Double Discretization Difference Schemes for Partial Integrodifferential Option Pricing Jump Diffusion Models

and Applied Analysis 3 For the sake of clarity in the presentation we recall that in a jump-diffusion model, the modified stochastic differential equation SDE for the underlying asset is dS S μdt σdz ( η − 1dq, 1.1 where S is the underlying stock price, μ is the drift rate, σ is the volatility, dz is the increment of Gauss-Wiener process, and dq is the Poisson process. The random variable representing the jump amplitude is denoted by η, and the expected relative jump size is denoted by K E η − 1 . The jump intensity of the Poisson process is denoted by λ. Based on the SDE 1.1 the resulting PIDE for a contingent claim V S, t is given by 7, 14, 29 : ∂V ∂t 1 2 σ2S2 ∂2V ∂S2 r − λK S ∂S − r λ V