwTd3Gct4BjONzZP20va9ajKJpwCs8x60xpitzZYtutnIqVPwIqt4+6mfeHrHfEqXkYJDaOm9D2VuGkHBgrpR/K/bnVhYZRKlOE/7kdVo3RpOngQ++URXowghxAOaN4dDh/QcWT/bd6LFhQVUqWriiy8g9kok9OypX+EI8RiSjIgkzzyjR3we/GERHB11l+CuVQ8TP3I0tG+vl9OnjQ5TCGFBnJzgww/1kPKNGumRAv73P/ixwjBYsED31lu2zOgwhYWTZEQk4+Cgn3IOH4bnnoOTcR58rv7HPexh3TpU1aowZgzcvm10qEIIC1Klip71d+5cKFIERt8Yxh7q6PfAXbvK/FjikSQZEamqUAECA2Hxj87M8fiEGhziF1phionRj0FVq+qm9Zbf5EgIkU1sbPQIASdPgu+ASjQ27WQcY4nDFpYsQcmYRiINkoyINJlMelyBo0eh+/jKvOC4iU6sJIxScPYs6rXX5ElHCJFCwYIwfTrsCbFn8zPjaMguTlIB0z//6DGN5s83OkRhYSQZEY+VJ49+MxN63ITq2AlPQvmI0YxQk/l2VSHi49E1JDKsvBDiATVr6lc3A3+oy3PFQviatwinON0XteX4caOjE5ZEkhGRbmXLwurVsHpjPn6o+BGfRr/JG29ArVrw50eBUK6c7pYTF2d0qEIIC2EywSuvwIFT+Tjzv6+paXuUJb8WpVo1GPC2ImrOEhkoTUgyIszXurVu4Dptmq6OPXwYLoyZA5cv60EHvLxg40ajwxRCWBAXF/j8c9h+tBDPPw/x8XB15lJc+nfnctm63Nt70OgQhYEkGREZ4uAAgwbBX3/B4MHQ1XYlg5jGVQrpRiZ+fjprOXTI6FCFEBakUiX48Uc9YFrxsnm4QmGKhR/EVNeHI/4fou7FGh2iMIAkI+KJFCoEU6fCwVAHznccxNP8xRSG6q7Av/yC8vKCsWONDlMIYWGaNYPP/+rAr9OOEujUEXviqLZ8DH8V9OHQN78bHZ7IZpKMiExRoYJuT/LjtoIs8Z6CJ6Esowsmpdj4rzex8rAjhHiIrS10HeRG039XserFRVyhMBVuH6Jav4b84DmRw4eNjlBkF0lGRKZq0gT27IFx35fnvTLLqMoR/Ga1p0oVWLIEEqbP0BPhSJdgIcR/8jmb6LSqO3GHj7OzwmvYoAg43oCaNeHVV+Hvv42OUGQ1SUZEprOx0QXIiRPQ/6uqFC1q4q+/oF/3KKKGjIVPPkGVK6dn+JTuwEKI/xSvVoRGJ+fz97pjFHmpGUrBwoUwvOKPjO1xhogIoyMUWUWSEZFlHB3hnXf0U82HH4Ipf35ejZ/PIapjunEDRo2C8uV1t5w7d4wOVwhhIcq19WTFCti3D15uHMaC+Jd574eqfF36Ez4YEcuNG0ZHKDKbJCMiyzk76/lu/j5jovKw9jRwDOFlFnKacnDpEgwZosco2bDB6FCFEBbE2xsWLogn1qsuebnDh7Ej6PyJN52f2s24cUhSkoNIMiKyTeHC8NlncOIvW5zfeJnqtqH05VvOUoaEiEv8ea2s0SEKISyNhwcF/9yMmr+AmPyFqcFhNt1qhNv4N6lR+gZjx0oTtJxAkhGR7Z56Sg/UeuwvB2xe70sV25O0IgjvVzxp2RJ27ACGDdN9hmV2YCGEyYTptR44/n0c1bMXNijeZDY7omvw6YQ7lC2LJCVWTpIRYZiyZeGbb3RS8vQbLbCzg82boWfjv4ifMhWGDtVtSqZMgagoo8MVQhitSBFM3wXA1q2oypW53fEVKlTPQ1QUTJigy5QxY+DaNaMDFeaSZEQYrmxZXVNy6hS88Qb8Y1uGN/iGM5SFiAgYNgxVujSMHAnh4UaHK4QwWtOmmA4coPLiMRw4ACtXwsvldvNR1DvM/vAypUvD//4HFy4YHahIrwwlIzNnzsTDwwMnJye8vb3Zvn17uvbbuXMndnZ2eHl5ZeSwIodLTEqOn7bHvl8fqtmfpDfzCKUypshImDwZVbaszHsjhNDd9ZycsLGBTi8qfij5Hu8wgzM25Rl2axzffBFNuXLQp48eZkBYNrOTkWXLljF48GBGjx5NSEgIjRs3xs/Pj7CwsEfuFxkZSY8ePWjRokWGgxW5Q5kyMHs2nDprT5HhvamX7yjP8yM7aER0rBNzjza43xM4PBwSEgyNVwhhMJMJ07hx4ONDvoSbjGM8Yfbl6Rc7nR8C7uHpCS+9pLsKC8tkUkopc3aoV68etWvXZtasWUnrPD096dChA5MmTUpzv65du1KhQgVsbW1Zu3YtBw4cSPcxo6KicHV1JTIyEhcXF3PCFTnA9eswcyZ8+SU4/nueC5SiaFEYPEjx7nJv7O7e0gOavPYa5M9vdLg5kjXeg9YYs3hCSul3NqNG6Vk8gfC85eh3eyo/8zwALVroQaBbtACTychgc4f03odm1Yzcu3eP/fv34+vrm2y9r68vu3btSnO/7777jtOnTzM2nROmxcTEEBUVlWwRuVfBgjB6NJw9CyNmlKJMGfj3X5jzfhg3D/0NJ0/qZKRkST2F8OnTRocsDCDlhsBkgs6d4dgxmDULihenxO2/mTXhCq++qufC2bwZWrUCLy/47juIiTE6aAFmJiNXrlwhPj4eNze3ZOvd3NyISGOc3lOnTjFixAgWLVqEnZ1duo4zadIkXF1dk5ZSpUqZE6bIofLmhbff1g1df/gBXKuX4Sku8BZfc5xKEB0NX36JqlAB2reHvXuNDllkIyk3RBJ7e+jfX9eOTJ9OyZE9+P57/Zwyo/0mnnHcy6FD0Ls3lC4N48fD5ctGB527ZagBq+mhui2lVIp1APHx8XTv3p3x48dTsWLFdH//yJEjiYyMTFrOnz+fkTBFDmVvD6+8AgcPwo+/OhPW9i2qcIzWbCQQP0xKwbp1xF64ZHSoIhtJuSFSyJcPBgyA/x6EyxS7w9shfdkeU5fQ6p1p4naCy5dh3DidlPTpA0eOGBtybmVWMlKkSBFsbW1T1IJcvnw5RW0JQHR0NPv27WPAgAHY2dlhZ2fHhAkTOHjwIHZ2dmzZsiXV4zg6OuLi4pJsEeJhJpN+77tuHYQet6H8m615KU8gFTnBBD6g7Jt+fPih7h3MF1/Au+/CuXNGhy2yiJQb4rHu3ElqLFL58Eq2XqnKX83foJ3XBWJiICAAqlcHX19drsTHGx1w7pGhBqze3t7MnDkzaV2VKlV44YUXUjRgTUhI4NixY8nWzZw5ky1btrBy5Uo8PDzIly/fY48pDdFEel27pgdSmzED/vlHr8trG8M/dqUpEHMZZWOD6YUXYNAgaNJEWrClkzXeg9YYs8gmR47ohmg//QSAcnLi4ovv8P7NEXy/rlBSB70yZfTbnt69oVgxA+O1Yum+D5WZli5dquzt7dW8efPUsWPH1ODBg1W+fPnU2bNnlVJKjRgxQr366qtp7j927FhVs2ZNs44ZGRmpABUZGWluuCKXundPqUWLlGrYUCkT8aotP6tfaKmUbm+vF09PpaZOVerqVaPDtXjWeA9aY8wim+3cqVTjxvfLhJ071ZkzSg0bplShQvdXOzgo9fLLevOEBKODti7pvQ/NbjPi7+/PtGnTmDBhAl5eXgQHBxMYGEiZMmUACA8Pf+yYI0JkNXt76N4ddu6EP0NsKPlGOzrkDaIqR5hNP26RF0JD9YzB6ezlJYTIYRo2hG3bYP16PWRrw4aULasn9Pzn5z9ZEBBP3bpw7x4sWgSNGuleOHPmwM2bRgefs5j9msYIUt0qMkNkJHz/vR6z5OLxSLqzmH7MYZrXApoNrslLL0G+4/t1BvPqq7pPsQCs8x60xpiFhbhwASpVggoVYNo09jk/y6xZsHgx3L2rN8mfXxcTffpA7drGhmvJsmScESGsmaurHo7k2DH48TdXrnZ+kzq2ISw4UJOePaFECdjd7SsYNAjl7g49e8Lu3bqmVgiRexw7Bg4Oustes2b4jG3LvH57uHhRt4WvUEGPJDBzJnh7Q61aup2azBqccZKMiFzHZIJnn4Xly+FcmImPP9aTA0dHw7xTjTlEdUx378KCBboat2ZNXdLcuGF06EKI7ODrqwc0eustPVJaYCDUq0fBV9oypNEejh+HoCDw99c5y4ED+kGnRAn9enjzZpmlwlzymkYIdMGxbRvMmwerVipqxvxBP+bgzzLyoifCUVWrYjp8OFf2wLHGe9AaYxYW6K+/4KOPYOFC3dc3b17dVa9AAQCuXtXtSebNg0OH7u/m4QG9eukK1tw8/p68phHCDDY20KyZLm/CI0z0+Lo+M2p/hzsXeYevOEJVJoW9zLDhJg4eRLdomzNHN0QRQuRcTz8N8+fD8eN6/qt33klKRAAK/3ucgQN17cjevborsIsLnDkDY8bo7sHNm+sxTGSGgrRJzYgQj3DggH7iWbRQEX0jjjjsARhWahmfne9KQp682HTrCm+8AXXr5thaE2u8B60xZmEFlLp/n+/apbvYtG2re+XVqQPA7duwapUuO7Ztu7+rkxM8/7xu+Nq6te71l9NJzYgQmcDLC6ZPh4hLJlassadTJ/2O+NR5R45SBZs7t/UjT/36xFeXtiVC5HgPPnD88YeuVl2/Xj+MtGsHe/eSN69OOLZu1RN8fvwxVK6se+IsX66nznJ315Use/ZIG3mQmhEhzHb9up6l/IfvFQk7dvI639KF5eRB9/mLc8hD7PG/yeNR3OBIM4813oPWGLOwQqdO6Wzjhx/ut1p9qKYEdMLx55/6VfCSJXDpgamzKlaEbt2gSxeoUiWb489i6b0PJRkR4gmcPavHHvhx/nXqnlrIG3xDJK74Oe/g+ed14eLHBhwa14NChYwON8Os8R60xpiFFXs4KSlTRjd+TWW2+rg4+PVXvemaNXrKnERVq+pyo0sXXZti7SQZESIbJT71LF2i2LjsBkcu6AHTCnOFfyiJycbE5cYvUWxEbxx8n9VVu1bEGu9Ba4xZ5ACJSUnjxnpENIDYWDh8ONXR0aKj4ccf9eubjRv1polq1NBJSefOuvbEGkkyIoRBlNLvgZcvh8MLD/Lp5dfw4mDS5/86l+Vau9coM+Y1nDw9DIw0/azxHrTGmEUO9d13era9du306xsfn1Q3u3FDz923bBn88ouuQUnk5aWTkhdftK4aE0lGhLAACQnw+27F7un7cPv5W9rfXoYr9/v3fVF3KcXe8adtW8sefd4a70FrjFnkUKNHw+TJyduUjB4NDRqkucv167B2rX6o+fXX5IlJpUrQoYNe6ta17IpWSUaEsDAJCfD7ltv89dkaPLbNp25MMKU4z78Uw9YWBnjtoPEzirpDn6FUacvqImyN96A1xixysFOn7g+elpiU1K8Pw4ZBp06P3PXqVd22ZPVqPbrrvXv3PytRAl54QScmzZrp3n6WRJIRISyYUnDot6us2lqYtWv16+StNKUpwZziaYLcexLXvQfPvlqK6tWNH77EGu9Ba4xZ5AKnTulakoULdVbh6wubNqV796go2LBB15qsX6/bnCRycYE2bXRi0rp1srHZDCPJiBBW5K/jcdx5rR/l9y0jb8ItABIw8Sst+blQT+jYkVbP56F5c3B2zv74rPEetMaYRS4SEQFffw0tWujJsgAuXtRjFQ0YoAcieYyYGD2Wydq1uhFsePj9z2xt74/H1qaN7qVjxEONJCNCWKObN4kMWMWtmfNxP7E1afWPPE8HfsTBAZo2vV/AVKiQPWFZ4z1ojTGLXG7kSF1rYm+vZ9z73/+gevV07ZqQoBvOJyYmx48n/7xUKV1mtG2rh6fPly/zw0+NjMAqhDVydsZ14Gu4H/8NTp8mdtRYbhcrw/WWXShbVtfqHgm6SMTgSTSreIGKFWHwYF3L++BYBUIIK9Skia7OiI3Vs4bXqKHft2ze/NhhWm1sdBOUyZMhNBROn9aVLH5+ehj68+f1dFrPP6+HPGrdGr78Ek6csIwRYKVmRAhLl5AACQkoWztOnIDLwz6lyfr3SMDEZlqwgNdYQ0fiHfPxzDPQsiW0agW1amVeK3trvAetMWYhAD3M/JQpeoKbxMaujRvrdzIZuKlv39a7rl+vl3Pnkn9eqpQuM1q10m+NihZ94jNIIq9phMipfvwRvvgCgoOTVt00ObNcdeZ7ehBMExQ2FC6sC5ZWrXSCUrZsxg9pjfegNcYsRDJnzsDUqTB3rh5Abfr0+5/FxmZopj2l9CucwEC97NiRvHcO6DFNEpOTZ56BPHkyfgqSjAiR0/39tx5P+vvv9b+BOHsnXmkRQeBO12St7EHPhJ6YmDRtCoULp/9Q1ngPWmPMQqTqyhVdQ1KsmP77jz+gY0fdpqR//ydqAHL7NmzfDkFBejl0KPnnjo46IUmsNalVSzeOTS9JRoTILZSCnTv1O2ZbW5g9m9hY3ZjNaeAbBEXW4ZMz/txIuH/vmEz6dXTz5npsgsc1aLPGe9AaYxYiXfr2hXnz9L+LFoXhw+HNNzOlq92lS7qJSmJy8s8/yT93ddVNW5o10w82j2tfm+77UGXA119/rcqWLascHR1V7dq1VXBwcJrbrlq1SrVs2VIVKVJE5c+fX9WvX19t3LjRrONFRkYqQEVGRmYkXCFyp8OHldKpikrIm1eda/6amvpisKrimZC4Omk5cuTRX2WN96A1xixEusTEKDVvnlLlyt2/iYsUUeqTT5SKjs60wyQkKHXsmFJffaVU+/ZKubomLzeee+7x35He+9DsljDLli1j8ODBjB49mpCQEBo3boyfnx9hYWGpbh8cHEyrVq0IDAxk//79NGvWjPbt2xMSEmLuoYUQ5iheHD75BCpVwnT7NqW3LGDw6iYcjatE1KjJrJkVwRtv6BGpc9q05ULkaA4Oeq6b48dh/nwoX16/ynnvPf0ONpNeeJhM4OkJ77yj58y5ehX27oVPP9W9dNq2zZTD6GMpZV7U9erVo3bt2syaNStpnaenJx06dGDSpEnp+o6qVavi7+/PmDFj0rW9VLcK8QSUgt27ISBAz8B186Zev3atHkc6HazxHrTGmIXIkLg4WLRIDzc/aJAeNC1x/fXrmds9xkxZMs7IvXv32L9/P76+vsnW+/r6smvXrnR9R0JCAtHR0RQqVCjNbWJiYoiKikq2CCEyyGSChg11i/zwcJ2UtGmjH21yECk3RK5lZwevvaYHGHnjjfvrlyzR3eiGDtWju1ows5KRK1euEB8fj5ubW7L1bm5uREREpOs7pkyZwq1bt+jSpUua20yaNAlXV9ekpVSpUuaEKYRIi7Mz9OqlBxuwtBm1npCUGyLXs7NLfl9v3Ki7y0ydCh4euufNmTPGxfcIGRoSyfTQAPdKqRTrUrNkyRLGjRvHsmXLKJbYRSkVI0eOJDIyMmk5f/58RsIUQuQiUm4I8ZCFC3VC0rixHkxkzhw9h8Rrr+kJ+yyInTkbFylSBFtb2xS1IJcvX05RW/KwZcuW0adPH1asWEHLli0fua2joyOOjo7mhCaEyOWk3BDiISaTHve9dWs9mMjHH+u5I77/Hs6ehW3bjI4wiVk1Iw4ODnh7exMUFJRsfVBQEA0bNkxzvyVLltCzZ08WL15M28xsfiuEEEKIx2vcWNeS7NkD7drBuHH3P4uMTD7lrwHMfk0zdOhQ5s6dS0BAAKGhoQwZMoSwsDD69+8P6KrSHj16JG2/ZMkSevTowZQpU6hfvz4RERFEREQQGRmZeWchhBBCiMerUwd+/lmPWpbo88919+B339X9dw1gdjLi7+/PtGnTmDBhAl5eXgQHBxMYGEiZMmUACA8PTzbmyJw5c4iLi+Ptt9+mRIkSScugQYMy7yyEEEIIYT6ldG3JnTvw2We6oevYsbq2JBvJcPBCiMeyxnvQGmMWwhBKwYYN8P77kDggacGCuqbknXeeaO6bLBlnRAghhBA5jMmkxx7atw9WrtTDrl6/DiNH6iUbSDIihBBCCLCxgU6d4PBh3ePG01MPmJbo6lWIjc2aQ2fJtwohhBDCOtnawquvwtGjegTXRP376wRl4UKIj8/UQ0oyIoQQQoiUHhzM9Pp1PVbJ6dM6UalfHxISMu1QkowIIYQQ4tEKFoS//oKJE6FAAd012CbzUgizRmAVQgghRC7l7KwbtL75ZqZ/tSQjQgghhEi/AgUy/SvlNY0QQgghDCXJiBBCCCEMJcmIEEIIIQwlyYgQQgghDCXJiBBCCCEMJcmIEEIIIQwlyYgQQgghDCXJiBBCCCEMJcmIEEIIIQwlyYgQQgghDCXJiBBCCCEMJcmIEEIIIQwlyYgQQgghDJWhZGTmzJl4eHjg5OSEt7c327dvf+T227Ztw9vbGycnJ8qVK8fs2bMzFKwQQgghch6zk5Fly5YxePBgRo8eTUhICI0bN8bPz4+wsLBUtz9z5gxt2rShcePGhISEMGrUKAYOHMiqVaueOHghhBBCWD+TUkqZs0O9evWoXbs2s2bNSlrn6elJhw4dmDRpUort33vvPX766SdCQ0OT1vXv35+DBw+ye/fudB0zKioKV1dXIiMjcXFxMSdcIUQmsMZ70BpjFiKnSe99aFbNyL1799i/fz++vr7J1vv6+rJr165U99m9e3eK7Vu3bs2+ffuIjY1NdZ+YmBiioqKSLUII8ShSbghhvcxKRq5cuUJ8fDxubm7J1ru5uREREZHqPhEREaluHxcXx5UrV1LdZ9KkSbi6uiYtpUqVMidMIUQuJOWGENYrQw1YTSZTsr+VUinWPW771NYnGjlyJJGRkUnL+fPnMxKmECIXkXJDCOtlZ87GRYoUwdbWNkUtyOXLl1PUfiQqXrx4qtvb2dlRuHDhVPdxdHTE0dHRnNCEELmclBtCWC+zakYcHBzw9vYmKCgo2fqgoCAaNmyY6j4NGjRIsf0vv/yCj48P9vb2ZoYrhBBCiJzG7Nc0Q4cOZe7cuQQEBBAaGsqQIUMICwujf//+gK4q7dGjR9L2/fv359y5cwwdOpTQ0FACAgKYN28ew4YNy7yzEEIIIYTVMus1DYC/vz9Xr15lwoQJhIeHU61aNQIDAylTpgwA4eHhycYc8fDwIDAwkCFDhvD111/j7u7OV199RadOnTLvLIQQQghhtcweZ8QIkZGRFChQgPPnz8t4AUIYICoqilKlSnHjxg1cXV2NDiddpNwQwnjpLTvMrhkxQnR0NIB01RPCYNHR0VaTjEi5IYTleFzZYRU1IwkJCVy8eJH8+fM/sgtxYgaWk5+E5BxzBms7R6UU0dHRuLu7Y2NjHfNrprfcAOv7PTJCztH6WeP5pbfssIqaERsbG5566ql0b+/i4mI1P1RGyTnmDNZ0jtZSI5LI3HIDrOv3yCg5R+tnbeeXnrLDOh5xhBBCCJFjSTIihBBCCEPlqGTE0dGRsWPH5uhRGOUcc4bccI7WJDf8HnKO1i8nn59VNGAVQgghRM6Vo2pGhBBCCGF9JBkRQgghhKEkGRFCCCGEoSQZEUIIIYShJBkRQgghhKEkGRFCCCGEoSQZsXI3b95k8ODBuLu74+TkhJeXF0uXLn3sftHR0bz77rv4+vpStGhRTCYT48aNy/qAHxIfH0+xYsWYOnVqth/7QZlxPcz5LTL6uwnxONlRJmzZsoXevXtTuXJl8uXLR8mSJXnhhRfYv39/im23bt2KyWRKdfn999+f9HTTxVLKGXiysia9190Srrm5JBmxci+++CILFixg7NixbNiwgTp16tCtWzcWL178yP2uXr3KN998Q0xMDB06dMieYFMRHBzMv//+y4svvmhYDJA518Oc3yKjv5sQj5MdZcKsWbM4e/YsgwYNIjAwkC+//JLLly9Tv359tmzZkuo+EydOZPfu3cmWatWqZfQ0zWIp5Qw8WVlj7nU38pqbTQmrtX79egWoxYsXJ1vfqlUr5e7uruLi4tLcNyEhQSUkJCillPr3338VoMaOHZuV4abqrbfeUj4+Ptl+3Ic96fUw57d4kt9NiEfJrjLh0qVLKdZFR0crNzc31aJFi2Trf/vtNwWoFStWmHk2mcdSyhmlnqysSe91t4Rrbi6pGckEcXFxfPbZZ9SoUYM8efKkqBYrXbp0lhx3zZo1ODs707lz52Tre/XqxcWLF/njjz/S3DcxtqyQ3uuhlGLNmjV06tQp2f579uzB39+fsmXLkidPHooVK0bHjh05ffp0lsQLT349zPktnuR3E9Yhp5cJxYoVS7HO2dmZKlWqcP78efOCziBrLGfgycoaS7juWUWSkUzQp08fRo4cScuWLVmzZg3z589P+o9myJAhjB8/Ptn2Sini4uLStTzKkSNH8PT0xM7OLtn6GjVqJH1uhPRej127dhEeHp6ikDhw4AA1a9bkyy+/ZNOmTUydOpWTJ0+mWcWaWdfzSZjzW1jq7yYyT24sEyIjI/nzzz+pWrVqqp+//fbb2NnZ4eLiQuvWrdmxY8cTHS83ljOpedR1z+xrnqWMrJbJCRYtWqQA9c033yRb/9133ylA/fzzzyn2SaxCS89y5syZNI9doUIF1bp16xTrL168qAA1ceLEdJ1DZr6mMed6DB48WFWvXv2R3xcfH69iY2PV3LlzFaCuX7+eYpvMup6JMnI9zPktMut3E5Ypt5YJL7/8srKzs1P79u1Ltv7PP/9UgwYNUmvWrFHBwcEqICBAeXp6KltbW7Vx48Z0f/+DckI5o1TmlL2pXfesuOZZLXn6LMw2Z84cPD09ef3115Ot9/T0BODatWsp9vH29mbv3r3p+n53d/dHfv6o6r6seg3zKOZcj9WrV9O7d+9k2ymlWLVqFTNnzuT48eNERESg/pvL0cbGhjx58qQ4ZmZezydhzm9hab+byDy5sUz44IMPWLRoEdOnT8fb2zvZZ7Vq1aJWrVpJfzdu3JiOHTtSvXp13n33XVq3bm328XJzOfOgtK57VlzzrCbJyBO4fv0627dvZ+jQoSk+u3DhAgBPPfVUis+cnZ3x8vJK1zEerm59UOHChbl69WqK9Yk3YqFChdJ1jMxizvXYs2cPYWFhKapO33jjDebPn0+/fv0YOHAgRYsWxdHRkb59+3Lnzp1Up87OrOv5JMz5LSztdxOZJzeWCePHj+ejjz7i448/ZsCAAenap0CBArRr147Zs2dz586dVP/PPy25uZx5kLnX/UmueXaQNiNP4Pz58yilUs2C165dS5EiRWjSpEmKz7Zt24a9vX26lrNnz6Z5/OrVqxMaGpriHeXhw4cBsr0LlznXY9WqVVSsWDFZjCdOnGDu3LlMnDiRGTNm0KFDBxo1akTZsmU5evQoPj4+qR43s67nkzDnt7C0301kntxWJowfP55x48Yxbtw4Ro0aZda+iTUR5tbW5OZyJlFGr3tGr3l2kJqRJ1CgQAEAQkNDk63ftWsXS5YsYezYsalmyJlV3dexY0e+/fZbVq1ahb+/f9L6BQsW4O7uTr169dJ1jMxizvVYtWoVXbp0SbbduXPnAKhSpUqy9YMGDSIuLi7NQsISqk/N+S0s7XcTmSc3lQkffvgh48aN4/3332fs2LFm7Xv9+nXWrVuHl5cXTk5OZu2bm8sZyPh1f5Jrni2MaqySUzRp0kTZ2dmpjz/+WAUFBamPP/5Y5cuXT/n5+an4+PgsP36rVq1UwYIF1TfffKO2bNmiXn/9dQWohQsXJm2zdetWZWtrq8aPH59s38DAQLVixQoVEBCgANW5c2e1YsUKtWLFCnXr1q1k2wKqadOmj40nPdcjJCREASkaukVERKi8efOqWrVqqfXr16uVK1eq1q1bq/LlyytABQcHZ/AqpU96r0da1zM9v0VGthXWJTeUCZ9//rkC1HPPPad2796dYnlQt27d1HvvvadWrFihfvvtN/XNN9+oSpUqKTs7OxUUFJRs29xQziiVvuuc2m+U3utuzjW3FJKMPKFLly6pbt26qQIFCigHBwdVrVo19fnnn6vY2NhsOX50dLQaOHCgKl68uHJwcFA1atRQS5YsSbZNYivwh1tslylTJl2twaOjoxWgunbt+th40nM93n//fVWmTJlU91+3bp2qXLmycnR0VFWqVFFffvml+uijj5SNjY2Kjo5O93XJiPRej7SuZ3p+i4xsK6xLbigTmjZt+sjeJA+aNGmS8vLyUq6ursrW1lYVLVpUdezYUe3ZsydF3LmhnFEqfdc5td8ovdc9vdfckpiU+u8lkhBpCAwMpF27dhw8eJDq1as/8fdVqVIFPz8/pkyZkgnRCSFyAilncjdJRsRjDR8+nH/++UfmTRFCZBkpZ3I3SUaEEEIIYSjp2iuEEEIIQ0kyIoQQQghDSTIihBBCCENJMiKEEEIIQ1nFCKwJCQlcvHiR/PnzW+QwtkLkdEopoqOjcXd3x8bGOp5hpNwQwnjpLTusIhm5ePEipUqVMjoMIXK98+fPpzrRmyWSckMIy/G4ssMqkpH8+fMD+mRcXFwMjkaI3CcqKopSpUol3YvWQMoNIYyX3rLDKpKRxCpWFxcXKVSEMJA1ve6QckMIy/G4ssM6Xv4KIYQQIscyOxkJDg6mffv2uLu7YzKZWLt27WP32bZtG97e3jg5OVGuXDlmz56dkViFEEIIkQOZnYzcunWLmjVrMmPGjHRtf+bMGdq0aUPjxo0JCQlh1KhRDBw4kFWrVpkdrBBCCCFyHrPbjPj5+eHn55fu7WfPnk3p0qWZNm0aAJ6enuzbt4/PP/+cTp06mXv4R4qIgDNnoEGDTP1aIUQOFxgILVqAo6PRkQiRO2V5m5Hdu3fj6+ubbF3r1q3Zt28fsbGxqe4TExNDVFRUsuVxzp+HRo3gx2bTOLHsQGaELoSwIhkpNwCmTYM+bcNZ7zWa+HvxWRukECJVWZ6MRERE4Obmlmydm5sbcXFxXLlyJdV9Jk2ahKura9KSnrECihaFt2znMDlmCAW6+3Fu65lMiV8IYR0yUm4AVK8cy1aa8eLxiWz3GYxKkInMhchu2dKb5uEuPUqpVNcnGjlyJJGRkUnL+fPnH3sMJyfoG+TPSafquCVEkODbmstH/33y4IUQViEj5QZAi+fsuTZwHADPHp7Bb76TsjBKIURqsjwZKV68OBEREcnWXb58GTs7OwoXLpzqPo6OjkljA5gzRoBrmQK47trIBbsyeMSe4nLdtkRdvPnE5yCEsHwZLTcAGnzZle0vfQlA882j2frqvKwKUwiRiixPRho0aEBQUFCydb/88gs+Pj7Y29tn+vHcarkTt24TV02FqXZ7LyeqdeJu1L1MP44QImdpvGIgwQ1H6H8vfINdI382OCIhcg+zk5GbN29y4MABDhw4AOiuuwcOHCAsLAzQVaU9evRI2r5///6cO3eOoUOHEhoaSkBAAPPmzWPYsGGZcwapKNu6Epe/W88t8lLn+i/sqdab+Dh5DyyEeLTG2yeyq2JPbEmg1uQu7J+x2+iQhMgVzE5G9u3bR61atahVqxYAQ4cOpVatWowZMwaA8PDwpMQEwMPDg8DAQLZu3YqXlxcffvghX331VaZ3632Y52v1ODlxFTE4sOx8Awa8Y0JJPiKEeASTjYl6B79hn1tbzlKWHiPcCQkxOiohcj6TUpb/f9FRUVG4uroSGRlp9hwTP888zwsDSqEUjB4NH32URUEKkYM9yT1olCeJ+e6123Rpf4efdxWmWDEIDoZKlbIoUCFysPTehzl+bpr2b5UicbDYmR9fY3nPQGMDEkJYPKdCefkhsDC1asHly/BRow2EHbhmdFhC5Fg5PhkBeOst+HLMVbbTmI4LXuCntzYaHZIQwsK5usKmTfBeie9ZcLUtl+s/z8XTd4wOS4gcKVckIwADxxYkrlot7Imj+ayX+PmDPUaHJISwcEWLwtCFtYm2ccUnZifHvbryb3ic0WEJkePkmmQEGxtq7AvgeBlfnLlFo4+eY9NkaZkmhHi0Ys2rcXvJT9zFkeY3f2JntX7cuJZgdFhC5Ci5JxkBTI4OVDq8itNuDSjEdeqMbMG2aZKQCCEerUSXxlz9einx2NDhWgDBld/gZpQkJEJkllyVjACY8jtTNnQjJ4vohKT6kBb8PvuA0WEJISxcybc68M+kH4jHhuf/nceOSn24fVMSEiEyQ65LRgBsC7pQ7sRGThSsTxQu9BxcgM2bjY5KCGHpSo/oztmPFxOHLYciivJCBxO3bxsdlRDWL1cmIwB2hVwoe2IT45tt40RMWdq3RxISIcRjlR/lz+Hv9vNhvk/4dbOJF15AEhIhnlCuTUYAHIu6MHtDGdq2hTt3YHabn/hjzgGjwxJCWLhaPWuyYaMJZ2fY/utdFtX8lNtR0stGiIzK1ckIgKMjrFoFI+ttYfG9Tjzdv4UkJEKIx3rmGdgQqFhp25XX/3qPfRW6cTsy1uiwhLBKuT4ZAZ2QjP3Jm9MFvCnMNUlIhBDp8kxjEx4f9yUGB5pcXsmfFfy5fUNmCRfCXJKM/MexmCseJzZxvEC9+wnJNweNDksIYeGqvteOvz5dw10ceebfNRys8BK3r8cYHZYQVkWSkQekSEj6Nef3OZKQCCEererwNvz1+Y/cwYkGV37mcIUXuXX1rtFhCWE1JBl5SGJCcqJAXQpzjQr9m/Pr3LNGhyWEsHDV/teav6b+zB2cqHc1kN8r9yQy0uiohLAOkoykwrGYK2VP/MLJgvVYQ0f8+pdh2TKjoxJCWLrqg1vy91friTAVZ9SVIbRoAVevGh2VEJZPkpE0OBZzpdyZzQR3n0NcvIlu3SBgnjI6LCGEhav6TnMidv7N30XqsX8/PPssRIRL2SHEo0gy8gh2rvmY/4Mt/fqBjYojX9+ubOyx2OiwhBAWzqtBHrZtgxIlIM+RPVzyqMc/u84ZHZYQFkuSkcewsYFZs2Bxq/n4s5znfniZoLZTjQ5LCGHhqlSB7cGKeQ5vUjNmL/aN6xO2Zr/RYQlhkSQZSQeTCTpv6M0f9QYC0CpwKDvrDEbFxRscmRDCkpV/2kTh7T9y3KEGxRIiKNKpCee+Xmd0WEJYnAwlIzNnzsTDwwMnJye8vb3Zvn37I7dftGgRNWvWJG/evJQoUYJevXpx1cpadZlsbai3expb234GQKN9X/JnRX/ib94xODIhhCVzr/sUhY5uZ7dzK/Kq2zw14AX+HjoDlLQjESKR2cnIsmXLGDx4MKNHjyYkJITGjRvj5+dHWFhYqtvv2LGDHj160KdPH44ePcqKFSvYu3cvffv2feLgs53JxLPrhvFrnyXE4ID3mVWcLNOKu/9YV2IlhMhexZ52odJf6/m5aG9sSaDc1He40PxViJHB0YSADCQjX3zxBX369KFv3754enoybdo0SpUqxaxZs1Ld/vfff6ds2bIMHDgQDw8PnnnmGfr168e+ffueOHijtJzbld/HbeIGrpS+FsKbL1zkxg2joxJCWLJCbvY0/3su8yp/Rhy2/LH1Lt8tcjA6LCEsglnJyL1799i/fz++vr7J1vv6+rJr165U92nYsCEXLlwgMDAQpRSXLl1i5cqVtG3bNuNRW4CmY5/lVMAOeudZyvz91WnSBC5eNDoqIYQly+dsosehYUzy205v5tG7j4nJk0FdvwFxMuuvyL3MSkauXLlCfHw8bm5uyda7ubkRERGR6j4NGzZk0aJF+Pv74+DgQPHixSlQoADTp09P8zgxMTFERUUlWyxRnV7VGLW7PcWLw+HDMKzWZq6//DbcvGl0aELkOtZSbtjbw/vrG/Dme64AjBwJh+r0Rvn4wG+/GRydEMbIUANWk8mU7G+lVIp1iY4dO8bAgQMZM2YM+/fvZ+PGjZw5c4b+/fun+f2TJk3C1dU1aSlVqlRGwswWNWvCrl1QpXwMEy/3oeDimdz19IIdO4wOTYhcxZrKDZMJJk+GqVOhJBcodXorpoMHoXlzaN8eQkONDlGIbGVWMlKkSBFsbW1T1IJcvnw5RW1JokmTJtGoUSOGDx9OjRo1aN26NTNnziQgIIDw8PBU9xk5ciSRkZFJy/nz580JM9t5eMDW3Y58VnEuYZTC6cJpVJMmMGiQ1JIIkU2srdwAGDwYPl30FFVtTzCdAcSbbGHdOqheHd56Cy5fNjpEIbKFWcmIg4MD3t7eBAUFJVsfFBREw4YNU93n9u3b2NgkP4ytrS2ga1RS4+joiIuLS7LF0hUtCp/sb8mgZocJoBcmpeCrr3Sh8uuvRocnRI5njeUGQPfusCCwKKOcp1NFHWWz8wsQH69HW3z6adi92+gQhchyZr+mGTp0KHPnziUgIIDQ0FCGDBlCWFhY0muXkSNH0qNHj6Tt27dvz+rVq5k1axZ///03O3fuZODAgdStWxd3d/fMOxML4OwMyze58vvrAbRmI+coDWfPQqtWYMW9h4QQWcvXV7/ZvVWyEi1vrqVDga3c9PSBggWhVi2jwxMiy9mZu4O/vz9Xr15lwoQJhIeHU61aNQIDAylTpgwA4eHhycYc6dmzJ9HR0cyYMYP//e9/FChQgObNm/PJJ59k3llYEHt7mDMHPi3fmmojjjCRUdQuEUHNyj44Gx2cEMJi1awJf/wB7drBjweaUuzOH6yadh4/Jye9QVycblPSoQO8/jrkz29ovEJkJpNK612JBYmKisLV1ZXIyEirqXoFWLECXn0VYmPi8apty88/g7v9v7r5/McfQxrtbISwNNZ4D1pjzADR0dC1KwQG6oaun34K//sfmFYsB39/vZGrK/TvDwMHQg6rYRY5S3rvQ5mbJgt17qx76hUqYsuff0L9+nC95xCYN0/PorVwoQwJLYRIJn9++PFHePttXTwMHw5vvglxbZ6Hb7+FSpUgMhI++QTKloXeveHoUaPDFuKJSDKSxRo00FWvlSrB+fPQ/rehRHrUhGvXdLXJs89CSIjRYQohLIidHUyfrrv+mkz61a9fRyeuvdgXjh3T2cozz0BsLHz3HVSrBsePGx22EBkmyUg2KFdON4hv1gx23qlN0TN72dryI5STEwQHg7c39O0Lly4ZHaoQwkKYTLrr75o1kDev7pRXty4cO24Dzz8P27frguXFF3ViUrny/Z1374a7dw2LXQhzSTKSTQoWhE2b9NABsdjT7NfRDGh5grjO3XRd7Lx5+jFICCEe8MILemDFMmXg9Gn9unfduv8+rF8fVq2CLVvu7/Dvv7oHX4UKukpFhpkXVkCSkWxkbw9ffw2zZ+tq2JnrSlPv9GIurd4Jfn66YWuia9ekPYkQAtA9bfbuhSZNdAPX55/XTUaSigh7+/sb//WXfvq5cEE3cvX21jWwQlgwSUYM0K8fbN4MRYrAn39CzTcbsuv9QN1CHnQJ88IL0KiRbnAihMj1ihaFoCCdXygFI0bAK6/AnTsPbdigAZw6BdOm6aTk0CFo2lSPrvbPP0aELsRjSTJikCZN9JNOjRq6qcizz+o3NQCcOKGzlN27dTXsyy/r1q9CiFzNwUEPzDpzpq5dXbwYGjdOpXhwctLTUZw8qZ9+TCZYskQ3dI2MNCR2IR5FkhEDlS0LO3dCp066UXzfvnoso7tlK+snm549dSGyeLFunDZpEsTEGB22EMJgb76pa0kKF4b9+6F27TRmnShSRL8X3rdP15j07n2/BlYICyLJiMGcnWH5cvjwQ513zJ2rG8afi3XXXfb27dMrbt+GUaP0XDdnzhgdthDCYM8+q2tXa9WCK1egdWv9vJKQkMrGtWvr8eYnTry/7swZ3TJWCAsgyYgFsLGB99+HjRuTP+ls2oT+R3Aw/PCDHrHVyQkseGp0IUT28fDQtau9e+skZNQo6NgRbtxIZWMbG3B01P++exdeeklnNCtWZGPEQqROkhEL4uurExEfH92Zxs9P15gkKJNuqXbihC447P6bUig2FpYulV43QuRiefLo9mbffqvblPz0E9SpA4cPP2Kn+HidycTG6iHmAwKyLV4hUiPJiIUpU0aPZfTGGzrHGDNGd+O7fh39rrdSpfsbf/QRdOsGbdrAxYuGxSyEMF7fvrqWpHRp3bu3Xj1YtCiNjfPlg2XLdONWpXRjtV9+ydZ4hXiQJCMWyMlJj1UUEKBrVdev1++Ff//9oQ2LFtUbb9yoW8mvXWtEuEIIC+Hjo2tXfX11l99XXtF5xu3bqWxsa6u75vTqpd/xdOkiQ8oLw0gyYsF69dLty8qVg3PndBe+Tz99oIHagAG6C7C3t6466dhRbyCvbYTItYoU0TP+fvDB/UbxdevqKW1SMJl0QtKoke7y27lzKgOXCJH1JBmxcLVr63zD31+P6vzee9C2rR7xGQBPTz0eyYAB+u/33tPzjUtCIkSuZWsLEybo7r9ubnpSXx8fXduaomhwdISVK/WG0dEyppEwhCQjVsDVVY9X9M0399/K1KwJW7f+t4G9vZ7ic9o0/fesWbqxqxAiV2vRAg4e1FPV3LkDffroVzfR0Q9tWLy4fh984ABUrGhEqCKXk2TESphM+t3vnj26MiQ8XBc048bphvGAHnHx22/19OIPzuAphMi13Nz0A8ykSbrGZPHi+zWuyXh7Q4EC9/+W2lWRjSQZsTLVq+uBjhLHFRg/XiclYWH/bdC3r269lujiRSlUhMjlbGz0XDbbtulhiv76Sw/IOm1aKoOkKaVb0Pv6yoy/IttIMmKF8uXT4wosXKhHcN22Tc9xs3jxQxueOKGfdt58M41hGYUQuUmjRvpNzPPPw717MGSIHrk12fx5ly7Bu+/q8eU//NCoUEUuI8mIFXv5ZQgJ0XPpRUbqv7t1+29MEtD1sJcu6aecfv0kIRFCUKiQHgVg5kw9YNqvv+oa1+XL/9ugeHFdZoAey2j7dqNCFblIhpKRmTNn4uHhgZOTE97e3mx/zH+sMTExjB49mjJlyuDo6Ej58uUJkBH/MsXTT+uyYvx4/T546VJdS7JlCzoz+f57XUc7d65+hZPUwEQIkVuZTLrCNCRE97K5fl332OvR479Jfbt2hdde0w8wL7/8wBOOEFnD7GRk2bJlDB48mNGjRxMSEkLjxo3x8/MjLKnRQkpdunRh8+bNzJs3jxMnTrBkyRIqSwPLTGNnp0dq3bULKlSACxd0O5JhwyCm8yv6fY6NjZ54r3dvSUiEEIAe0HnXLj03lo2NngKrZs3/KkOmT9dPO+fP3x8SWoisosxUt25d1b9//2TrKleurEaMGJHq9hs2bFCurq7q6tWr5h4qSWRkpAJUZGRkhr8jt7h5U6l+/ZTSJYdS1asrFRKilFq2TClbW73y5ZeVio01OlRhRazxHrTGmI20c6dS5crpIsJkUurdd5W6u32PUnZ2euW33xodorBC6b0PzaoZuXfvHvv378f3wd4agK+vL7vSmIr6p59+wsfHh08//ZSSJUtSsWJFhg0bxp1HjPIXExNDVFRUskWkT758MHs2/PwzFCumJ8uqUwfGHu1C7KJluhrl5EkZZVHkOFJuPJmGDXXj1t699aPMp59CrTfqENbvY11tcuWK0SGKHMysZOTKlSvEx8fj5uaWbL2bmxsRERGp7vP333+zY8cOjhw5wpo1a5g2bRorV67k7bffTvM4kyZNwtXVNWkpVaqUOWEKoF07nYh06qR7502YAD4TO3Hqy0A9IVb+/EaHKESmknLjyeXPr3vq/fijbscaGgrlZg5j2qv7uTt4hNHhiRwsQw1YTSZTsr+VUinWJUpISMBkMrFo0SLq1q1LmzZt+OKLL5g/f36atSMjR44kMjIyaTkvwxNnSLFiepTn5cv1fBWHDoHnwFZ8MKUAMTH/bbRkCdy6ZWicQmQGKTcyz/PP6yHkX30V4pUNQxZ4UauWnnlCeuWJrGBWMlKkSBFsbW1T1IJcvnw5RW1JohIlSlCyZElcXV2T1nl6eqKU4sKFC6nu4+joiIuLS7JFZFznznqSrC5ddNvVjz7SLejPjZwN3bvrsaKvXTM6TCGeiJQbmatQId0Z76efoEQJPaFvn4ahXCjhQ8xPm4wOT+QwZiUjDg4OeHt7ExQUlGx9UFAQDRs2THWfRo0acfHiRW7evJm07uTJk9jY2PDUU09lIGSREUWLwrJlsGKF/veRI/DKpzW441hAP+40bqy74QghxAPat9e1JD16wOt8w1OXQ4h68TV2rblkdGgiBzH7Nc3QoUOZO3cuAQEBhIaGMmTIEMLCwujfvz+gq0p79OiRtH337t0pXLgwvXr14tixYwQHBzN8+HB69+5Nnjx5Mu9MRLq89JIuWLp2hR0JDakTs50IW3ddddKokUywJ4RIoWBBWLAAKq+aSKhdNYrGX+Lmi6/yep8EqVQVmcLsZMTf359p06YxYcIEvLy8CA4OJjAwkDJlygAQHh6ebMwRZ2dngoKCuHHjBj4+Prz88su0b9+er776KvPOQpilaFHdVGTtWrhRshr14ndxgooQFkZCo2f05DdCCPEQvxfzUHL7MmLs8uJLEG4BE/H01FNRyDAk4kmYlLL8/4SioqJwdXUlMjJS3gNnsuhoPeDRkq/+ZT1tqMM+Yh2dsTv7F6biqbcDErmPNd6D1hiz1ViwAHr2JB4bWrCZbTyLry/MmgXlyhkdnLAk6b0PZW6aXC5/fvjyS1i/pyiDqm3hV1owJmYUzbq6yRsbIUTqXnsNevXClgTWOXejlMMlfvkFqlWDTz6B2FijAxTWRpIRAeiB0YJD8nNo8ga+yjMiaSbgce/e5tZNi688E0JktxkzoGpVnGuUY+uvcTRvrsdSHDECatWCrVuNDlBYE0lGRBI7Oxj6nj1Hj5nw8wPHe1G0+6wJC0sMZ8VyJe+EhRD35c0LmzbB1q2Ua1ySX3/Vb28KF9aN5Js103N1Sic9kR6SjIgUypaF9evh12Gb8GE//W5OIdL/dVq3jOfYMaOjE0JYjJIlwd4e0DMB92h+gZMn4a239AjyS5dC5cr61U3SQItCpEKSEZEqkwnqftaZe7MDSDDZ0Jd59NnSHZ8a9xg2DGTaDyFEkvh4GD4cKlWi0PmDfP017Nun57u5dUu/uqlRQ1ekCJEaSUbEIzn064XNiuUoe3v8Wc7K+A7MnHKbSpX0dOMyMrQQAtCTYd2+DR07wtWr1KoFO3boUVzd3PT8nM89pz8+c8boYIWlkWREPF6nTph+/hny5KENG9jm9By3IyLp0QPq19cFjhAiF7O11YONlCunM41u3SAuDpNJz29z4gQMHao3W7tWv7p5912IjDQ6cGEpJBkR6dO6NQQFgYsLPgX/YvLwazg76/HRGjfWI7uePm10kEIIwxQqBGvW6IatQUEwenTSR66uMGUKHDwILVrAvXvw2Wfw9NPw9dfSFVhIMiLM0agRbN2K6ZdfePNTD/76C954QzdUW7UKPD1h2DC4ft3oQIUQhqhRA777Tv/700/1hFgPqFpV5ynr1unakStXYMAAvdv69TKKa24myYgwT61aemQj9HvgOZ1/5diGc7RurZ9upkzRTzvTp8vTjhC5Upcu+h0MQJ8+cCn5hHomE7RtC4cO6VqRIkX0jMDt2ukJxA8eNCBmYThJRkTGbdsG7dpR6fUmbJzxFxs26Cefa9dg4ED97xUrpJGrELnOxIm6pWpAgH5qSYW9ve4C/NdfOndxcIDNm/XzTs+ecO5c9oYsjCXJiMi4p5+GMmUgLAyaNuW5ssc5cADmzIFixeDUKf2QVKeO7tInVbBC5BK2trB6tS4AHsPVVY9Dcvw4+PvrcmLBAqhYEQYNgsuXsyFeYThJRkTGlSypa0eqVoWLF6FpU+xCD/PGG/ppZ9w4PffNn3/qLn3Nm8PvvxsdtBAi2128CN9888hNPDz0IGl//HG/ketXX+kOOmPGSM+bnE6SEfFkihfXk1DUqqUfYZ59FvbsIX9+GDtW97AZMkRXwW7dCg0aQIcOcOSIsWELIbLJtWvg4wP9+uneNo9Rty78+qtu6OrjowdN+/BDKF9et0m7cycbYhbZTpIR8eSKFNEve+vV0wVPs2Z6ACSgaFH44gv9yqZ3b93z5scfdev5Hj30eiFEDlaoEHTvrv/dp0+6J6tp2RL27IGVK3XPm6tXdW+9ChX0q+B797IwZpHtJBkRmaNgQf0489xzull81arJPi5dGubN0zUinTrp98I//KALmddek6REiBxt4kRdzXH9un4KiY9P124mky4vDh/W5UepUvDPP9C/vyQlOY0kIyLzODvDTz/p8Z9t/vtPKzY2WctVT0/9pLN3r+7el5CgN5ekRIgczMFBj9CaNy/89pt+32IGOztds3ryJEybBiVK6HbzkpTkHJKMiMxlbw+OjvrfCQk6w+jbN8WgIz4+euCjPXtSJiU9euhCRwiRg1SooFukgh6ddf9+s7/CyUn3sDl9Gr78MnlS8vTTkpRYM0lGRNbZs0ePwBgQAC+8ADdvptikTp37SUm7djop+eEHXYPy6qtw9KgBcQshskbv3vq9S1ycbuGeQXny6LGMTp/W+U2JEnD+/P2k5Ouv9Zx9wnpIMiKyTv36elasPHlgwwbdsDWNQQPq1IGff9avbxKTkoUL9WCvL7wAu3dnb+hCiCxgMukuvsOG6X68TyhPHnjnHfj77+RJyYABULYsfPyxTE9hLTKUjMycORMPDw+cnJzw9vZm+/bt6dpv586d2NnZ4eXllZHDCmvUvr1+R1ykCOzbp2fVO3s2zc19fHRSsm+ffoAymXQzlIYNoWlT2LhRBk8TwqoVKqRnyXN2zrSvdHK6n5R8/bVORP79F95/X4/L+O67eqgTYbnMTkaWLVvG4MGDGT16NCEhITRu3Bg/Pz/CwsIeuV9kZCQ9evSgRYsWGQ5WWKl69WDnTl0qnDypJ9z7r+tvWry9dUPX0FDdG9DeHoKDwc9PD2mydKmu6RVCWLGEBJgxQ3eRyQROTnqI+VOnYNEiqF4doqN17uPhoSf2lEbylsnsZOSLL76gT58+9O3bF09PT6ZNm0apUqWYNWvWI/fr168f3bt3p0GDBhkOVlixihV1QlK1qp6qM511p5Uqwdy5cOYM/O9/kC+fnkirWzf92ddfp9oURQhhDYYP11Ua3bplastTOzs9tMnBg7pN2jPP6K//9lvdSL5LFxkN2tKYlYzcu3eP/fv34+vrm2y9r68vu3btSnO/7777jtOnTzM2nQ2WYmJiiIqKSraIHKBkSdi+Xb+HadLE7F0//1y3nJ8wAQoX1lWyAwbosQfee0+/Kxa5l5QbVqhfPz1nxPbtOinJ5HewiTMEb9+ul8T2aCtW6NGgGzSA5culltUSmJWMXLlyhfj4eNwemoXRzc2NiIiIVPc5deoUI0aMYNGiRdjZ2aXrOJMmTcLV1TVpKVWqlDlhCktWsCA8mMz++afOKO7eTdfuhQrBBx/oGT1nzNAt52/cgE8/1dWw3brpuS1E7iPlhhWqWFG/c01s2DpzZpYd6pln9HPQoUPQq5ce+uT33/XkfOXL64edGzey7PDiMTLUgNVkMiX7WymVYh1AfHw83bt3Z/z48VSsWDHd3z9y5EgiIyOTlvPyyJszxcZC1676XUv9+mYNLpIvH7z9Npw4oRu4NmumB3VculR/VcOG+ulHnnhyDyk3rFSbNnraXtCDiGzZkqWHq15djzYQFqYn4CtaVP97+HB46qn7XYZFNlNmiImJUba2tmr16tXJ1g8cOFA1adIkxfbXr19XgLK1tU1aTCZT0rrNmzen67iRkZEKUJGRkeaEK6zBpk1KFS2qFCjl7KzUokUZ/qqQEKV69FDK3l5/HShVurRSEycqdelS5oWcG1njPWiNMedaCQlKvfqqvmkLFVLq77+z7dB37ig1d65SVaveLzdMJqXatVMqMFCp+PhsCyVHSu99aFbNiIODA97e3gQFBSVbHxQURMOGDVNs7+LiwuHDhzlw4EDS0r9/fypVqsSBAweoV69eRnMokVP4+sKBA7rf7s2b8PLLerl2zeyv8vKCBQv0K5z339e9icPCYNQo/cTz8su6Da10DRbCwphMevhUHx/d/eXPP7Pt0E5Ousfe4cPwyy+6x55SuuFrmzZ64NjPPtMT9YksZG6Ws3TpUmVvb6/mzZunjh07pgYPHqzy5cunzp49q5RSasSIEerVV19Nc/+xY8eqmjVrmnVMecLJBWJjlRozRikbG/1oUqKEUufOPdFX3r6t1Pz5StWte/+JB5SqUUOp2bOVio7OpNhzAWu8B60x5lzv/Hmldu0yOgp1/LhSgwcr5ep6v9xwdNQ1r7//rityRPpkSc0IgL+/P9OmTWPChAl4eXkRHBxMYGAgZcqUASA8PPyxY44IkYKdHYwfr4darVwZatTQ3WSeQJ48emqcP/7QI7v27q2fgg4d0sNGu7vrBvzHjmXSOQghnsxTT+kuLoliYgwJo1IlmDpVD38yd64e2ygmRs+fVb++rsCZN0+GnM9MJqUsv9I6KioKV1dXIiMjcXFxMTockdXu3IFbt/R7FoCoKD2pVrNmT/zV16/rVzkzZyYf/KhhQ11V26VLpg4MmWNY4z1ojTGLBxw8CC++qMd5b9vW0FCU0vNnzZypp9tKzJFcXHQPvj59dIKSSj+OXC+996HMTSMsT5489xMRgKFDoXlz3cz9zp0n+uqCBWHwYDh+HIKCoEMHsLWFXbt0gVKihJ5kePduaVsihKECAvRgQt276xvWQCaTHkh6wQK4cEEPJVCunH5OmjMH6taFmjX1TMLStiRjJBkRli0hQb9bAZg+XY8THxLyxF9rYwMtW8KaNXqwtMmTdUO1mzd19WvDhnqw2ClT0pzbTwiRlT77TA8OEhWlnxoiI42OCNDPScOH65rVzZt1ruToqBvADh6sX//6++vGsAkJRkdrPeQ1jbAOmzZBz54QEaEnqvnoIz0+vK1tph1CKdixQycjy5ffr4Sxs4Pnn9ftT557Tg+WlNtY4z1ojTGLh1y6pN9/XLigX9X8+GOm3vOZ5fp1WLJElx0PdgQqXVqXG6++qh92cqP03oeSjAjrceWKnulqzRr9d9OmejaskiUz/VBRUXoAtXnz9LviRIUL66eeV17RDdlyyztia7wHrTFmkYrE2b7v3tWvbKdMMTqiRzpwQJcbCxcmH9G1Xj2dlPj7J38LndNJMiJyJqXgu+90+5F8+XTdaLFiWXrIw4dh/nz95BMefn99+fI6KXn55Zz/1GON96A1xizSsGSJfh8CuuFGjx7GxpMOd+/q56YfftCvbOLj9Xo7Oz2WySuvQPv2uolcTibJiMjZTp/W/e4enHDv9m3ImzfLDhkfr98RL1wIq1frDj+J6tfXhUtOfeqxxnvQGmMWjzBpkr4BV60CV1ejozHLpUs6n1q4UHcMTOTiAi+9pMuOpk11W7acRpIRkbssXw7DhumBAJ59NssPd+sWrF2rn3qCgu43VLO1hRYtdFLSoYOe2C8nsMZ70BpjFo+glH4iSOeEq5YqNFQnJQsX6hGiE5UoAZ076+EFGjTIOYmJJCMi91BKv5Ddu1c34hg+HD78MNtamkZE3H/qebDxmp0dtGqlC5cXXtDdiq2VNd6D1hizMMNHH+nedX5+RkeSIQkJusH8Dz/oST0f7CxUsuT9xMTa26ZJMiJyl5s3YcgQPVwi6EJq8WI9RXk2OnlSFyzLl+uRXhPZ2+tpePz9dc8cK6tltsp70BpjFum0YoX+f2p7e/0k0KmT0RE9kZgYXcO6fLmucY2Ovv9Z6dL3E5M6dawvMZFkROROa9boUcuuXdMNXL/6Cnr1MuQOPn5cFy7Ll8PRo/fXOzjoGpMOHXRiksXtbzOFNd6D1hizSKd793TL8ZUr9b09dSoMGmR0VJni7l09ksHy5fDTT/o5K1GZMtCxoy47GjWyjjdWkoyI3OvCBd3a/rff9N979+qxCgx09Kh+mFu2LPlgkiaTLlQ6dNBL+fJGRfho1ngPWmPMwgxxcXpyqdmz9d99+sCMGfcHScwB7tyBjRt1YvLzz8kbzRcurHvjdOyoH24stVeOJCMid4uPh88/18OnWtC4BErpxGTtWr082LIeoFq1+08+tWpZTpWsNd6D1hizMJNSeqTWESP0v318dG3JfxO35iS3b+suwmvX6sTk2rX7n+XNC61b63KjXTvLajgvyYgQDwsL0wOGjByp3zVbgLAwXRW7di1s3Xp/LALQkxY//7weePLZZ4198rHGe9AaYxYZ9MsvehySq1dh/Xpo08boiLJUXBxs337/oebBXjm2trqbcLt2+jJUrGjsQ40kI0I8KCFBz/obHKwbt86dC15eRkeVzLVrEBioC5cNG5JPT54nj54rsE0bvZQtm72xWeM9aI0xiydw7pxuBdq3r9GRZCul9KiviYnJgw3nQb/6TSw3mjbN/ocaSUaEeNiyZdC/vx6j2dZWdwEeM8YiX7beuQO//qof8tav181gHlSlyv0C5plnsr6ixxrvQWuMWWSis2dh7FjdiN3auq89gb//1rWtgYGwbZtu65soTx49DlJi2ZEdb7MkGREiNeHheij5lSv1308/Dd9+my0DpWWUUnDkiC5cAgNh587kr3NcXPQMxL6+uiFbuXKZH4M13oPWGLPIJErpluG7d+u5Glav1g2ycpmbN/WgtYllR2oPNc89p8uNJk2yZgBrSUaEeJS1a+Htt+HiRf33jz/qBhpW4Pp1XRsdGKhf51y+nPzzcuV0ctKqlX61kxmN2azxHrTGmEUm2rtXj7UeFqb/X3bOHD3uei6llJ5nKzEx2bUr+UONg4PO31q10uVH7dqZM0GyJCNCPE5kpG6Fv3277tbi6Gh0RGZLSNChb9qkE5Rdu3TjtkQmk+5gkJicNGyYsdO0xnvQGmMWmezKFejWTb/zBD3r95df5qjuvxmV+FDzyy/6fx9sBAv6IaZ58/vJSUZrXCUZESK9HpxgLzYW3ntPT1X+1FPGxpUBN2/q98RBQXo5diz553nz6tnYmzXTS+3a6Rs4yRrvQWuMWWSB+HiYMEFPEZH4+uannyyr/6vBlIJTp3TOFhQEW7ZAVFTybcqV0+1NEsuO4sXT992SjAiREZ98omtLXF1h+nRdrWspg31kwD//6HfGicnJpUvJP3dx0e+Kp07VzWfSYo33oDXGLLLQpk16Poby5XXG7uxsdEQWKy5Ov+VKLDd+/z15jStA5cq60mnMmEd/V3rvwwzNCzhz5kw8PDxwcnLC29ub7du3p7nt6tWradWqFUWLFsXFxYUGDRqwadOmjBxWiKzXti3Uratf4fTooee8eLhRhhUpWVKfxg8/6La7hw7BtGl64j5XV/30s26ddU/iJ0S6tG6t32OuWyeJyGPY2emZg8eM0W+xr13TA60NHXp/MMbjx3Vv6sxidjKybNkyBg8ezOjRowkJCaFx48b4+fkR9vALp/8EBwfTqlUrAgMD2b9/P82aNaN9+/aEhIQ8cfBCZLpq1XR3lY8+0v1l16yBSpX0kNMPtvayQiYTVK+up/BYu1aPD7VvH8ybp4eWFiLHq1IFSpS4//dnn+l5GsQj5c+vB1GbMkXPTH7lii4a+/fPvGOY/ZqmXr161K5dm1mzZiWt8/T0pEOHDkyaNCld31G1alX8/f0Z87j6nf9IdaswxIED0Ls3JCbO77yjxyzIhazxHrTGmEU2+u033UIT9OvZ4cOt+pWspcqS1zT37t1j//79+Pr6Jlvv6+vLrl270vUdCQkJREdHU+gRjYdiYmKIiopKtgiR7by8YM8enYAUKQJvvWV0ROIRpNwQZmnSRI85BLrR+qBBunuaMIRZyciVK1eIj4/Hzc0t2Xo3NzciIiLS9R1Tpkzh1q1bdOnSJc1tJk2ahKura9JSqlQpc8IUIvPY2ekakbAw3WIr0YABeo6bB2erEoaSckOYxdZWd/OdOlX/PX06dO4M0dHGxpVLZagBq+mhqiylVIp1qVmyZAnjxo1j2bJlFCtWLM3tRo4cSWRkZNJy/vz5jIQpROZ5cMj4v/+GWbNg8mQ9Sczo0Sm7qYhsJ+WGyJDBg2HJEt1GbPVq3YD94T7xIsuZlYwUKVIEW1vbFLUgly9fTlFb8rBly5bRp08fli9fTsuWLR+5raOjIy4uLskWISyGh4duvVWzpn6KmjhRT/Lw1ls6URGGkHJDZFjXrnra7JIldTeRgweNjijXMSsZcXBwwNvbm6CgoGTrg4KCaNiwYZr7LVmyhJ49e7J48WLatm2bsUiFsBQmkx46/s8/9ZNUvXoQE6NrSypU0EPLCyGsS8OG+p6eOVMPoCGyldmvaYYOHcrcuXMJCAggNDSUIUOGEBYWRv//+viMHDmSHj16JG2/ZMkSevTowZQpU6hfvz4RERFEREQQGRmZeWchhBFsbKBjRz0Z19atesap/PmTT7p37Zoe3lAIYfmKFYM337z/d0SEHmvo4RnmRKYzOxnx9/dn2rRpTJgwAS8vL4KDgwkMDKTMf3MRh4eHJxtzZM6cOcTFxfH2229TokSJpGXQoEGZdxZCGMlkgqZN9ax1p07dn65cKT2Vbr16ugbFyscpESLX6d9f37u1a8PGjUZHk6PJcPBCZJVTp6BGDbh7V/9dsSK8+64eYt7KJuWzxnvQGmMWFub0aT3z74ED+u/u3XXvm0d0wBDJZelw8EKIdKhQQY+X/P77UKAAnDwJffvqGae+/lq3MxFCWK7y5fUQ8oMG6deyixfrLv4BAfL6NZNJMiJEVipWTM8WGhamx1IuWRIuXtTjlKxfb3R0QojHyZNHT+j0xx96IMTr16FPHz1FhMg0kowIkR3y59ezTJ0+rWtF/PygQ4f7n584IW1KhLBkPj56KtvPPtOTPL32mtER5SiSjAiRnRwd9XgkgYG62hfg1i3dALZ6dVi+XIakFsJS2dnBsGF6vqq8efW6+Hh49VV4aMgLYR5JRoQw2pEjcO8ehIaCv7+eo/vHH+WdtBCWytb2/r/nzYOFC3XPuU6dQEb+zRBJRoQwWr16cOYMjBsHLi5w6JB+hePtrRvMxcYaHaEQIi1duugGrra2uhuwp6duYxIXZ3RkVkWSESEsgasrjB2rk5JRoyBfPl0V/PLLup2JEMIyFSigk48DB6BRI/3adcgQPcfNli0GB2c9JBkRwpIUKgQff6y7BH/4oW61/+BswUuW6N44QgjLUq0aBAfDt99CwYL6YWLcOHndmk6SjAhhiQoX1uOTzJ17f925c7qhXNmy0KuXbmsihLAcNjZ6LKETJ+Cdd+CTT/QIzaAfIvbtMzY+CybJiBDWIipKT+YVGwvz5+veN35+sHmzPH0JYUmKFoWvvoIGDe6v++orqFNH38OLF98fmVkAkowIYT2qV9fVwL//roeotrHR82W0bKkbux47ZnSEQoi03L4N9vZ6Ys2XXwZ3d117sm+fPEwgyYgQ1qdePVixQg8vP2CAHu/gr7/06K6JpHATwrJ89ZUeiXn8eChVSo/kOmOGri1p1Mjo6AwnyYgQ1qp8eZg+XRdwq1Ylny34uedgxAhp7CqEJSleHMaM0b3mNm7U4wrlzavHFkoUH68HVtu8OVd1D5ZZe4XIaXbtuv+kZW+vX+m89ZZel9iYzkzWeA9aY8wiF7p9W3cHLlpU/x0crEdkBt2Q/YUX9GBqLVpY3WzfILP2CpF71a+vR3Bt3Fg3dl2yRP+7Rg348kv491+jIxRCJMqb934iAjoB6dsXihSBq1f1DMFt2+pJN195BQ4fNi7WLCTJiBA5jY0NPP+8fsLav18XbHnz6q7AgwfDwYP3t7X8ilEhcpeqVfVYJeHhetC0t9+GEiV0b7pFi3RNSqLwcL0+B5BkRIicrHZtXbD9849uX9KmDTz77P3PhwyBPXsMC08IkQY7O2jWTDdyvXABdu6EDz7QDV4TffCBrlVp3x6++w4uXTIu3ickbUaEyK2U0g3n9uwBB4dHbmqN96A1xiyEWZ55RicpD6pWTbcvadkS2rUzJq4HSJsRIcSjmUzw22+PTUSEEBZq+3bdhmTcOPDy0uuOHNFtw0aNSr7t6tV6Es74+OyOMl0ylIzMnDkTDw8PnJyc8Pb2Zvv27Y/cftu2bXh7e+Pk5ES5cuWYPXt2hoIVQmSyggWNjkAIkVEmk64JGTtWz4Vz+TIsXw79+umB1RLdvQtdu0LNmnoIgGef1e3HvvtOtyuzgNFg7czdYdmyZQwePJiZM2fSqFEj5syZg5+fH8eOHaN06dIptj9z5gxt2rTh9ddfZ+HChezcuZO33nqLokWL0qlTp0w5CSGEECLXK1oUOnfWy4OuXtU96vbuheho2LZNL4m6ddND1APcu6d78JQvD08/rQdoszM7VTCb2W1G6tWrR+3atZk1a1bSOk9PTzp06MCkSZNSbP/ee+/x008/ERoamrSuf//+HDx4kN27d6frmPLuVwhjWeM9aI0xC5Gl4uPh+HGdlBw8qF/bHDwIw4fDe+/pbU6cSD5TuL29Hrq+eHG9dOkC3bun+5DpvQ/NSnfu3bvH/v37GTFiRLL1vr6+7Nq1K9V9du/eja+vb7J1rVu3Zt68ecTGxmJvb29OCEIIIYTICFtb3XW4atX765RKPtJrQoJu+PrXX/D337qm5Nw5vYDuoZcFzEpGrly5Qnx8PG5ubsnWu7m5ERERkeo+ERERqW4fFxfHlStXKFGiRIp9YmJiiImJSfo7Kof0oxZCZB0pN4TIAJNJ134k8vSEn3/W/46P18MC/POP7jYcEZG8a3EmytCLINNDQ0orpVKse9z2qa1PNGnSJMaPH5+R0IQQuZSUG0JkMltbKF1aL1nMrN40RYoUwdbWNkUtyOXLl1PUfiQqXrx4qtvb2dlRuHDhVPcZOXIkkZGRScv58+fNCVMIkQtJuSGE9TIrGXFwcMDb25ugoKBk64OCgmjYsGGq+zRo0CDF9r/88gs+Pj5pthdxdHTExcUl2SKEEI8i5YYQ1svscUaGDh3K3LlzCQgIIDQ0lCFDhhAWFkb//v0B/XTSo0ePpO379+/PuXPnGDp0KKGhoQQEBDBv3jyGDRuWeWchhBBCCKtldpsRf39/rl69yoQJEwgPD6datWoEBgZSpkwZAMLDwwkLC0va3sPDg8DAQIYMGcLXX3+Nu7s7X331lYwxIoQQQgjASuamiYyMpECBApw/f16qXoUwQFRUFKVKleLGjRu4uroaHU66SLkhhPHSW3Zk/bBqmSA6OhqAUqVKGRyJELlbdHS01SQjUm4IYTkeV3ZYRc1IQkICFy9eJH/+/I/sQpyYgeXkJyE5x5zB2s5RKUV0dDTu7u7Y2FjH/JrpLTfA+n6PjJBztH7WeH7pLTusombExsaGp556Kt3b54aW9HKOOYM1naO11IgkMrfcAOv6PTJKztH6Wdv5pafssI5HHCGEEELkWJKMCCGEEMJQOSoZcXR0ZOzYsTg6OhodSpaRc8wZcsM5WpPc8HvIOVq/nHx+VtGAVQghhBA5V46qGRFCCCGE9ZFkRAghhBCGkmRECCGEEIaSZEQIIYQQhspRycjMmTPx8PDAyckJb29vtm/fbnRI6RIcHEz79u1xd3fHZDKxdu3aZJ8rpRg3bhzu7u7kyZOHZ599lqNHjybbJiYmhnfeeYciRYqQL18+nn/+eS5cuJCNZ/FokyZNok6dOuTPn59ixYrRoUMHTpw4kWwbaz/PWbNmUaNGjaQBiRo0aMCGDRuSPrf288uprLXcgJxfdki5Yf3nl24qh1i6dKmyt7dX3377rTp27JgaNGiQypcvnzp37pzRoT1WYGCgGj16tFq1apUC1Jo1a5J9PnnyZJU/f361atUqdfjwYeXv769KlCihoqKikrbp37+/KlmypAoKClJ//vmnatasmapZs6aKi4vL5rNJXevWrdV3332njhw5og4cOKDatm2rSpcurW7evJm0jbWf508//aTWr1+vTpw4oU6cOKFGjRql7O3t1ZEjR5RS1n9+OZE1lxtK5fyyQ8oN6z+/9MoxyUjdunVV//79k62rXLmyGjFihEERZczDBUpCQoIqXry4mjx5ctK6u3fvKldXVzV79myllFI3btxQ9vb2aunSpUnb/PPPP8rGxkZt3Lgx22I3x+XLlxWgtm3bppTKuedZsGBBNXfu3Bx7ftYup5QbSuWOskPKjZxxfqnJEa9p7t27x/79+/H19U223tfXl127dhkUVeY4c+YMERERyc7N0dGRpk2bJp3b/v37iY2NTbaNu7s71apVs9jzj4yMBKBQoUJAzjvP+Ph4li5dyq1bt2jQoEGOO7+cICeXG5Dz7imQcgOs+/weJUckI1euXCE+Ph43N7dk693c3IiIiDAoqsyRGP+jzi0iIgIHBwcKFiyY5jaWRCnF0KFDeeaZZ6hWrRqQc87z8OHDODs74+joSP/+/VmzZg1VqlTJMeeXk+TkcgNyzj2VSMqN+6zt/NLDKmbtTa+HpwlXSj126nBrkZFzs9TzHzBgAIcOHWLHjh0pPrP286xUqRIHDhzgxo0brFq1itdee41t27YlfW7t55cT5eRyA3LOf3NSbtxnbeeXHjmiZqRIkSLY2tqmyAIvX76cIqO0NsWLFwd45LkVL16ce/fucf369TS3sRTvvPMOP/30E7/99luy6d1zynk6ODjw9NNP4+Pjw6RJk6hZsyZffvlljjm/nCQnlxuQc+4pkHLD2s8vPXJEMuLg4IC3tzdBQUHJ1gcFBdGwYUODosocHh4eFC9ePNm53bt3j23btiWdm7e3N/b29sm2CQ8P58iRIxZz/kopBgwYwOrVq9myZQseHh7JPs8p5/kwpRQxMTE59vysWU4uNyBn3FNSbuTM80tV9raXzTqJXfTmzZunjh07pgYPHqzy5cunzp49a3RojxUdHa1CQkJUSEiIAtQXX3yhQkJCkroXTp48Wbm6uqrVq1erw4cPq27duqXateupp55Sv/76q/rzzz9V8+bNLapr15tvvqlcXV3V1q1bVXh4eNJy+/btpG2s/TxHjhypgoOD1ZkzZ9ShQ4fUqFGjlI2Njfrll1+UUtZ/fjmRNZcbSuX8skPKDes/v/TKMcmIUkp9/fXXqkyZMsrBwUHVrl07qfuXpfvtt98UkGJ57bXXlFK6+9rYsWNV8eLFlaOjo2rSpIk6fPhwsu+4c+eOGjBggCpUqJDKkyePateunQoLCzPgbFKX2vkB6rvvvkvaxtrPs3fv3kn//RUtWlS1aNEiqUBRyvrPL6ey1nJDqZxfdki5Yf3nl14mpZTKvnoYIYQQQojkckSbESGEEEJYL0lGhBBCCGEoSUaEEEIIYShJRoQQQghhKElGhBBCCGEoSUaEEEIIYShJRoQQQghhKElGhBBCCGEoSUaEEEIIYShJRoQQQghhKElGhBBCCGEoSUaEEEIIYaj/AyC05LlAuD02AAAAAElFTkSuQmCC", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "HW.scen_size = 1000\n", "\n", "fig, axs = plt.subplots(2, 2, sharex=True, sharey=True)\n", "fig.suptitle(r\"$a=$\" + str(HW.a))\n", "for sigma, (h, v) in zip([0.05, 0.075, 0.1, 0.125], [(0, 0), (0, 1), (1, 0), (1, 1)]):\n", " HW.sigma = sigma\n", " axs[h, v].set_title(r\"$\\sigma=$\" + str(sigma) + r\", $\\sigma/a=$\" + \"%.2f\" % (sigma/HW.a))\n", " axs[h, v].plot(range(HW.step_size+1), [HW.mkt_zcb(i) for i in range(HW.step_size+1)], \"b-\")\n", " axs[h, v].plot(range(HW.step_size+1), HW.mean_disc_factor(), \"r--\")" ] }, { "cell_type": "code", "execution_count": null, "id": "71a47989", "metadata": { "id": "71a47989", "outputId": "a5a03bfe-0d56-4c2b-b781-76d97083a31d" }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "HW.scen_size = 1000\n", "HW.sigma = 0.1\n", "\n", "fig, axs = plt.subplots(2, 2, sharex=True, sharey=True)\n", "fig.suptitle(r\"$\\sigma=$\" + str(HW.sigma))\n", "for a, (h, v) in zip([0.05, 0.1, 0.15, 0.2], [(0, 0), (0, 1), (1, 0), (1, 1)]):\n", " HW.a = a\n", " axs[h, v].set_title(r\"$a=$\" + str(a) + r\", $\\sigma/a=$\" + \"%.2f\" % (HW.sigma/HW.a))\n", " axs[h, v].plot(range(HW.step_size+1), [HW.mkt_zcb(i) for i in range(HW.step_size+1)], \"b-\")\n", " axs[h, v].plot(range(HW.step_size+1), HW.mean_disc_factor(), \"r--\")" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.10.13" }, "colab": { "provenance": [] } }, "nbformat": 4, "nbformat_minor": 5 }