Finite Difference Methods for Option Pricing under Lévy Processes: Wiener-Hopf Factorization Approach
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 factorizat...
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| Language: | English |
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Wiley
2013-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2013/963625 |
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| author | Oleg Kudryavtsev |
| author_facet | Oleg Kudryavtsev |
| author_sort | Oleg Kudryavtsev |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-03f3fd28bb63454ebb44085663b4f382 |
| institution | OA Journals |
| issn | 1537-744X |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-03f3fd28bb63454ebb44085663b4f3822025-08-20T02:03:18ZengWileyThe Scientific World Journal1537-744X2013-01-01201310.1155/2013/963625963625Finite Difference Methods for Option Pricing under Lévy Processes: Wiener-Hopf Factorization ApproachOleg Kudryavtsev0Department of Informatics, Russian Customs Academy Rostov Branch, Budennovskiy 20, Rostov-on-Don 344002, RussiaIn 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.http://dx.doi.org/10.1155/2013/963625 |
| spellingShingle | Oleg Kudryavtsev Finite Difference Methods for Option Pricing under Lévy Processes: Wiener-Hopf Factorization Approach The Scientific World Journal |
| title | Finite Difference Methods for Option Pricing under Lévy Processes: Wiener-Hopf Factorization Approach |
| title_full | Finite Difference Methods for Option Pricing under Lévy Processes: Wiener-Hopf Factorization Approach |
| title_fullStr | Finite Difference Methods for Option Pricing under Lévy Processes: Wiener-Hopf Factorization Approach |
| title_full_unstemmed | Finite Difference Methods for Option Pricing under Lévy Processes: Wiener-Hopf Factorization Approach |
| title_short | Finite Difference Methods for Option Pricing under Lévy Processes: Wiener-Hopf Factorization Approach |
| title_sort | finite difference methods for option pricing under levy processes wiener hopf factorization approach |
| url | http://dx.doi.org/10.1155/2013/963625 |
| work_keys_str_mv | AT olegkudryavtsev finitedifferencemethodsforoptionpricingunderlevyprocesseswienerhopffactorizationapproach |