Comparison of Option Pricing with Stochastic Volatility in Heston and Heston Nandi Model

The significance of the capital market in driving the economic growth and development of a country necessitates a thorough examination of this market from multiple perspectives. Participating in this market invariably involves a heightened level of risk, prompting the emergence of various tools aimed at mitigating these risks. One of the main factors affecting investment decisions is the accurate valuation of derivatives, including options. The Black-Scholes model is used to price a wide range of options contracts. The basic assumption in this fixed model is to consider volatility, which reduces the accuracy of calculating the option price. The main purpose of this research is to determine the price of a European call option with stochastic volatility.

The Heston-Nandi model is a closed pricing formula for European options that shares numerous assumptions with the Heston model. The main difference between the Heston-Nandy model and the Black-Scholes model is the use of the variance type when option pricing. The Heston-Nandy model considers the non-normal distribution of returns and random fluctuations more realistically. Since the Heston model is one of the effective models among the random turbulence models, in this study, the option pricing under Heston and Heston Nandi random stochastic is discussed, which has been investigated considering the non-normality of the data distribution.

In this study, data from Iran Khodro was utilized, spanning the period from November 21, 2020, to December 14, 2022. To increase the accuracy, the volatility was calculated using two historical and implied methods. Following the application of option pricing using all three models, namely Black-Scholes, Heston, and Heston-Nandi, and subsequent comparison of the results, it was determined that the Heston-Nandi model exhibited superior performance when compared to the other two models.

The findings of this research indicate that, in both the short, medium, and long terms, the Heston-Nandi model yields prices that closely align with market prices and exhibits lower error rates. Consequently, it can be inferred that the Heston-Nandi model demonstrates a high degree of flexibility. The Heston-Nandi model outperforms the Black-Scholes and Heston models by capturing unusual patterns like skewness and elongation. This makes it a good alternative to those models.