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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
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    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.

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    File URL: http://www.tandfonline.com/doi/abs/10.1080/13504860600658992
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    Bibliographic Info

    Article provided by Taylor & Francis Journals in its journal Applied Mathematical Finance.

    Volume (Year): 13 (2006)
    Issue (Month): 4 ()
    Pages: 333-352

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    Handle: RePEc:taf:apmtfi:v:13:y:2006:i:4:p:333-352

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    Related research

    Keywords: Bridge monte carlo methods; simulations bias; exotic options valuation; levy processes;

    References

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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.
    2. Jing-zhi Huang & Liuren Wu, 2004. "Specification Analysis of Option Pricing Models Based on Time-Changed Levy Processes," Econometric Society 2004 North American Winter Meetings 405, Econometric Society.
    3. Madan, Dilip B & Seneta, Eugene, 1990. "The Variance Gamma (V.G.) Model for Share Market Returns," The Journal of Business, University of Chicago Press, vol. 63(4), pages 511-24, October.
    4. Geman, Helyette, 2002. "Pure jump Levy processes for asset price modelling," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1297-1316, July.
    5. Frank Milne & Dilip Madan, 1991. "Option Pricing With V. G. Martingale Components," Working Papers 1159, Queen's University, Department of Economics.
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    Cited by:
    1. 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.
    2. 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.
    3. Ye, Zhi-Sheng, 2013. "On the conditional increments of degradation processes," Statistics & Probability Letters, Elsevier, vol. 83(11), pages 2531-2536.

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