Articlegreen2011

A Second-Order Tridiagonal Method for American Options under Jump-Diffusion Models

67 citations0/0 files storedSIAM Journal on Scientific Computing

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Stochastic processes and financial applications Advanced Numerical Methods in Computational Mathematics Differential Equations and Numerical Methods

Abstract

We propose an implicit numerical method for pricing American options where the underlying asset follows a jump-diffusion model. Using the fact that the prices of American options are given by linear complementarity problems (LCPs), we combine an implicit finite difference method with an operator splitting method. The proposed method is constructed on three time levels, and the operator splitting method is used to treat American constraints. We concentrate on the formulation of the numerical method which leads to linear systems with tridiagonal coefficient matrices. Numerical experiments show that the implicit method has the second-order convergence rate, and the prices of American options can be obtained in a fraction of a second on a computer.

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References

1973The Pricing of Options and Corporate Liabilities 1976Option pricing when underlying stock returns are discontinuous 2002A Jump-Diffusion Model for Option Pricing 2002The Fine Structure of Asset Returns: An Empirical Investigation 1997Processes of normal inverse Gaussian type 1998New Insights into Smile, Mispricing, and Value at Risk: The Hyperbolic Model 1991Option Pricing With V. G. Martingale Components1 2004Robust numerical methods for contingent claims under jump diffusion processes

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