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Option pricing in a Garch model with tempered stable innovations

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  • Mercuri, Lorenzo

Abstract

The key problem for option pricing in Garch models is that the risk-neutral distribution of the underlying at maturity is unknown. Heston and Nandi solved this problem by computing the characteristic function of the underlying by a recursive procedure. Following the same idea, Christoffersen, Heston and Jacobs proposed a Garch-like model with inverse Gaussian innovations and recently Bellini and Mercuri obtained a similar procedure in a model with Gamma innovations. We present a model with tempered stable innovations that encompasses both the CHJ and the BM models as special cases. The proposed model is calibrated on S&P500 closing option prices and its performance is compared with the CHJ, the BM and the Heston-Nandi models.

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File URL: http://www.sciencedirect.com/science/article/B7CPP-4SNNT76-1/2/94b2de087b96e17edf52a42a343c1fb9
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Bibliographic Info

Article provided by Elsevier in its journal Finance Research Letters.

Volume (Year): 5 (2008)
Issue (Month): 3 (September)
Pages: 172-182

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Handle: RePEc:eee:finlet:v:5:y:2008:i:3:p:172-182

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Web page: http://www.elsevier.com/locate/frl

Related research

Keywords: Option pricing Garch Tempered stable distribution Semi-analytical valuation Esscher transform;

References

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  1. Peter Christoffersen & Steve Heston & Kris Jacobs, 2003. "Option Valuation with Conditional Skewness," CIRANO Working Papers 2003s-50, CIRANO.
  2. Peter Carr & Liuren Wu, 2003. "The Finite Moment Log Stable Process and Option Pricing," Journal of Finance, American Finance Association, vol. 58(2), pages 753-778, 04.
  3. Benoit Mandelbrot, 1963. "New Methods in Statistical Economics," Journal of Political Economy, University of Chicago Press, vol. 71, pages 421.
  4. Jin-Chuan Duan, 1995. "The Garch Option Pricing Model," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 13-32.
  5. Heston, Steven L & Nandi, Saikat, 2000. "A Closed-Form GARCH Option Valuation Model," Review of Financial Studies, Society for Financial Studies, vol. 13(3), pages 585-625.
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Cited by:
  1. Shin Kim, Young & Rachev, Svetlozar T. & Leonardo Bianchi, Michele & Fabozzi, Frank J., 2010. "Tempered stable and tempered infinitely divisible GARCH models," Journal of Banking & Finance, Elsevier, vol. 34(9), pages 2096-2109, September.
  2. Christophe Chorro & Dominique Guegan & Florian Ielpo, 2010. "Martingalized Historical approach for Option Pricing," Post-Print halshs-00437927, HAL.
  3. Chorro, C. & Guégan, D. & Ielpo, F., 2010. "Martingalized historical approach for option pricing," Finance Research Letters, Elsevier, vol. 7(1), pages 24-28, March.
  4. Küchler, Uwe & Tappe, Stefan, 2013. "Tempered stable distributions and processes," Stochastic Processes and their Applications, Elsevier, vol. 123(12), pages 4256-4293.

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