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

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  • Peng Cheng

    (HEC-University of Lausanne and FAME)

  • Olivier Scaillet

    (HEC-University of Genève and FAME)

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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Bibliographic Info

Paper provided by International Center for Financial Asset Management and Engineering in its series FAME Research Paper Series with number rp67.

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Date of creation: Nov 2002
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Handle: RePEc:fam:rpseri:rp67

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Keywords: Linear-quadratic models; affine models; jump-diffusions; generalized Fourier transform; option pricing; stochastic volatility;

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References

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Cited by:
  1. 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.
  2. 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, 04.
  3. 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.
  4. Niels Rom-Poulsen, 2007. "Semi-analytical MBS Pricing," The Journal of Real Estate Finance and Economics, Springer, vol. 34(4), pages 463-498, May.
  5. Antonio Diez de los Rios, 2006. "Can Affine Term Structure Models Help Us Predict Exchange Rates?," Working Papers 06-27, Bank of Canada.
  6. Stefano Galluccio & Yann Le Cam, 2005. "Implied Calibration of Stochastic Volatility Jump Diffusion Models," Finance 0510028, EconWPA.

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