Exchange option pricing under the hybrid exponential jump diffusion model

This paper deals with the pricing of exchange options under the stochastic interest rate, stochastic volatility and mixed exponential jump diffusion model. On the basis of Heston volatility model, random interest rate and mixed index jump diffusion are introduced, and considering the negative interest rate in the market in recent years, this paper assumes that the interest rate model satisfies the Hull-White process (H-W), and establishes the mixed index jump Heston-HW (MEJ-Heston-HW) model. By using the idea of measure transformation, deduced the pricing formula of exchange options by Fourier transform method. Finally, based on the fast Fourier algorithm, the numerical solution of option value is obtained, and the influences of fluctuation term, correlation coefficient and jump intensity in random volatility on option value are emphatically analyzed. Compared with the double exponential jump Heston-HW model (DEJ-Heston-HW) and Black-Scholes model, the MEJ-Heston-HW model can better describe the price changes of financial assets in numerical simulation. Therefore, the exchange option pricing formula under the MEJHeston-HW model is more consistent with the law of financial market, and the obtained results extend the existing conclusions on exchange option pricing.