Finite difference methods for option pricing under Lévy processes: Wiener-Hopf factorization approach.

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ID: 30620
2013
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Abstract
In the paper, we consider the problem of pricing options in wide classes of Lévy processes. We propose a general approach to the numerical methods based on a finite difference approximation for the generalized Black-Scholes equation. The goal of the paper is to incorporate the Wiener-Hopf factorization into finite difference methods for pricing options in Lévy models with jumps. The method is applicable for pricing barrier and American options. The pricing problem is reduced to the sequence of linear algebraic systems with a dense Toeplitz matrix; then the Wiener-Hopf factorization method is applied. We give an important probabilistic interpretation based on the infinitely divisible distributions theory to the Laurent operators in the correspondent factorization identity. Notice that our algorithm has the same complexity as the ones which use the explicit-implicit scheme, with a tridiagonal matrix. However, our method is more accurate. We support the advantage of the new method in terms of accuracy and convergence by using numerical experiments.
Reference Key
kudryavtsev2013finitethescientificworldjournal Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Kudryavtsev, Oleg;
Journal TheScientificWorldJournal
Year 2013
DOI
10.1155/2013/963625
URL
Keywords Keywords not found

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