2022 Volume 8, Issue 2

Mina Masry

Abstract

In this paper, while introducing Heston's model of stochastic variance, regarding the jump process and the long-term memory feature of prices, a new model for pricing subordinate shares is presented. In the following, the performance of this model is discussed in comparison to the two other models of random variance, Heston and Bates. In this research, the Fractional-Jump Heston Model has been created by combining the jump process and Hurst exponent. The new model has been generated while the long-term memory characteristics of the stock market price trends and the vulnerability of prices in response to sudden changes have been taken into consideration. Then we have determined the characteristic function of the underlying asset price process in the new model, which has been used to derive a formula for subordinate shares pricing using the Monte Carlo method and the variance reduction technique. To test and Compare the option pricing models, we have used the subordinate shares data during 2012-2017. After calibrating and pricing subordinate shares by all three models and comparing the results, it was found that the Fractional-Jump Heston model has a better performance than the other two models in terms of the valuation of Tabai options. The comparison results show that the estimation by the Fractional-Jump Heston model is closer to the actual results of the subordinate shares’ prices, and is better than the two well-known models of stochastic variance, Heston and Bates.

Keywords: Fractional stochastic, volatility model, Jump-Diffusion, Long memory, Option pricing, Tabai option