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arXiv · 2211.07765

Efficient evaluation of double-barrier options and joint cpdf of a L\'evy process and its two extrema

Svetlana Boyarchenko·Sergei Levendorskiĭ
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Abstract

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

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Svetlana Boyarchenko, Sergei Levendorskiĭ. 2022-10-30. Efficient evaluation of double-barrier options and joint cpdf of a L\'evy process and its two extrema. https://arxiv.org/abs/2211.07765

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