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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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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

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

References

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  1. 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.
  2. Benoit Mandelbrot, 1963. "New Methods in Statistical Economics," Journal of Political Economy, University of Chicago Press, vol. 71, pages 421.
  3. Peter Christoffersen & Steve Heston & Kris Jacobs, 2003. "Option Valuation with Conditional Skewness," CIRANO Working Papers 2003s-50, CIRANO.
  4. Jin-Chuan Duan, 1995. "The Garch Option Pricing Model," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 13-32.
  5. 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.
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Cited by:
  1. Küchler, Uwe & Tappe, Stefan, 2014. "Exponential stock models driven by tempered stable processes," Journal of Econometrics, Elsevier, vol. 181(1), pages 53-63.
  2. Christophe Chorro & Dominique Guegan & Florian Ielpo, 2009. "Martingalized historical approach for option pricing," Documents de travail du Centre d'Economie de la Sorbonne 09021, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  3. Lorenzo Mercuri & Fabio Bellini, 2014. "Option Pricing in a Dynamic Variance-Gamma Model," Papers 1405.7342, arXiv.org.
  4. Kim, Young Shin & Rachev, Svetlozar T. & Bianchi, Michele Leonardo & Fabozzi, Frank J., 2011. "Tempered stable and tempered infinitely divisible GARCH models," Working Paper Series in Economics 28, Karlsruhe Institute of Technology (KIT), Department of Economics and Business Engineering.
  5. Chih-Chung Yang & Yungho Leu & Chien-Pang Lee, 2014. "A Dynamic Weighted Distancedbased Fuzzy Time Series Neural Network with Bootstrap Model for Option Price Forecasting," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 0(2), pages 115-129, June.
  6. repec:hal:journl:halshs-00437927 is not listed on IDEAS
  7. 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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