Forward starting options pricing with double stochastic volatility, stochastic interest rates and double jumps

We present an extension of double Heston stochastic volatility model by introducing CIR stochastic interest rate and double exponential jumps in the stock price process. We derive the characteristic function and forward characteristic function of the log asset price and thereby forward starting options are well evaluated by the COS method. We also provide efficient simulation of the proposed model and Monte Carlo solutions to forward starting options pricing based on the QE scheme. Numerical results show that the COS method is fast and efficient for pricing forward starting options.