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Correcting for Simulation Bias in Monte Carlo Methods to Value Exotic Options in Models Driven by Levy Processes

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  • Claudia Ribeiro
  • Nick Webber

Abstract

Levy processes can be used to model asset return's distributions. Monte Carlo methods must frequently be used to value path dependent options in these models, but Monte Carlo methods can be prone to considerable simulation bias when valuing options with continuous reset conditions. This paper shows how to correct for this bias for a range of options by generating a sample from the extremes distribution of the Levy process on subintervals. The method uses variance-gamma and normal inverse Gaussian processes. The method gives considerable reductions in bias, so that it becomes feasible to apply variance reduction methods. The method seems to be a very fruitful approach in a framework in which many options do not have analytical solutions.

Suggested Citation

  • Claudia Ribeiro & Nick Webber, 2006. "Correcting for Simulation Bias in Monte Carlo Methods to Value Exotic Options in Models Driven by Levy Processes," Applied Mathematical Finance, Taylor & Francis Journals, vol. 13(4), pages 333-352.
    • Handle: RePEc:taf:apmtfi:v:13:y:2006:i:4:p:333-352
    DOI: 10.1080/13504860600658992
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    References listed on IDEAS

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    1. Ernst Eberlein & Sebastian Raible, 1999. "Term Structure Models Driven by General Lévy Processes," Mathematical Finance, Wiley Blackwell, vol. 9(1), pages 31-53, January.
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    Cited by:

    1. Ye, Zhi-Sheng, 2013. "On the conditional increments of degradation processes," Statistics & Probability Letters, Elsevier, vol. 83(11), pages 2531-2536.
    2. Kenichiro Shiraya & Hiroki Uenishi & Akira Yamazaki, 2019. "A General Control Variate Method for Lévy Models in Finance (Published in European Journal of Operational Research.)," CARF F-Series CARF-F-455, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Jan 2020.
    3. Shiraya, Kenichiro & Uenishi, Hiroki & Yamazaki, Akira, 2020. "A general control variate method for Lévy models in finance," European Journal of Operational Research, Elsevier, vol. 284(3), pages 1190-1200.
    4. Alberto Bueno-Guerrero & Steven P. Clark, 2023. "Option Pricing under a Generalized Black–Scholes Model with Stochastic Interest Rates, Stochastic Strings, and Lévy Jumps," Mathematics, MDPI, vol. 12(1), pages 1-39, December.
    5. N. Hilber & N. Reich & C. Schwab & C. Winter, 2009. "Numerical methods for Lévy processes," Finance and Stochastics, Springer, vol. 13(4), pages 471-500, September.
    6. Jos'e E. Figueroa-L'opez & Peter Tankov, 2012. "Small-time asymptotics of stopped L\'evy bridges and simulation schemes with controlled bias," Papers 1203.2355, arXiv.org, revised Jul 2014.
    7. Lee, Hangsuck & Ha, Hongjun & Kong, Byungdoo & Lee, Minha, 2024. "Valuing three-asset barrier options and autocallable products via exit probabilities of Brownian bridge," The North American Journal of Economics and Finance, Elsevier, vol. 73(C).
    8. Wang, Chuan-Ju & Kao, Ming-Yang, 2016. "Optimal search for parameters in Monte Carlo simulation for derivative pricing," European Journal of Operational Research, Elsevier, vol. 249(2), pages 683-690.

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