Tempered stable and tempered infinitely divisible GARCH models
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.
|Date of creation:||2011|
|Contact details of provider:|| Web page: http://www.wiwi.kit.edu/|
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Jérémy Poirot & Peter Tankov, 2006. "Monte Carlo Option Pricing for Tempered Stable (CGMY) Processes," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 13(4), pages 327-344, December.
- 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.
- Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "Normal modified stable processes," Economics Papers 2001-W6, Economics Group, Nuffield College, University of Oxford.
- Jin-Chuan Duan & Jean-Guy Simonato, 1995. "Empirical Martingale Simulation for Asset Prices," CIRANO Working Papers 95s-43, CIRANO.
- 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.
- 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.
- 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.
- Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
- Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
- 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.
- 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.
- Lars Stentoft, 2008. "American Option Pricing using GARCH models and the Normal Inverse Gaussian distribution," CREATES Research Papers 2008-41, Department of Economics and Business Economics, Aarhus University.
- 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.
- 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.
- 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.
- repec:spr:compst:v:69:y:2009:i:3:p:411-438 is not listed on IDEAS
- Mercuri, Lorenzo, 2008. "Option pricing in a Garch model with tempered stable innovations," Finance Research Letters, Elsevier, vol. 5(3), pages 172-182, September.
- Jin-Chuan Duan, 1995. "The Garch Option Pricing Model," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 13-32.
- Jin-Chuan Duan & Jean-Guy Simonato, 1998. "Empirical Martingale Simulation for Asset Prices," Management Science, INFORMS, vol. 44(9), pages 1218-1233, September.
- Sorwar, Ghulam & Dowd, Kevin, 2010. "Estimating financial risk measures for options," Journal of Banking & Finance, Elsevier, vol. 34(8), pages 1982-1992, August.
- 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. Full references (including those not matched with items on IDEAS)