Fade-in Options [Loxx]
// This source code is subject to the terms of the Mozilla Public License 2.0 at https://mozilla.org/MPL/2.0/
// © loxx

//@version=5
indicator("Fade-in Options [Loxx]", 
     shorttitle ="FIO [Loxx]",
     overlay = true, 
     max_lines_count = 500)

if not timeframe.isdaily
    runtime.error("Error: Invald timeframe. Indicator only works on daily timeframe.") 

import loxx/loxxexpandedsourcetypes/4
import loxx/cnd/1
import loxx/cbnd/1

color darkGreenColor = #1B7E02 
string callString = "Call"
string putString = "Put"

string rogersatch = "Roger-Satchell"
string parkinson = "Parkinson"
string c2c = "Close-to-Close"
string gkvol = "Garman-Klass"
string gkzhvol = "Garman-Klass-Yang-Zhang"
string ewmavolstr = "Exponential Weighted Moving Average"

string timtoolbar= "Time Now = Current time in UNIX format. It is the number of milliseconds that have elapsed since 00:00:00 UTC, 1 January 1970."
string timtoolnow = "Time Bar = The time function returns the UNIX time of the current bar for the specified timeframe and session or NaN if the time point is out of session."
string timetooltrade = "Trading Day = The beginning time of the trading day the current bar belongs to, in UNIX format (the number of milliseconds that have elapsed since 00:00:00 UTC, 1 January 1970)."

ewmavol(float src, int per) => 
    float lambda = (per - 1) / (per + 1)
    float temp = na
    temp := lambda * nz(temp[1], math.pow(src, 2)) + (1.0 - lambda) * math.pow(src, 2)
    out = math.sqrt(temp)
    out
    
rogerssatchel(int per) =>
    float sum = math.sum(math.log(high/ close) * math.log(high / open)
         + math.log(low / close) * math.log(low / open), per) / per
    float out = math.sqrt(sum) 
    out

closetoclose(float src, int per) => 
    float avg = ta.sma(src, per)
    array<float> sarr = array.new<float>(per, 0)
    for i = 0 to per - 1 
        array.set(sarr, i,  math.pow(nz(src[i]) - avg, 2))
    float out = math.sqrt(array.sum(sarr) / (per - 1))
    out 

parkinsonvol(int per)=>
    float volConst = 1.0 / (4.0 * per * math.log(2))
    float sum = volConst * math.sum(math.pow(math.log(high / low), 2), per)
    float out = math.sqrt(sum) 
    out

garmanKlass(int per)=>
    float hllog = math.log(high / low)
    float oplog = math.log(close / open)
    float garmult = (2 * math.log(2) - 1)
    float parkinsonsum = 1 / (2 * per) * math.sum(math.pow(hllog, 2), per)
    float garmansum = garmult / per * math.sum(math.pow(oplog, 2), per)
    float sum = parkinsonsum - garmansum
    float devpercent = math.sqrt(sum)  
    devpercent

gkyzvol(int per)=>
    float gzkylog = math.log(open / nz(close[1]))
    float pklog = math.log(high / low)
    float gklog = math.log(close / open)
    float garmult = (2 * math.log(2) - 1)
    float gkyzsum = 1 / per * math.sum(math.pow(gzkylog, 2), per)
    float parkinsonsum = 1 / (2 * per) * math.sum(math.pow(pklog, 2), per)
    float garmansum = garmult / per * math.sum(math.pow(gklog, 2), per)
    float sum = gkyzsum + parkinsonsum - garmansum
    float devpercent = math.sqrt(sum)  
    devpercent

ND(float x)=> 
    float out = math.exp(-x * x * 0.5) / math.sqrt(2 * math.pi)
    out 

// via Espen Gaarder Haug; The Complete Guide to Option Pricing Formulas
convertingToCCRate(float r, float Compoundings)=>
    float ConvertingToCCRate = 0
    if Compoundings == 0 
        ConvertingToCCRate := r
    else
        ConvertingToCCRate := Compoundings * math.log(1 + r / Compoundings)
    ConvertingToCCRate

FadeInOption(string CallPutFlag, float S, float X, float L, float H, float T, float r, float b, float v, float n)=>
    float dt = T / n
    float d1 = (math.log(S / X) + (b + v * v / 2) * T) / (v * math.sqrt(T))
    float d2 = d1 - v * math.sqrt(T)
    float d3 = 0
    float d4 = 0
    float d5 = 0
    float d6 = 0
    float sum = 0
    for i = 1 to n
        t1 = i * dt
        float rho = math.sqrt(t1) / math.sqrt(T)
        d3 := (math.log(S / L) + (b + v * v / 2) * t1) / (v * math.sqrt(t1))
        d4 := d3 - v * math.sqrt(t1)
        d5 := (math.log(S / H) + (b + v * v / 2) * t1) / (v * math.sqrt(t1))
        d6 := d5 - v * math.sqrt(t1)
        if CallPutFlag == callString
            sum := sum + S * math.exp((b - r) * T) * (cbnd.CBND3(-d5, d1, -rho) - cbnd.CBND3(-d3, d1, -rho)) 
                 - X * math.exp(-r * T) * (cbnd.CBND3(-d6, d2, -rho) - cbnd.CBND3(-d4, d2, -rho))
        else 
            sum := sum + X * math.exp(-r * T) * (cbnd.CBND3(-d6, -d2, rho) - cbnd.CBND3(-d4, -d2, rho)) 
                 - S * math.exp((b - r) * T) * (cbnd.CBND3(-d5, -d1, rho) - cbnd.CBND3(-d3, -d1, rho))
    FadeInOption = 1 / n * sum
    FadeInOption
 
smthtype = input.string("Kaufman", "Heikin-Ashi Better Caculation Type", options = ["AMA", "T3", "Kaufman"], group = "Asset Price Settings")
srcin = input.string("Close", "Asset Price", group= "Asset Price Settings", 
     options = 
     ["Close", "Open", "High", "Low", "Median", "Typical", "Weighted", "Average", "Average Median Body", "Trend Biased", "Trend Biased (Extreme)", 
     "HA Close", "HA Open", "HA High", "HA Low", "HA Median", "HA Typical", "HA Weighted", "HA Average", "HA Average Median Body", "HA Trend Biased", "HA Trend Biased (Extreme)",
     "HAB Close", "HAB Open", "HAB High", "HAB Low", "HAB Median", "HAB Typical", "HAB Weighted", "HAB Average", "HAB Average Median Body", "HAB Trend Biased", "HAB Trend Biased (Extreme)"])

string OpType = input.string(callString, "Option type", options = [callString, putString], group = "Basic Settings")   

float K = input.float(100, "Strike Price", group = "Basic Settings")  
float L = input.float(80., "Lower Barrier", group = "Basic Settings")  
float H = input.float(130., "Upper Barrier", group = "Basic Settings")   
float n = input.float(183., "Fixings", group = "Basic Settings")

float r = input.float(10., "% Risk-free Rate", group = "Rates Settings") / 100
float b = input.float(5., "% Cost of Carry", group = "Rates Settings") / 100
float v = input.float(20., "% Volatility", group = "Rates Settings") / 100

int histvolper = input.int(22, "Historical Volatility Period", group = "Historical Volatility Settings", tooltip =  "Not used in calculation. This is here for comparison to implied volatility")
string hvoltype = input.string(c2c, "Historical Volatility Type", options = [c2c, gkvol, gkzhvol, rogersatch, ewmavolstr, parkinson], group = "Historical Volatility Settings")

string timein = input.string("Time Now", title = "Time Now Type", options = ["Time Now", "Time Bar", "Trading Day"], group = "Time Intrevals", tooltip = timtoolnow + "; " + timtoolbar + "; " + timetooltrade)
int daysinyear = input.int(252, title = "Days in Year", minval = 1, maxval = 365, group = "Time Intrevals", tooltip = "Typically 252 or 365")
float hoursinday = input.float(24, title = "Hours Per Day", minval = 1, maxval = 24, group = "Time Intrevals", tooltip = "Typically 6.5, 8, or 24")

int thruMonth = input.int(3, title = "Expiry Month", minval = 1, maxval = 12, group = "Time to Maturity Date/Time")
int thruDay = input.int(31, title = "Expiry Day", minval = 1, maxval = 31, group = "Expiry Date/Time")
int thruYear = input.int(2023, title = "Expiry Year", minval = 1970, group = "Expiry Date/Time")
int mins = input.int(0, title = "Expiry Minute", minval = 0, maxval = 60, group = "Expiry Date/Time")
int hours = input.int(9, title = "Expiry Hour", minval = 0, maxval = 24, group = "Expiry Date/Time")
int secs = input.int(0, title = "Expiry Second", minval = 0, maxval = 60, group = "Expiry Date/Time")

string txtsize = input.string("Auto", title = "Text Size", options = ["Small", "Normal", "Tiny", "Auto", "Large"], group = "UI Options")

string outsize = switch txtsize
    "Small"=> size.small
    "Normal"=> size.normal
    "Tiny"=> size.tiny
    "Auto"=> size.auto
    "Large"=> size.large

// seconds per year given inputs above
int spyr = math.round(daysinyear * hoursinday * 60 * 60)

// precision calculation miliseconds in time intreval from time equals now
start = timein == "Time Now" ? timenow : timein == "Time Bar" ? time : time_tradingday
finish = timestamp(thruYear, thruMonth, thruDay, hours, mins, secs) 
temp = (finish - start) 
float T = (finish - start) / spyr / 1000

kfl=input.float(0.666, title="* Kaufman's Adaptive MA (KAMA) Only - Fast End", group = "Moving Average Inputs")
ksl=input.float(0.0645, title="* Kaufman's Adaptive MA (KAMA) Only - Slow End", group = "Moving Average Inputs")
amafl = input.int(2, title="* Adaptive Moving Average (AMA) Only - Fast", group = "Moving Average Inputs")
amasl = input.int(30, title="* Adaptive Moving Average (AMA) Only - Slow", group = "Moving Average Inputs")

haclose = request.security(ticker.heikinashi(syminfo.tickerid), timeframe.period, close)
haopen = request.security(ticker.heikinashi(syminfo.tickerid), timeframe.period, open)
hahigh = request.security(ticker.heikinashi(syminfo.tickerid), timeframe.period, high)
halow = request.security(ticker.heikinashi(syminfo.tickerid), timeframe.period, low)
hamedian = request.security(ticker.heikinashi(syminfo.tickerid), timeframe.period, hl2)
hatypical = request.security(ticker.heikinashi(syminfo.tickerid), timeframe.period, hlc3)
haweighted = request.security(ticker.heikinashi(syminfo.tickerid), timeframe.period, hlcc4)
haaverage = request.security(ticker.heikinashi(syminfo.tickerid), timeframe.period, ohlc4)

float S = switch srcin
	"Close" => loxxexpandedsourcetypes.rclose()
	"Open" => loxxexpandedsourcetypes.ropen()
	"High" => loxxexpandedsourcetypes.rhigh()
	"Low" => loxxexpandedsourcetypes.rlow()
	"Median" => loxxexpandedsourcetypes.rmedian()
	"Typical" => loxxexpandedsourcetypes.rtypical()
	"Weighted" => loxxexpandedsourcetypes.rweighted()
	"Average" => loxxexpandedsourcetypes.raverage()
    "Average Median Body" => loxxexpandedsourcetypes.ravemedbody()
	"Trend Biased" => loxxexpandedsourcetypes.rtrendb()
	"Trend Biased (Extreme)" => loxxexpandedsourcetypes.rtrendbext()
	"HA Close" => loxxexpandedsourcetypes.haclose(haclose)
	"HA Open" => loxxexpandedsourcetypes.haopen(haopen)
	"HA High" => loxxexpandedsourcetypes.hahigh(hahigh)
	"HA Low" => loxxexpandedsourcetypes.halow(halow)
	"HA Median" => loxxexpandedsourcetypes.hamedian(hamedian)
	"HA Typical" => loxxexpandedsourcetypes.hatypical(hatypical)
	"HA Weighted" => loxxexpandedsourcetypes.haweighted(haweighted)
	"HA Average" => loxxexpandedsourcetypes.haaverage(haaverage)
    "HA Average Median Body" => loxxexpandedsourcetypes.haavemedbody(haclose, haopen)
	"HA Trend Biased" => loxxexpandedsourcetypes.hatrendb(haclose, haopen, hahigh, halow)
	"HA Trend Biased (Extreme)" => loxxexpandedsourcetypes.hatrendb(haclose, haopen, hahigh, halow)
	"HAB Close" => loxxexpandedsourcetypes.habclose(smthtype, amafl, amasl, kfl, ksl)
	"HAB Open" => loxxexpandedsourcetypes.habopen(smthtype, amafl, amasl, kfl, ksl)
	"HAB High" => loxxexpandedsourcetypes.habhigh(smthtype, amafl, amasl, kfl, ksl)
	"HAB Low" => loxxexpandedsourcetypes.hablow(smthtype, amafl, amasl, kfl, ksl)
	"HAB Median" => loxxexpandedsourcetypes.habmedian(smthtype, amafl, amasl, kfl, ksl)
    "HAB Typical" => loxxexpandedsourcetypes.habtypical(smthtype, amafl, amasl, kfl, ksl)
	"HAB Weighted" => loxxexpandedsourcetypes.habweighted(smthtype, amafl, amasl, kfl, ksl)
	"HAB Average" => loxxexpandedsourcetypes.habaverage(smthtype, amafl, amasl, kfl, ksl)
    "HAB Average Median Body" => loxxexpandedsourcetypes.habavemedbody(smthtype, amafl, amasl, kfl, ksl)
	"HAB Trend Biased" => loxxexpandedsourcetypes.habtrendb(smthtype, amafl, amasl, kfl, ksl)
	"HAB Trend Biased (Extreme)" => loxxexpandedsourcetypes.habtrendbext(smthtype, amafl, amasl, kfl, ksl)
	=> haclose

float hvolout = switch hvoltype
    parkinson => parkinsonvol(histvolper)
    rogersatch => rogerssatchel(histvolper) 
    c2c => closetoclose(math.log(S / nz(S[1])), histvolper) 
    gkvol => garmanKlass(histvolper) 
    gkzhvol => gkyzvol(histvolper) 
    ewmavolstr => ewmavol(math.log(S / nz(S[1])), histvolper) 

if barstate.islast

    float amaproxprice = FadeInOption(OpType, S, K, L, H, T, r, b, v, n)

    var testTable = table.new(position = position.middle_right, columns = 2, rows = 17, bgcolor = color.gray, border_width = 1)

    table.cell(table_id = testTable, column = 0, row = 0,  text = "Fade-in Options", bgcolor=color.yellow, text_color = color.black, text_size = outsize, text_halign = text.align_left)
    table.cell(table_id = testTable, column = 0, row = 1,  text = "Asset Price: " + str.tostring(S, format.mintick) , bgcolor=darkGreenColor, text_color = color.white, text_size = outsize, text_halign = text.align_left)
    table.cell(table_id = testTable, column = 0, row = 2,  text = "Strike Price: " + str.tostring(K, format.mintick), bgcolor=darkGreenColor, text_color = color.white, text_size = outsize, text_halign = text.align_left)
    table.cell(table_id = testTable, column = 0, row = 3,  text = "Lower Bound: " + str.tostring(L, "##.##"), bgcolor=darkGreenColor, text_color = color.white, text_size = outsize, text_halign = text.align_left)
    table.cell(table_id = testTable, column = 0, row = 4,  text = "Upper Bound: " + str.tostring(H, "##.##"), bgcolor=darkGreenColor, text_color = color.white, text_size = outsize, text_halign = text.align_left)
    table.cell(table_id = testTable, column = 0, row = 5,  text = "Time Now: " + str.format("{0,date,MMMM dd, yyyy - HH:mm:ss}", timenow), bgcolor=darkGreenColor, text_color = color.white, text_size = outsize, text_halign = text.align_left)
    table.cell(table_id = testTable, column = 0, row = 6,  text = "Time to Maturity: " + str.format("{0,date,MMMM dd, yyyy - HH:mm:ss}", finish), bgcolor=darkGreenColor, text_color = color.white, text_size = outsize, text_halign = text.align_left)
    table.cell(table_id = testTable, column = 0, row = 7,  text = "% Risk-free Rate: " + str.tostring(r * 100, "##.##") + "%", bgcolor=darkGreenColor, text_color = color.white, text_size = outsize, text_halign = text.align_left)
    table.cell(table_id = testTable, column = 0, row = 8,  text = "% Cost of Carry: " + str.tostring(b * 100, "##.##") + "%", bgcolor=darkGreenColor, text_color = color.white, text_size = outsize, text_halign = text.align_left)
    table.cell(table_id = testTable, column = 0, row = 9,  text = "% Volatility (annual): " + str.tostring(v * 100, "##.##") + "%", bgcolor=darkGreenColor, text_color = color.white, text_size = outsize, text_halign = text.align_left)
    table.cell(table_id = testTable, column = 0, row = 10, text = "Fixings: " + str.tostring(n, "##.##"), bgcolor=darkGreenColor, text_color = color.white, text_size = outsize, text_halign = text.align_left)

    table.cell(table_id = testTable, column = 0, row = 11, text = "Calculated Values", bgcolor=color.yellow, text_color = color.black, text_size = outsize, text_halign = text.align_left)
    table.cell(table_id = testTable, column = 0, row = 12, text = "Hist. Volatility Type: " + hvoltype, bgcolor=darkGreenColor, text_color = color.white, text_size = outsize, text_halign = text.align_left)
    table.cell(table_id = testTable, column = 0, row = 13, text = "Hist. Daily Volatility: " + str.tostring(hvolout * 100, "##.##") + "%", bgcolor=darkGreenColor, text_color = color.white, text_size = outsize, text_halign = text.align_left)
    table.cell(table_id = testTable, column = 0, row = 14, text = "Hist. Annualized Volatility: " + str.tostring(hvolout * math.sqrt(daysinyear) * 100, "##.##") + "%", bgcolor=darkGreenColor, text_color = color.white, text_size = outsize, text_halign = text.align_left)

    table.cell(table_id = testTable, column = 0, row = 15, text = "Option Ouput", bgcolor=color.yellow, text_color = color.black, text_size = outsize, text_halign = text.align_left)
    table.cell(table_id = testTable, column = 0, row = 16, text = "Fade-in Option Value: " + str.tostring(amaproxprice, "##.#############"), bgcolor=darkGreenColor, text_color = color.white, text_size = outsize, text_halign = text.align_left)
