EUROPEAN PUT OPTION PRICING MODEL WITH GRAM-CHARLIER EXPANSION IN THIRD MOMENTS

Abstract

The Black-Scholes model is one of the most popular and widely applied option pricing models in both academic and practical contexts developed by Black and Scholes (1973). The practical assumption in the Black-Scholes model is stock return following the normal distribution with constant volatility. However, many stock returns are not normally distributed, so should consider the skewness and kurtosis of the stock return. This developmental model adapts the Gram-Charlier expansion to adapt skewness and kurtosis to the Black-Scholes formula. Approximation method used is an alternative approach with Hermite polynomial. The observed stocks are SPG, C, and AXP by taking stock price data from November 11, 2016  to November 11, 2017 with maturity date at January 18, 2019 and interest rate (r) of 1,25%. After comparing the average MSE of both models, found that the third moment Gram-Charlier expansion is better than the Black-Scholes model in modeling SPG, C, and TSLA stock prices