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Simulation of jump diffusions and the pricing of options

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  • DiCesare, Joe
  • Mcleish, Don

Abstract

We present importance sampling and acceptance-rejection simulation methods for one dimensional diffusions. This effectively reduces the computation of many path functionals of general diffusions to a similar computation for the Brownian bridge. We use this approach to efficiently obtain Monte Carlo prices of path-dependent derivative securities such as Barrier and Look-back options for a CEV jump-diffusion model.

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  • DiCesare, Joe & Mcleish, Don, 2008. "Simulation of jump diffusions and the pricing of options," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 316-326, December.
    • Handle: RePEc:eee:insuma:v:43:y:2008:i:3:p:316-326
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    1. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
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    10. Boyle, Phelim P. & Tian, Yisong “Samâ€, 1999. "Pricing Lookback and Barrier Options under the CEV Process," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(2), pages 241-264, June.
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    Cited by:

    1. Hatem Ben-Ameur & Rim Chérif & Bruno Rémillard, 2016. "American-style options in jump-diffusion models: estimation and evaluation," Quantitative Finance, Taylor & Francis Journals, vol. 16(8), pages 1313-1324, August.
    2. Metzler Adam & Scott Alexandre, 2014. "Rare event simulation for diffusion processes via two-stage importance sampling," Monte Carlo Methods and Applications, De Gruyter, vol. 20(2), pages 77-100, June.
    3. Fernández Lexuri & Hieber Peter & Scherer Matthias, 2013. "Double-barrier first-passage times of jump-diffusion processes," Monte Carlo Methods and Applications, De Gruyter, vol. 19(2), pages 107-141, July.

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