Fast and accurate pricing of barrier options under Lévy processes
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.
scientific article; zbMATH DE number 5697475
scientific article