Abstract: In this paper, the pricing problem on forward-start power options with product of two assets followed jump diffusion models in a stochastic interest rate framework is considered. Using the Feynman-Kac theorem, the joint characteristic function and the Fourier inverse transformation techniques, the closed-explicit solutions of the European forward-start power options with product of two asset are obtained. Some numerical examples for the option price are implemented by the fast Fourier transform (FFT), and the validity of the proposed method is verified by Monte Carlo simulation. The changes of option price in the proposed model were compared with that of other three different models (Black-Scholes, Merton and CIR+Black-Scholes), and the sensitivity of the price of the forward-start power options with product of two assets to some main parameters were analyzed, including the power factor, jump risk factors, maturity date, the correlation coefficient, average recovery speed and long term average level of interest rate, in the proposed model. Numerical results show that the power factor, jump risk factors, maturity date, the correlation coefficient, and long term average level of interest rate have more significant effect on the option price, and average recovery speed of interest rate has some effects on the option price. These are beneficial to risk management and hedging for investors.

Key words: power option, product option, forward-start option, CIR stochastic interest rate model, Girsanov theorem, Fourier inverse transformation