Robust and Efficient IMEX Schemes for Option Pricing under Jump-Diffusion Models
18 Pages Posted: 11 Apr 2013
Date Written: April 10, 2013
We propose families of IMEX time discretization schemes for the partial integro-differential equation derived for the pricing of options under a jump diffusion process. The schemes include the families of IMEX-midpoint, IMEXCNAB and IMEX-BDF2 schemes. Each family is defined by a convex parameter c ∈ [0, 1], which divides the zeroth-order term due to the jumps between the implicit and explicit part in the time discretization. These IMEX schemes lead to tridiagonal systems, which can be solved extremely efficiently. The schemes are studied through Fourier stability analysis and numerical experiments. It is found that, under suitable assumptions and time step restrictions, the IMEX-midpoint family is absolutely stable only for c = 0, while the IMEX-CNAB and the IMEX-BDF2 families are absolutely stable for all c ∈ [0, 1]. The IMEX-CNAB c = 0 scheme produced the smallest error in our numerical experiments.
Keywords: Implicit-explicit methods, Linear multistep methods, Jump-diffusion model, Option pricing, Stability
JEL Classification: G13, C63
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