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Alternative models for FX, arbitrage opportunities and efficient pricing of double barrier options in L\'evy models

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  • Svetlana Boyarchenko
  • Sergei Levendorskii

Abstract

We analyze the qualitative differences between prices of double barrier no-touch options in the Heston model and pure jump KoBoL model calibrated to the same set of the empirical data, and discuss the potential for arbitrage opportunities if the correct model is a pure jump model. We explain and demonstrate with numerical examples that accurate and fast calculations of prices of double barrier options in jump models are extremely difficult using the numerical methods available in the literature. We develop a new efficient method (GWR-SINH method) based of the Gaver-Wynn-Rho acceleration applied to the Bromwich integral; the SINH-acceleration and simplified trapezoid rule are used to evaluate perpetual double barrier options for each value of the spectral parameter in GWR-algorithm. The program in Matlab running on a Mac with moderate characteristics achieves the precision of the order of E-5 and better in several several dozen of milliseconds; the precision E-07 is achievable in about 0.1 sec. We outline the extension of GWR-SINH method to regime-switching models and models with stochastic parameters and stochastic interest rates.

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  • Svetlana Boyarchenko & Sergei Levendorskii, 2023. "Alternative models for FX, arbitrage opportunities and efficient pricing of double barrier options in L\'evy models," Papers 2312.03915, arXiv.org.
    • Handle: RePEc:arx:papers:2312.03915
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    References listed on IDEAS

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    1. Svetlana Boyarchenko & Sergei Levendorskiä¬ & J. Lars Kyrkby & Zhenyu Cui, 2021. "Sinh-Acceleration For B-Spline Projection With Option Pricing Applications," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 24(08), pages 1-50, December.
    2. Sergei Levendorskiĭ, 2017. "ULTRA-FAST PRICING BARRIER OPTIONS AND CDSs," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(05), pages 1-27, August.
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