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Splitting and Matrix Exponential Approach for Jump-Diffusion Models with Inverse Normal Gaussian, Hyperbolic and Meixner Jumps

19 Pages Posted: 11 Dec 2014  

Andrey Itkin

New York University (NYU)

Date Written: December 11, 2014

Abstract

This paper is a further extension of the method proposed in Itkin (2014) as applied to another set of jump-diffusion models: Inverse Normal Gaussian, Hyperbolic and Meixner. To solve the corresponding PIDEs we accomplish few steps. First, a second-order operator splitting on financial processes (diffusion and jumps) is applied to these PIDEs. To solve the diffusion equation we use standard finite-difference methods. For the jump part, we transform the jump integral into a pseudo-differential operator and construct its second order approximation on a grid which supersets the grid used for the diffusion part. The proposed schemes are unconditionally stable in time and preserve positivity of the solution which is computed either via a matrix exponential, or via its Páde approximation. Various numerical experiments are provided to justify these results.

Keywords: Jump-diffusion, PIDE, splitting, matrix exponential, unconditionally stable schemes

Suggested Citation

Itkin, Andrey, Splitting and Matrix Exponential Approach for Jump-Diffusion Models with Inverse Normal Gaussian, Hyperbolic and Meixner Jumps (December 11, 2014). Algorithmic Finance 2014, 3:3-4, pp. 233-250. Available at SSRN: https://ssrn.com/abstract=2536801

Andrey Itkin (Contact Author)

New York University (NYU) ( email )

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