Pricing Discrete Barrier Options Under the Jump-Diffusion Model with Stochastic Volatility and Stochastic Intensity

Abstract

This paper considers the problem of numerically evaluating discrete barrier option prices when the underlying asset follows the jump-diffusion model with stochastic volatility and stochastic intensity. We derive the three-dimensional characteristic function of the log-asset price, the volatility and the jump intensity. We also provide the approximate formula of the discrete barrier option prices by the three-dimensional Fourier cosine series expansion (3D-COS) method. Numerical results show that the 3D-COS method is rather correct, fast and competent for pricing the discrete barrier options.

Keywords

Option pricing / Discrete barrier options / Jump-diffusion model / Stochastic volatility / Stochastic intensity

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Funding

Fundamental Research Funds for the Central Universities(2018JBM320)