README.md

metadata

title: Hull-White Simulator
emoji: 📊
colorFrom: blue
colorTo: indigo
sdk: gradio
sdk_version: 5.31.0
app_file: app.py
pinned: false
license: mit
tags:
  - actuarial
  - finance
  - stochastic-models
  - monte-carlo
  - interest-rates
  - quantitative-finance
  - gradio
  - dashboard
  - hull-white
  - risk-management
short_description: Simulate Hull-White interest rate paths and dynamics.

📊 Hull-White Interest Rate Model Dashboard

An interactive web dashboard for exploring the Hull-White short rate model, designed specifically for actuaries and financial professionals.

🎯 Overview

The Hull-White model is a widely-used short rate model in quantitative finance, particularly valuable for:

• Interest rate derivatives pricing
• Risk management and ALM
• Solvency II capital calculations
• Insurance liability valuation

This dashboard provides an intuitive interface to explore the model's behavior through Monte Carlo simulations.

📈 Model Description

The Hull-White model follows the stochastic differential equation:

$$dr(t)=(\theta (t)-ar(t))dt+\sigma dWdr(t)\; =\; (\theta (t)\; -\; ar(t))dt\; +\; \sigma dW$$

Where:

• r(t) = instantaneous short rate at time t
• a = mean reversion speed parameter
• σ = volatility parameter
• θ(t) = time-dependent drift function
• dW = Wiener process increment

🚀 Features

Interactive Visualizations

• 📊 Short Rate Paths: Visualize multiple simulated interest rate trajectories
• 📉 Mean Convergence: Compare Monte Carlo means against theoretical expectations
• 📈 Variance Analysis: Examine variance convergence properties
• 💰 Discount Factors: Analyze zero-coupon bond pricing convergence
• 🔍 Parameter Sensitivity: Study the critical σ/a ratio effects
• 📋 Statistics Table: Summary statistics at key time points

Adjustable Parameters

Parameter	Range	Description
Scenarios	100 - 10,000	Number of Monte Carlo paths
Time Horizon	5 - 50 years	Simulation time length
Time Steps	100 - 500	Discretization granularity
Mean Reversion (a)	0.01 - 0.5	Speed of mean reversion
Volatility (σ)	0.01 - 0.3	Interest rate volatility
Initial Rate (r₀)	0.01 - 0.15	Starting interest rate

🎛️ How to Use

1. Adjust Model Parameters: Use the sliders in the left panel to modify Hull-White parameters
2. Explore Visualizations: Click through the tabs to see different aspects of the model
3. Analyze Convergence: Pay special attention to the σ/a ratio - values > 1 show poor convergence
4. Compare Theory vs Practice: Observe how simulated results converge to theoretical expectations
5. Generate Statistics: Review the summary table for quantitative analysis

📊 Key Insights

Convergence Properties

• σ/a < 1: Good Monte Carlo convergence
• σ/a ≈ 1: Moderate convergence issues
• σ/a > 1: Poor convergence, especially for discount factors

Practical Considerations

• More scenarios improve convergence but increase computation time
• Higher volatility requires more scenarios for stable results
• Longer time horizons show more pronounced convergence issues

🔧 Technical Implementation

Model Features

• Gaussian Process: Exploits Hull-White's analytical properties
• Conditional Moments: Uses exact conditional mean and variance formulas
• Vector Operations: Efficient numpy-based simulations
• Reproducible Results: Fixed random seed for consistency

Performance Optimized

• Real-time parameter updates
• Efficient matrix operations
• Responsive visualization updates
• Memory-efficient data handling

📚 Educational Value

Perfect for:

• University Finance Courses: Teaching stochastic interest rate models
• Actuarial Training: Understanding ALM and risk management
• Professional Development: Exploring quantitative finance concepts
• Model Validation: Testing parameter sensitivity and convergence

🎓 Theoretical Background

The implementation follows established literature:

• Brigo & Mercurio: Interest Rate Models - Theory and Practice
• Glasserman: Monte Carlo Methods in Financial Engineering
• Hull: Options, Futures, and Other Derivatives

Key Mathematical Properties

• Mean: E[r(t)|ℱₛ] = r(s)e^(-a(t-s)) + α(t) - α(s)e^(-a(t-s))
• Variance: Var[r(t)|ℱₛ] = (σ²/2a)(1 - e^(-2a(t-s)))
• Alpha Function: α(t) = f^M(0,t) + (σ²/2a²)(1-e^(-at))²

🛠️ Installation & Deployment

Local Development

# Clone the repository
git clone https://github.com/alidenewade/hull-white-dashboard.git
cd hull-white-dashboard

# Install dependencies
pip install -r requirements.txt

# Run the application
python app.py