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Tempered stable and tempered infinitely divisible GARCH models

  • Kim, Young Shin
  • Rachev, Svetlozar T.
  • Bianchi, Michele Leonardo
  • Fabozzi, Frank J.

In this paper, we introduce a new GARCH model with an infinitely divisible distributed innovation, referred to as the rapidly decreasing tempered stable (RDTS) GARCH model. This model allows the description of some stylized empirical facts observed for stock and index returns, such as volatility clustering, the non-zero skewness and excess kurtosis for the residual distribution. Furthermore, we review the classical tempered stable (CTS) GARCH model, which has similar statistical properties. By considering a proper density transformation between infinitely divisible random variables, these GARCH models allow to find the risk-neutral price process, and hence they can be applied to option pricing. We propose algorithms to generate scenario based on GARCH models with CTS and RDTS innovation. To investigate the performance of these GARCH models, we report a parameters estimation for Dow Jones Industrial Average (DJIA) index and stocks included in this index, and furthermore to demonstrate their advantages, we calculate option prices based on these models. It should be noted that only historical data on the underlying asset and on the riskfree rate are taken into account to evaluate option prices.

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File URL: http://econstor.eu/bitstream/10419/45636/1/659395126.pdf
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Paper provided by Karlsruhe Institute of Technology (KIT), Department of Economics and Business Engineering in its series Working Paper Series in Economics with number 28.

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Date of creation: 2011
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Handle: RePEc:zbw:kitwps:28
Contact details of provider: Web page: http://www.wiwi.kit.edu/

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  1. Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "Normal modified stable processes," Economics Papers 2001-W6, Economics Group, Nuffield College, University of Oxford.
  2. Jin-Chuan Duan, 1995. "The Garch Option Pricing Model," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 13-32.
  3. 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.
  4. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  5. Rachev, Svetlozar & Jasic, Teo & Stoyanov, Stoyan & Fabozzi, Frank J., 2007. "Momentum strategies based on reward-risk stock selection criteria," Journal of Banking & Finance, Elsevier, vol. 31(8), pages 2325-2346, August.
  6. Giovanni Barone-Adesi & Robert F. Engle & Loriano Mancini, 2008. "A GARCH Option Pricing Model with Filtered Historical Simulation," Review of Financial Studies, Society for Financial Studies, vol. 21(3), pages 1223-1258, May.
  7. Mercuri, Lorenzo, 2008. "Option pricing in a Garch model with tempered stable innovations," Finance Research Letters, Elsevier, vol. 5(3), pages 172-182, September.
  8. Jérémy Poirot & Peter Tankov, 2006. "Monte Carlo Option Pricing for Tempered Stable (CGMY) Processes," Asia-Pacific Financial Markets, Springer, vol. 13(4), pages 327-344, December.
  9. repec:spr:compst:v:69:y:2009:i:3:p:411-438 is not listed on IDEAS
  10. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
  11. Farinelli, Simone & Ferreira, Manuel & Rossello, Damiano & Thoeny, Markus & Tibiletti, Luisa, 2008. "Beyond Sharpe ratio: Optimal asset allocation using different performance ratios," Journal of Banking & Finance, Elsevier, vol. 32(10), pages 2057-2063, October.
  12. Jin-Chuan Duan & Peter Ritchken & Zhiqiang Sun, 2006. "Approximating Garch-Jump Models, Jump-Diffusion Processes, And Option Pricing," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 21-52.
  13. Lars Stentoft, 2008. "American Option Pricing using GARCH models and the Normal Inverse Gaussian distribution," CREATES Research Papers 2008-41, School of Economics and Management, University of Aarhus.
  14. Kim, Young Shin & Rachev, Svetlozar T. & Bianchi, Michele Leonardo & Fabozzi, Frank J., 2008. "Financial market models with Lévy processes and time-varying volatility," Journal of Banking & Finance, Elsevier, vol. 32(7), pages 1363-1378, July.
  15. Chernov, Mikhail & Ghysels, Eric, 2000. "A study towards a unified approach to the joint estimation of objective and risk neutral measures for the purpose of options valuation," Journal of Financial Economics, Elsevier, vol. 56(3), pages 407-458, June.
  16. Sorwar, Ghulam & Dowd, Kevin, 2010. "Estimating financial risk measures for options," Journal of Banking & Finance, Elsevier, vol. 34(8), pages 1982-1992, August.
  17. Jin-Chuan Duan & Jean-Guy Simonato, 1998. "Empirical Martingale Simulation for Asset Prices," Management Science, INFORMS, vol. 44(9), pages 1218-1233, September.
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