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Linear-Quadratic Jump-Diffusion Modelling with Application to Stochastic Volatility

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  • Olivier Scaillet.

Abstract

We aim at accommodating the existing affine jump-diffusion and quadratic models under the same roof, namely the linear-quadratic jump-diffusion (LQJD) class. We give a complete characterization of the dynamics underlying this class of models as well as identification constraints, and compute standard and extended transforms relevant to asset pricing. We also show that the LQJD class can be embedded into the affine class through use of an augmented state vector. We further establish that an equivalence relationship holds between both classes in terms of transform analysis. An option pricing application to multifactor stochastic volatility models reveals that adding nonlinearity into the model significantly reduces pricing errors, and further addition of a jump component in the stock price largely improves goodness-of-fit for in-the-money calls but less for out-of-the-money ones.
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Suggested Citation

  • Olivier Scaillet., 2003. "Linear-Quadratic Jump-Diffusion Modelling with Application to Stochastic Volatility," THEMA Working Papers 2003-29, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
  • Handle: RePEc:ema:worpap:2003-29
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    File URL: http://www.u-cergy.fr/IMG/documents//2003-29Scaillet.pdf
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    References listed on IDEAS

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    Cited by:

    1. Stefano Galluccio & Yann Le Cam, 2005. "Implied Calibration of Stochastic Volatility Jump Diffusion Models," Finance 0510028, University Library of Munich, Germany.
    2. Antonio Diez De Los Rios, 2009. "Can Affine Term Structure Models Help Us Predict Exchange Rates?," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 41(4), pages 755-766, June.
    3. Santa-Clara, Pedro & Yan, Shu, 2004. "Jump and Volatility Risk and Risk Premia: A New Model and Lessons from S&P 500 Options," University of California at Los Angeles, Anderson Graduate School of Management qt5dv8v999, Anderson Graduate School of Management, UCLA.
    4. Torben G. Andersen & Luca Benzoni, 2010. "Do Bonds Span Volatility Risk in the U.S. Treasury Market? A Specification Test for Affine Term Structure Models," Journal of Finance, American Finance Association, vol. 65(2), pages 603-653, April.
    5. Niels Rom-Poulsen, 2007. "Semi-analytical MBS Pricing," The Journal of Real Estate Finance and Economics, Springer, vol. 34(4), pages 463-498, May.
    6. Glasserman, Paul & Kim, Kyoung-Kuk, 2009. "Saddlepoint approximations for affine jump-diffusion models," Journal of Economic Dynamics and Control, Elsevier, vol. 33(1), pages 15-36, January.
    7. repec:wsi:ijtafx:v:10:y:2007:i:02:n:s0219024907004238 is not listed on IDEAS

    More about this item

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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