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Alternative models for FX: pricing double barrier options in regime-switching L\'evy models with memory

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  • Svetlana Boyarchenko
  • Sergei Levendorskiu{i}

Abstract

This paper is a supplement to our recent paper ``Alternative models for FX, arbitrage opportunities and efficient pricing of double barrier options in L\'evy models". We introduce the class of regime-switching L\'evy models with memory, which take into account the evolution of the stochastic parameters in the past. This generalization of the class of L\'evy models modulated by Markov chains is similar in spirit to rough volatility models. It is flexible and suitable for application of the machine-learning tools. We formulate the modification of the numerical method in ``Alternative models for FX, arbitrage opportunities and efficient pricing of double barrier options in L\'evy models", which has the same number of the main time-consuming blocks as the method for Markovian regime-switching models.

Suggested Citation

  • Svetlana Boyarchenko & Sergei Levendorskiu{i}, 2024. "Alternative models for FX: pricing double barrier options in regime-switching L\'evy models with memory," Papers 2402.16724, arXiv.org.
    • Handle: RePEc:arx:papers:2402.16724
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    References listed on IDEAS

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    1. Svetlana Boyarchenko & Sergei Levendorskiu{i}, 2022. "Efficient evaluation of double-barrier options and joint cpdf of a L\'evy process and its two extrema," Papers 2211.07765, arXiv.org.
    2. Svetlana Boyarchenko & Sergei Levendorskiĭ, 2020. "Static and semistatic hedging as contrarian or conformist bets," Mathematical Finance, Wiley Blackwell, vol. 30(3), pages 921-960, July.
    3. Boyarchenko, Svetlana & Levendorskii[caron], Sergei, 2007. "Optimal stopping made easy," Journal of Mathematical Economics, Elsevier, vol. 43(2), pages 201-217, February.
    4. Svetlana I Boyarchenko & Sergei Z Levendorskii, 2002. "Non-Gaussian Merton-Black-Scholes Theory," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 4955, August.
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