Robust and Efficient IMEX Schemes for Option Pricing under Jump-Diffusion Models

18 Pages Posted: 11 Apr 2013

See all articles by Santtu Salmi

Santtu Salmi

University of Jyväskylä - Department of Mathematical Information Technology

Jari Toivanen

University of Jyväskylä - Department of Mathematical Information Technology; Stanford University

Date Written: April 10, 2013

Abstract

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

Suggested Citation

Salmi, Santtu and Toivanen, Jari, Robust and Efficient IMEX Schemes for Option Pricing under Jump-Diffusion Models (April 10, 2013). Available at SSRN: https://ssrn.com/abstract=2247916 or http://dx.doi.org/10.2139/ssrn.2247916

Santtu Salmi (Contact Author)

University of Jyväskylä - Department of Mathematical Information Technology ( email )

P.O. Box 35 (Agora)
Jyvaskyla, 40014
Finland

Jari Toivanen

University of Jyväskylä - Department of Mathematical Information Technology ( email )

P.O. Box 35 (Agora)
Jyvaskyla, 40014
Finland

Stanford University ( email )

Stanford, CA 94305
United States

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