A fast numerical approach to option pricing with stochastic interest rate, stochastic volatility and double jumps

This study proposes a pricing model through allowing for stochastic interest rate and stochastic volatility in the double exponential jump-diffusion setting. The characteristic function of the proposed model is then derived. Fast numerical solutions for European call and put options pricing based on characteristic function and fast Fourier transform (FFT) technique are developed. Simulations show that our numerical technique is accurate, fast and easy to implement, the proposed model is suitable for modeling long-time real-market changes. The model and the proposed option pricing method are useful for empirical analysis of asset returns and risk management in firms.