![]() ![]() ![]() maxIter is the maximum allowable number of iterations.Vol_1 = vol_1 - (OptionValue - Value_1) / dx If Abs(dx) < epsilon Or i = maxIter Then Exit Do ![]() Value_2 = EuropeanOption(CallOrPut, S, K, vol_2, r, T, q) Value_1 = EuropeanOption(CallOrPut, S, K, vol_1, r, T, q) Function ImpliedVolatility(CallOrPut, S, K, r, T, q, OptionValue, guess)ĭim epsilon As Double, dVol As Double, vol_1 As Doubleĭim i As Integer, maxIter As Integer, Value_1 As Double, vol_2 As Double This VBA function calculates the implied volatility of a European option with Newton-Raphson iteration. Nnd2 = Application.NormSDist(-d2) If CallOrPut = "Call" ThenĮuropeanOption = S * Exp(-q * T) * nd1 - K * Exp(-r * T) * nd2ĮuropeanOption = -S * Exp(-q * T) * nnd1 + K * Exp(-r * T) * nnd2 Function EuropeanOption(CallOrPut, S, K, v, r, T, q)ĭim d1 As Double, d2 As Double, nd1 As Double, nd2 As Doubleĭim nnd1 As Double, nnd2 As Double d1 = (Log(S / K) + (r - q + 0.5 * v ^ 2) * T) / (v * Sqr(T))ĭ2 = (Log(S / K) + (r - q - 0.5 * v ^ 2) * T) / (v * Sqr(T)) This VBA function calculates the price of a European option with the Black-Scholes equation. Implied Volatility with Newton-Raphson Iteration V BS is the option price given by the Black-Scholes equation.V mkt is the market price of the option.The approach gives the following equation to calculate the implied volatility of an option. The theory behind the Newton-Raphson method for finding the root of an equation is well documented. Several technique are commonly used one method uses Excel’s Goal Seek functionality, while other approaches use bisection or Newton-Raphson iteration. Calculating implied volatility needs iterative solution methods. Implied volatility is the volatility estimated from the option price, asset price, strike price risk-free-rate, time to maturity and dividend yield. This article offers VBA code and an Excel spreadsheet to calculate the implied volatility of an option. This parameter is often compared to the historical volatility of the underlying asset to determine if the price of an option represents good value. ![]()
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