Efficient Evaluation of Double-Barrier Options and Joint CPDF of a Levy Process and Its Two Extrema

Download or read book Efficient Evaluation of Double-Barrier Options and Joint CPDF of a Levy Process and Its Two Extrema written by Svetlana Boyarchenko and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the paper, we develop a very fast and accurate method for pricing double barrier options with continuous monitoring in wide classes of Levy models; the calculations are in the dual space, and the Wiener-Hopf factorization is used. For wide regions in the parameter space, the precision of the order of 10-15 is achievable in seconds, and of the order of $10-9-10-8 - in fractions of a second. The Wiener-Hopf factors and repeated integrals in the pricing formulas are calculated using sinh-deformations of the lines of integration, the corresponding changes of variables and the simplified trapezoid rule. If the Bromwich integral is calculated using the Gaver-Wynn Rho acceleration instead of the sinh-acceleration, the CPU time is typically smaller but the precision is of the order of 10-9-10-6, at best. Explicit pricing algorithms and numerical examples are for no-touch options, digitals (equivalently, for the joint distribution function of a Levy process and its supremum and infimum processes), and call options. Several graphs are produced to explain fundamental difficulties for accurate pricing of barrier options using time discretization and interpolation-based calculations in the state space.