Download or read book Method of Paired Contours and Pricing Barrier Options and CDs of Long Maturities written by Sergei Levendorskii and published by . This book was released on 2013 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.