An Effective Algorithm for Pricing Option with Mixed-Exponential Jump and Double Stochastic Volatility

In order to combine the jump risk and stochastic volatility risk of actual asset price in the event of emergencies, the paper proposes a double stochastic volatility mixed-exponential jump-diffusion model by introducing mixed-exponential jump in the double Heston model. This paper obtains the characteristic function of logarithmic asset prices under the proposed model through Ito's formula and stochastic integration. Combing Fourier cosine series and fast Fourier transform algorithm, this paper proposes a new pricing algorithm for European options. Our algorithm truncates the integral interval of option pricing, expands the density function by Fourier COS expansion in the truncated interval, and transforms the density function into characteristic function by Fourier transform. The numerical results show that our algorithm is effective and has stable convergence for pricing European options.