Some bivariate options pricing in a regime-switching stochastic volatility jump-diffusion model with stochastic intensity, stochastic interest and dependent jump

This paper investigates the performance of bivariate options in the hypothesis of association between two underlying assets. Instead of the classical jump-diffusion process, the volatility of assets and the intensity of Poisson co-jump are both subject to the regime-switching square root process in this price dynamics. The endogenous and exogenous interest rate processes are introduced to examine the effect of interest rate on bivariate options pricing, respectively. An analytic pricing expression of bivariate options are deduced by joint discounted conditional characteristic function. Furthermore, the Fourier cosine expansion method is applied to obtain the approximated solutions of bivariate options price. Simulation and numerical examples are realized to examine the effect of the proposed model, the Fourier cosine expansion method, and the sensitivity of key arguments. The results indicate that embedding stochastic intensity, dependent structure of co-jump, and Markov regime-switching into the pricing dynamics have a significant influence on option pricing, and options prices are robust with respect to the choice of interest rate process.