A series solution of Black-Scholes equation under jump diffusion model

We introduce a series solution for a partial integro-differential equation which arises in option pricing when the Black-Scholes partial differential equations are considered under jump diffusion models. We construct a polynomial chaos solution using the Taylor expansion with respect to Hermite polynomials, which simplifies the integral term and derives a system of deterministic ordinary differential equations. Numerical examples show that the proposed method efficiently gives the desired accuracy for pricing options.