METHOD OF PAIRED CONTOURS AND PRICING BARRIER OPTIONS AND CDSs OF LONG MATURITIES

For prices of options with barrier and lookback features, defaultable bonds and credit default swaps (CDSs), and probability distribution functions in Levy models, as well as for joint probability distributions of a Levy process and its supremum or/and infimum, one can derive explicit analytical formulas in terms of inverse Laplace/Fourier transforms and the Wiener-Hopf factorization. Unless the characteristic exponent is rational, the main examples being Brownian motion, double exponential jump-diffusion and hyper-exponential jump-diffusion models, accurate numerical realization of these formulas is difficult or very time consuming, especially for options of very long and very short maturities. In this 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 CDSs of moderate and long maturities, much faster asymptotic formulas of comparable level of accuracy are developed.