Advanced Option Price Estimator

// This Pine Script™ code is subject to the terms of the Mozilla Public License 2.0 at https://mozilla.org/MPL/2.0/
// © jawauntb

//@version=5
indicator("Advanced Option Price Estimator", overlay=true)

// Inputs
riskFreeRate = request.security("RFR:TICKER", "D", close) // Assuming a ticker for risk-free rate
daysToExpiration = input.int(30, "Days to Expiration", step=1)
volatilityPeriod = input.int(20, "Volatility Period", step=1)

// Get the current price of the ticker
tickerPrice = close

// Function to fetch current market price of an option (placeholder)
getMarketOptionPrice(callPut, strike, expiration) => na // Implement actual fetching logic

// Function to calculate the PDF of the standard normal distribution
norm_pdf(x) =>
    (1 / sqrt(2 * pi)) * exp(-x * x / 2)

// Vega calculation using Black-Scholes components
calculateVega(s, k, t, r, v) =>
    d1 = (log(s / k) + (r + v * v / 2) * t) / (v * sqrt(t))
    s * sqrt(t) * norm_pdf(d1)

// Example usage in the Newton-Raphson method for implied volatility calculation
calculateImpliedVolatility(s, k, t, r, marketPrice, isCall) =>
    sigma = 0.20 // Initial guess for implied volatility
    for i = 0 to 100
        price = bsm(s, k, t, r, sigma, isCall)
        vega = calculateVega(s, k, t, r, sigma) // Vega calculation
        diff = marketPrice - price
        if abs(diff) < 0.0001
            break
        sigma := sigma + diff / vega
    sigma


// Function to calculate the BSM option price
bsm(s, k, t, r, v, isCall) =>
    d1 = (log(s / k) + (r + v * v / 2) * t) / (v * sqrt(t))
    d2 = d1 - v * sqrt(t)
    callPrice = s * norm_cdf(d1) - k * exp(-r * t) * norm_cdf(d2)
    putPrice = k * exp(-r * t) * norm_cdf(-d2) - s * norm_cdf(-d1)
    isCall ? callPrice : putPrice

// Calculate the time to expiration in years
timeToExpiration = daysToExpiration / 365

// Calculate the strike prices at 1.5% increments
increment = tickerPrice * 0.015
strikePrice = tickerPrice - (tickerPrice % increment)
maxStrikes = 20

// Graphical representation using plot shapes instead of labels
for i = 0 to maxStrikes
    callStrike = strikePrice + i * increment
    putStrike = strikePrice - i * increment

    marketPriceCall = getMarketOptionPrice("call", callStrike, timeToExpiration)
    marketPricePut = getMarketOptionPrice("put", putStrike, timeToExpiration)

    impliedVolatilityCall = calculateImpliedVolatility(tickerPrice, callStrike, timeToExpiration, riskFreeRate, marketPriceCall, true)
    impliedVolatilityPut = calculateImpliedVolatility(tickerPrice, putStrike, timeToExpiration, riskFreeRate, marketPricePut, false)

    callPrice = bsm(tickerPrice, callStrike, timeToExpiration, riskFreeRate, impliedVolatilityCall, true)
    putPrice = bsm(tickerPrice, putStrike, timeToExpiration, riskFreeRate, impliedVolatilityPut, false)

    plotshape(series=callPrice, location=location.absolute, color=color.green, style=shape.triangledown, title="Call Price")
    plotshape(series=putPrice, location=location.absolute, color=color.red, style=shape.triangleup, title="Put Price")