Long memory version of stochastic volatility jump-diffusion model with stochastic intensity

It is widely accepted that certain financial data exhibit long range dependence. We consider a fractional stochastic volatility jump difiusion model in which the stock price follows a double exponential jump difiusion process with volatility described by a long memory stochastic process and intensity rate expressed by an ordinary Cox, Ingersoll, and Ross (CIR) process. By calibrating the model with real data, we examine the performance of the model and also, we illustrate the role of long range dependence property by comparing our presented model with the Heston model.