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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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    References listed on IDEAS

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    1. MacBeth, James D & Merville, Larry J, 1980. "Tests of the Black-Scholes and Cox Call Option Valuation Models," Journal of Finance, American Finance Association, vol. 35(2), pages 285-301, May.
    2. Alexandros Beskos & Omiros Papaspiliopoulos & Gareth O. Roberts & Paul Fearnhead, 2006. "Exact and computationally efficient likelihood‐based estimation for discretely observed diffusion processes (with discussion)," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(3), pages 333-382, June.
    3. S. G. Kou, 2002. "A Jump-Diffusion Model for Option Pricing," Management Science, INFORMS, vol. 48(8), pages 1086-1101, August.
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    5. Emanuel, David C. & MacBeth, James D., 1982. "Further Results on the Constant Elasticity of Variance Call Option Pricing Model," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 17(4), pages 533-554, November.
    6. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    7. 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..
    8. Beckers, Stan, 1980. "The Constant Elasticity of Variance Model and Its Implications for Option Pricing," Journal of Finance, American Finance Association, vol. 35(3), pages 661-673, June.
    9. Boyle, Phelim P. & Tian, Yisong “Sam”, 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.
    10. Leif Andersen & Jesper Andreasen, 2000. "Volatility skews and extensions of the Libor market model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 7(1), pages 1-32.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.

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