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Pricing Bermudan options under local L\'evy models with default

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  • Anastasia Borovykh
  • Cornelis W. Oosterlee
  • Andrea Pascucci

Abstract

We consider a defaultable asset whose risk-neutral pricing dynamics are described by an exponential L\'evy-type martingale. This class of models allows for a local volatility, local default intensity and a locally dependent L\'evy measure. We present a pricing method for Bermudan options based on an analytical approximation of the characteristic function combined with the COS method. Due to a special form of the obtained characteristic function the price can be computed using a Fast Fourier Transform-based algorithm resulting in a fast and accurate calculation. The Greeks can be computed at almost no additional computational cost. Error bounds for the approximation of the characteristic function as well as for the total option price are given.

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  • Anastasia Borovykh & Cornelis W. Oosterlee & Andrea Pascucci, 2016. "Pricing Bermudan options under local L\'evy models with default," Papers 1604.08735, arXiv.org.
    • Handle: RePEc:arx:papers:1604.08735
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    References listed on IDEAS

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    1. Lord, Roger & Fang, Fang & Bervoets, Frank & Oosterlee, Kees, 2007. "A fast and accurate FFT-based method for pricing early-exercise options under Lévy processes," MPRA Paper 1952, University Library of Munich, Germany.
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    7. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
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    Cited by:

    1. Qian Feng & Cornelis W. Oosterlee, 2017. "Computing Credit Valuation Adjustment For Bermudan Options With Wrong Way Risk," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(08), pages 1-31, December.

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