Option Pricing with the Edgeworth Expansion
Posted by Chun-Yuan ChiuThe Black-Scholes model assumes that the log return of the underlying asset follows a normal distribution, which is not consistent with empirical evidence. Option pricing with the Edgeworth expansion gives us more degrees of freedom then just the first 2 moments. Given the mean, variance, skewness and kurtosis of the annual log return of the underlying asset under the risk neutral probability measure, this calculator outputs the corrected call price. It is user's responsibility to set up the parameters such that the model is arbitrage-free. As an example, the default parameters are from the Black-Scholes model with risk free rate r = 0.1 and volatility s = 0.3, where the annual log return is assumed to be normal with mean (r-s*s/2) = 0.055 and standard deviation s, and it is well known that a normal distribution has skewness 0 and kurtosis 3.
• Jan 4, 2014 •