Fast Fourier transform option pricing with stochastic interest rate, stochastic volatility and double jumps

Abstract

In this paper, we focus on pricing European options in a double exponential jump diffusion model with stochastic volatility and stochastic interest rate. Firstly, using fast Fourier transform (FFT) technique, we obtain numerical solutions for option prices. Then, we analyze several effects on option prices under the proposed model, including correlation between stock returns and volatility, stochastic interest rate. Simulations show that FFT is fast and efficient, stock returns are negatively correlated with volatility and the effect of stochastic interest rate over longer time horizons is significant.