Conditional expectation strategy under the long memory Heston stochastic volatility model

Abstract

This article deals with an European option pricing via proportional transaction costs in the incomplete environment with and without arbitrage opportunities under two long memory versions of the Heston model. Observing and introducing a traded proxy for the volatility in the modern market, we use the conditional expectation and the delta hedging strategies and present the generalized fractional Ito formula to obtain the option price partial differential equations (PDEs). To solve these PDEs, we apply the finite difference method and employ the K-antithetic variates algorithm based on the Monte-Carlo simulation as a benchmark for this method. Finally, we provide numerical results to illustrate the effectiveness of the proposed model.