Method of Paired Contours and Pricing Barrier Options and CDs of Long Maturities

44 Pages Posted: 20 May 2013

Date Written: May 19, 2013

Abstract

For prices of options with barrier and lookback features, defaultable bonds and CDS, and probability distribution functions in Levy models, joint probability distributions of the process and its supremum or/and infimum, one can derive explicit analytical formulas in terms of the Laplace inversion, Fourier inversion and the Wiener-Hopf factorization. Unless the characteristic exponent is rational, the main examples being BM, DEJD and HEJD models, accurate numerical realizations of these formulas are difficult or very time consuming, for options of very long and very short maturities especially. In the paper, a systematic approach to contour deformations in pricing formulas is developed, which greatly increases the accuracy and speed of calculations; the efficiency of the method is demonstrated with numerical examples. For options and CDS of moderate and long maturities, much faster asymptotic formulas of comparable level of accuracy are developed.

Keywords: Levy processes, Laplace inversion, Wiener-Hopf factorization,barrier options, lookbacks, Fourier transform, conformal deformations,CDS, joint distribution of a Levy process and its extrema, Gaver-Wynn-Rho algorithm, Gaver-Stehfest algorithm,

JEL Classification: C63

Suggested Citation

Levendorskii, Sergei Z., Method of Paired Contours and Pricing Barrier Options and CDs of Long Maturities (May 19, 2013). Available at SSRN: https://ssrn.com/abstract=2267107 or http://dx.doi.org/10.2139/ssrn.2267107

Sergei Z. Levendorskii (Contact Author)

Calico Science Consulting ( email )

Austin, TX
United States

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