Pricing options in a mixed fractional double exponential jump-diffusion model with stochastic volatility and interest rates

Under the hypothesis of underlying asset price with long-range correlations and jump, a new framework for pricing European option is developed in a mixed fractional Brownian motion and double exponential jump- diffusion model with stochastic volatility and stochastic interest rates. An analytic formula for pricing European option is proposed. The probability functions in the formula are computed by using the Fourier inversion formula for distribution functions. The main finding is that European options not only depend on future smiles and the evolution of the interest rates, but also directly on the long-range correlations and jump among the underlying asset.