Option pricing under non-normal distribution in mixed of Gram-Charlier model and fractional models (A case study of Iran Stock Exchange)

In order to reduce the risk of financial markets, various tools have emerged, and option contracts are the most common tools in this regard. The Black-Scholes model is used to price a wide range of options contracts. The basic assumption in this model is to follow the normal distribution of returns. But the reality of the market indicates the skewness and kurtosis of the data, which reduces the accuracy of calculating the option price. The Gram-Charlie model has more flexibility than Black-Scholes model with abnormal skewness and kurtosis. The main purpose of this research is to determine the European call option price using non-normal data. In this regard, we present new models, fractional Gram-Charlier model and mixed fractional Gram-Charlier model, for option pricing. For this purpose, the data of Shasta and Khodro symbols have been selected from Iran Stock Exchange that Khodro in the period ۲۰۲۰-۰۷-۲۷ to ۲۰۲۳-۱۱-۱ and Shasta in the period ۲۰۲۲-۷-۲۵ to ۲۰۲۳-۱۱-۱ have been used. The results of this research show that Shasta has more abnormal skewness and kurtosis than Khodro. The option price calculated with the Gram-Charlier and extended models of Gram-Charlier are shown a smaller error compared to other models in the Shasta. Also, the results show that under abnormal skewness and kurtosis, our new models have more flexibility than the Black-Scholes model and fractional models.

کلیدواژه ها:

Black-Scholes model ، fractional Brownian motion model ، Gram-Charlier expansion ، Option pricing ، Stochastic Volatility