Efficient Evaluation Of Double-Barrier Options

In the paper, we develop a very fast and accurate method for pricing double barrier options with continuous monitoring in wide classes of Lévy 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 Lévy 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.