Option pricing model based on sentiment using the Gram-Charlier expansion

It is observed from the empirical results that stock returns exhibit fat tails. Various authors have proposed different option pricing models for the non-Gaussian nature of the underlying returns distribution. Apart from that financial specialists sentiment do have a significant impact on the derivative pricing. For this purpose, it is necessary to obtain option price incorporating both non-Gaussian nature of the stock returns and investors sentiment. Here, we use the Gram-Charlier expansion for the analysis of stock returns distribution. This distribution captures the leptokurtic nature of the stock returns. Hence, in this paper, we propose an option pricing model with stock sentiment whenever the logarithmic of the stock price follows the Gram-Charlier distribution. Our option price behaves differently for bullish and bearish stock sentiment. Call option shows direct relation with stock sentiment while put option varies inversely with respect to stock sentiment. However, both call and put option price are directly related to the time remaining for expiration. Keywords-Gram-Charlier distribution; Investors sentiment; Non-Gaussian return;  Option price.