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Lecture Financial modeling - Topic 13A: Black-scholes-merton option pricing model, implied vols, and volatility estimation

After completing this unit, you should be able to: Value options using historical vol, moving average vol (MAV), exponentially weighted moving average (EWMA), and generalized autoregressive conditional heteroskedasticity (GARCH); calculate option model implied volatility surfaces -- time skew (a.k.a. terms structure of volatility), and strike skew (Smiles and Smirks); understand what volatility surfaces reveal about option prices, volatility, and the models. | Financial Modeling Topic #13a: Black-Scholes-Merton Option Pricing Model, Implied Vols, and Volatility Estimation L. Gattis 1 Learning Objectives Value options using historical vol, moving average vol (MAV), exponentially weighted moving average (EWMA), and generalized autoregressive conditional heteroskedasticity (GARCH). Calculate option model implied volatility surfaces -- time skew (a.k.a. terms structure of volatility), and strike skew (Smiles and Smirks) Understand what volatility surfaces reveal about option prices, volatility, and the models. 2 Black-Scholes-Merton Functions Function BSCall(s, k, v, r, t, d) d_1 = (Application.Ln(s / k) + (r - d + (v ^ 2) / 2) * t) / (v * t ^ 0.5) nd1 = Application.NormSDist(d_1) d_2 = d_1 - v * t ^ 0.5 nd2 = Application.NormSDist(d_2) BSCall = s * Exp(-d * t) * nd1 - k * Exp(-r * t) * nd2 End Function Function BSPut(s, k, v, r, t, d) d_1 = (Application.Ln(s / k) + (r - d + (v ^ 2) / 2) * t) / (v * t ^ 0.5) minus_nd1 = Application.NormSDist(-d_1) d_2 = d_1 - v * t ^ 0.5 minus_nd2 = Application.NormSDist(-d_2) BSPut = -s * Exp(-d * t) * minus_nd1 + k * Exp(-r * t) * minus_nd2 End Function 3 Google Options as of 2/28/2012 GOOG Spot = $614.27 Bloomberg: GOOG Equity OMON 5 Calculating Implied Volatility The March, $615 Strike, call and put are selling for $10.05 and $11.05 (Average of Bid & Ask) respectively? Implied volatility is the standard deviation input that equates the BSM model option price to the market price. Start with volatility guess (say 10%), then run solver to equate market model prices 6 Calculating Implied Volatility The March, $615 Strike, call and put are selling for $10.05 and $11.05 (Average of Bid & Ask) respectively? Implied volatility is the standard deviation input that equates the BSM model option price to the market price. Start with volatility guess (say 10%), then run solver to equate market model prices 7 Implied Volatility VBA Functions Function putvol(s, k, r, t, d, mkt) hivol = 1 lovol = 0 Do . | Financial Modeling Topic #13a: Black-Scholes-Merton Option Pricing Model, Implied Vols, and Volatility Estimation L. Gattis 1 Learning Objectives Value options using historical vol, moving average vol (MAV), exponentially weighted moving average (EWMA), and generalized autoregressive conditional heteroskedasticity (GARCH). Calculate option model implied volatility surfaces -- time skew (a.k.a. terms structure of volatility), and strike skew (Smiles and Smirks) Understand what volatility surfaces reveal about option prices, volatility, and the models. 2 Black-Scholes-Merton Functions Function BSCall(s, k, v, r, t, d) d_1 = (Application.Ln(s / k) + (r - d + (v ^ 2) / 2) * t) / (v * t ^ 0.5) nd1 = Application.NormSDist(d_1) d_2 = d_1 - v * t ^ 0.5 nd2 = Application.NormSDist(d_2) BSCall = s * Exp(-d * t) * nd1 - k * Exp(-r * t) * nd2 End Function Function BSPut(s, k, v, r, t, d) d_1 = (Application.Ln(s / k) + (r - d + (v ^ 2) / 2) * t) / (v * t ^ 0.5) minus_nd1 = .