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In the paper, the authors propose two new efficient methods for pricing barrier option in wide classes of L?evy processes with/without regime switching. Both methods are based on the numerical Laplace transform inversion formulae and the Fast Wiener-Hopf factorization method developed in Kudryavtsev and Levendorski?i (Finance Stoch. 13: 531 - 562, 2009). The first method uses the Gaver-Stehfest algorithm, the second one - the Post-Widder formula. They prove the advantage of the new methods in terms of accuracy and convergence by using Monte-Carlo simulations.
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