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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.

Suggested Citation

  • Mercuri, Lorenzo, 2008. "Option pricing in a Garch model with tempered stable innovations," Finance Research Letters, Elsevier, vol. 5(3), pages 172-182, September.
  • Handle: RePEc:eee:finlet:v:5:y:2008:i:3:p:172-182
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    References listed on IDEAS

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    1. 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, April.
    2. Christoffersen, Peter & Heston, Steve & Jacobs, Kris, 2006. "Option valuation with conditional skewness," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 253-284.
    3. Jin-Chuan Duan, 1995. "The Garch Option Pricing Model," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 13-32.
    4. Benoit Mandelbrot, 1963. "New Methods in Statistical Economics," Journal of Political Economy, University of Chicago Press, vol. 71, pages 421-421.
    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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    Citations

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    Cited by:

    1. Chorro, C. & Guégan, D. & Ielpo, F., 2010. "Martingalized historical approach for option pricing," Finance Research Letters, Elsevier, vol. 7(1), pages 24-28, March.
    2. 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.
    3. repec:spr:annopr:v:260:y:2018:i:1:d:10.1007_s10479-016-2394-y is not listed on IDEAS
    4. Küchler, Uwe & Tappe, Stefan, 2013. "Tempered stable distributions and processes," Stochastic Processes and their Applications, Elsevier, vol. 123(12), pages 4256-4293.
    5. Lorenzo Mercuri & Fabio Bellini, 2014. "Option Pricing in a Dynamic Variance-Gamma Model," Papers 1405.7342, arXiv.org.
    6. Fabio Bellini & Lorenzo Mercuri, 2014. "Option pricing in a conditional Bilateral Gamma model," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 22(2), pages 373-390, June.
    7. Fengler, Matthias & Melnikov, Alexander, 2017. "GARCH option pricing models with Meixner innovations," Economics Working Paper Series 1702, University of St. Gallen, School of Economics and Political Science.
    8. 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.
    9. repec:hal:journl:halshs-00437927 is not listed on IDEAS
    10. Küchler, Uwe & Tappe, Stefan, 2014. "Exponential stock models driven by tempered stable processes," Journal of Econometrics, Elsevier, vol. 181(1), pages 53-63.
    11. Lorenzo Mercuri & Edit Rroji, 2014. "Parametric Risk Parity," Papers 1409.7933, arXiv.org.

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