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Tempered stable and tempered infinitely divisible GARCH models

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

Abstract

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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Bibliographic Info

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

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Keywords: tempered infinitely divisible distribution; tempered stable distribution; rapidly decreasing tempered stable distribution; GARCH model option pricing;

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  1. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  2. 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.
  3. Lars Stentoft, 2008. "American Option Pricing Using GARCH Models and the Normal Inverse Gaussian Distribution," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 6(4), pages 540-582, Fall.
  4. 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.
  5. Jin-Chuan Duan, 1995. "The Garch Option Pricing Model," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 13-32.
  6. 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.
  7. Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "Normal modified stable processes," Economics Papers 2001-W6, Economics Group, Nuffield College, University of Oxford.
  8. Christian Menn & Svetlozar Rachev, 2009. "Smoothly truncated stable distributions, GARCH-models, and option pricing," Computational Statistics, Springer, vol. 69(3), pages 411-438, July.
  9. 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.
  10. 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.
  11. 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.
  12. 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.
  13. Jin-Chuan Duan & Jean-Guy Simonato, 1998. "Empirical Martingale Simulation for Asset Prices," Management Science, INFORMS, vol. 44(9), pages 1218-1233, September.
  14. Sorwar, Ghulam & Dowd, Kevin, 2010. "Estimating financial risk measures for options," Journal of Banking & Finance, Elsevier, vol. 34(8), pages 1982-1992, August.
  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. 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.
  17. Mercuri, Lorenzo, 2008. "Option pricing in a Garch model with tempered stable innovations," Finance Research Letters, Elsevier, vol. 5(3), pages 172-182, September.
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Citations

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Cited by:
  1. Berninghaus, Siegfried K. & Todorova, Lora & Vogt, Bodo, 2011. "A simple questionnaire can change everything: Are strategy choices in coordination games stable?," Working Paper Series in Economics 37, Karlsruhe Institute of Technology (KIT), Department of Economics and Business Engineering.
  2. Stoyanov, Stoyan V. & Rachev, Svetlozar T. & Fabozzi, Frank J., 2013. "CVaR sensitivity with respect to tail thickness," Journal of Banking & Finance, Elsevier, vol. 37(3), pages 977-988.
  3. Simon A. BRODA & Markus HAAS & Jochen KRAUSE & Marc S. PAOLELLA & Sven C. STEUDE, . "Stable Mixture GARCH Models," Swiss Finance Institute Research Paper Series 11-39, Swiss Finance Institute.
  4. Jaehyung Choi, 2014. "Maximum drawdown, recovery, and momentum," Papers 1403.8125, arXiv.org, revised May 2014.
  5. Meyborg, Mirja, 2011. "The impact of West-German universities on regional innovation activities: A social network analysis," Working Paper Series in Economics 35, Karlsruhe Institute of Technology (KIT), Department of Economics and Business Engineering.
  6. 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.
  7. Stoyanov, Stoyan V. & Rachev, Svetlozar T. & Racheva-Iotova, Boryana & Fabozzi, Frank J., 2011. "Fat-tailed models for risk estimation," Working Paper Series in Economics 30, Karlsruhe Institute of Technology (KIT), Department of Economics and Business Engineering.
  8. Kassberger, Stefan & Liebmann, Thomas, 2012. "When are path-dependent payoffs suboptimal?," Journal of Banking & Finance, Elsevier, vol. 36(5), pages 1304-1310.
  9. Schosser, Stephan & Vogt, Bodo, 2011. "The public loss game: An experimental study of public bads," Working Paper Series in Economics 33, Karlsruhe Institute of Technology (KIT), Department of Economics and Business Engineering.
  10. Kim, Young Shin & Rachev, Svetlozar T. & Bianchi, Michele Leonardo & Mitov, Ivan & Fabozzi, Frank J., 2011. "Time series analysis for financial market meltdowns," Journal of Banking & Finance, Elsevier, vol. 35(8), pages 1879-1891, August.
  11. Jaehyung Choi & Young Shin Kim & Ivan Mitov, 2014. "Reward-risk momentum strategies using classical tempered stable distribution," Papers 1403.6093, arXiv.org, revised May 2014.
  12. Michele Leonardo Bianchi & Frank J. Fabozzi & Svetlozar T. Rachev, 2014. "Calibrating the Italian smile with time-varying volatility and heavy-tailed models," Temi di discussione (Economic working papers) 944, Bank of Italy, Economic Research and International Relations Area.
  13. Schaffer, Axel, 2011. "Appropriate policy measures to attract private capital in consideration of regional efficiency in using infrastructure and human capital," Working Paper Series in Economics 31, Karlsruhe Institute of Technology (KIT), Department of Economics and Business Engineering.
  14. Young Kim & Frank Fabozzi & Zuodong Lin & Svetlozar Rachev, 2012. "Option pricing and hedging under a stochastic volatility Lévy process model," Review of Derivatives Research, Springer, vol. 15(1), pages 81-97, April.

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