Tridiagonal implicit method to evaluate European and American options under infinite activity Lévy models

Authors:
Jaewook Lee;Younhee Lee
Affiliations:
Department of Industrial Engineering, Seoul National University, Seoul, 151-742, Republic of Korea;Marine Technology Education and Research Center, Seoul National University, Seoul, 151-742, Republic of Korea
Venue:
Journal of Computational and Applied Mathematics
Year:
2013

Citing 5
Cited 0

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Abstract

We propose an efficient implicit method to evaluate European and American options when the underlying asset follows an infinite activity Levy model. Since the Levy measure of the infinite activity model has the singularity at the origin, we approximate infinitely many small jumps by samples of a diffusion. The proposed methods to solve partial integro-differential equations for European options and linear complementarity problems for American options via an operator splitting method involve solving linear systems with tridiagonal matrices and so can significantly reduce the computations associated with the discrete integral operators. The numerical experiments verify that the proposed method has the second-order convergence rate under an infinite activity Levy model.