Fast and accurate pricing of barrier options under Lévy processes
type: Item
instance of: scholarly article
title: Fast and accurate pricing of barrier options under Lévy processes
zbMATH Open document ID: 1194.91179
author: Oleg Kudryavtsev
author: Sergei Levendorskiĭ
published in: Finance and Stochastics
publication date: 2010-04-22T00:00:00Z
review text: The authors introduce the fast Wiener-Hopf factorization method (FWH method) and the iterative Wiener-Hopf method, for pricing barrier options for a wide class of Lévy processes. Both methods use the Wiener--Hopf factorization and the fast Fourier transform algorithm. The main new element of the fast Wiener-Hopf factorization method is an efficient approximations to the expected present value operators, which leads to fast and accurate pricing procedure. The FWH method is fully implicit because one approximates the operators in the exact formula for the solution of the boundary problem. The accuracy and fast convergence of both methods using Monte Carlo simulations and an accurate finite difference scheme are demonstrated, the results are compared with those obtained by the Cont-Voltchkova method. The appendices contain the background of the theory of Lévy processes and of partial differential operators, the behaviour of the price of the barrier option near the barrier, and explicit numerical algorithms.
reviewed by: Yuliya S. Mishura
Mathematics Subject Classification ID: 91G20
Mathematics Subject Classification ID: 91G60
Mathematics Subject Classification ID: 60G51
Mathematics Subject Classification ID: 60J75
Mathematics Subject Classification ID: 47A68
Mathematics Subject Classification ID: 42A85
zbMATH DE Number: 5697475
zbMATH Keywords: Lévy processes
zbMATH Keywords: barrier options
zbMATH Keywords: Wiener-Hopf factorization
zbMATH Keywords: numerical methods
MaRDI profile type: Publication
full work available at URL: s00780-009-0103-2
OpenAlex ID: W2928881687
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DOI: 10.1007/S00780-009-0103-2
description: scientific article; zbMATH DE number 5697475