Option Pricing with the Edgeworth Expansion

Posted by Chun-Yuan Chiu

Input:
Initial underlying asset price
Strike price
Time to maturity Years
Risk free interest rate (annulized)
The mean of annual log return
Standard deviation
Skewness
Kurtosis
Output:
Call value

The 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.

Tagged: Vanilla Option, Moments Methods, Edgeworth Expansion

 •  Jan 4, 2014  • 

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