Pricing bivariate option under GARCH-GH model with dynamic copula: application for Chinese market
This paper develops the method for pricing bivariate contingent claims under General Autoregressive Conditionally Heteroskedastic (GARCH) process. In order to provide a general framework being able to accommodate skewness, leptokurtosis, fat tails as well as the time varying volatility that are often found in financial data, generalized hyperbolic (GH) distribution is used for innovations. As the association between the underlying assets may vary over time, the dynamic copula approach is considered. Therefore, the proposed method proves to play an important role in pricing bivariate option. The approach is illustrated for Chinese market with one type of better-of-two-markets claims : call option on the better performer of Shanghai Stock Composite Index and Shenzhen Stock Composite Index. Results show that the option prices obtained by the GARCH-GH model with time-varying copula differ substantially from the prices implied by the GARCH-Gaussian dynamic copula model. Moreover, the empirical work displays the advantage of the suggested method.
|Date of creation:||Oct 2009|
|Date of revision:|
|Publication status:||Published, European Journal of Finance, 2009, 15, 7-8, 777-795|
|Note:||View the original document on HAL open archive server: http://halshs.archives-ouvertes.fr/halshs-00368336|
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- Morten B. Jensen & Asger Lunde, 2001. "The NIG-S&ARCH model: a fat-tailed, stochastic, and autoregressive conditional heteroskedastic volatility model," Econometrics Journal, Royal Economic Society, vol. 4(2), pages 10.
- Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring.
- Stulz, ReneM., 1982. "Options on the minimum or the maximum of two risky assets : Analysis and applications," Journal of Financial Economics, Elsevier, vol. 10(2), pages 161-185, July.
- Eric Jondeau & Michael Rockinger, 2002. "Conditional Dependency of Financial Series: The Copula-GARCH Model," FAME Research Paper Series rp69, International Center for Financial Asset Management and Engineering.
- D. Guegan & J. Zhang, 2010.
"Change analysis of a dynamic copula for measuring dependence in multivariate financial data,"
Taylor & Francis Journals, vol. 10(4), pages 421-430.
- Dominique Guegan & Jing Zhang, 2006. "Change analysis of dynamic copula for measuring dependence in multivariate financial data," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00189141, HAL.
- Dominique Guégan & Jing Zhang, 2006. "Change analysis of dynamic copula for measuring dependence in multivariate financial data," Cahiers de la Maison des Sciences Economiques b06090, Université Panthéon-Sorbonne (Paris 1).
- Dominique Guegan & Jing Zhang, 2010. "Change analysis of a dynamic copula for measuring dependence in multivariate financial data," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00368334, HAL.
- Lawrence R. Glosten & Ravi Jagannathan & David E. Runkle, 1993.
"On the relation between the expected value and the volatility of the nominal excess return on stocks,"
157, Federal Reserve Bank of Minneapolis.
- Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. " On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
- Granger, Clive W.J. & Terasvirta, Timo & Patton, Andrew J., 2006.
"Common factors in conditional distributions for bivariate time series,"
Journal of Econometrics,
Elsevier, vol. 132(1), pages 43-57, May.
- Timo Terasvirta & Clive W.J Granger & Andrew Patton, 2003. "Common factors in conditional distributions for Bivariate time series," FMG Discussion Papers dp455, Financial Markets Group.
- Johnson, Herb, 1987. "Options on the Maximum or the Minimum of Several Assets," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(03), pages 277-283, September.
- U. Cherubini & E. Luciano, 2002. "Bivariate option pricing with copulas," Applied Mathematical Finance, Taylor & Francis Journals, vol. 9(2), pages 69-85.
- Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
- Merton, Robert C., 1975.
"Option pricing when underlying stock returns are discontinuous,"
787-75., Massachusetts Institute of Technology (MIT), Sloan School of Management.
- Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
- Christoffersen, Peter & Heston, Steve & Jacobs, Kris, 2006.
"Option valuation with conditional skewness,"
Journal of Econometrics,
Elsevier, vol. 131(1-2), pages 253-284.
- Gourieroux, C. & Monfort, A., 2007. "Econometric specification of stochastic discount factor models," Journal of Econometrics, Elsevier, vol. 136(2), pages 509-530, February.
- Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
- Joshua Rosenberg, 1999. "Semiparametric Pricing of Multivariate Contingent Claims," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-028, New York University, Leonard N. Stern School of Business-.
- Andrew J. Patton, 2006.
"Modelling Asymmetric Exchange Rate Dependence,"
International Economic Review,
Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 47(2), pages 527-556, 05.
- Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
- Heynen, Ronald & Kemna, Angelien & Vorst, Ton, 1994. "Analysis of the Term Structure of Implied Volatilities," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 29(01), pages 31-56, March.
- Brennan, M J, 1979. "The Pricing of Contingent Claims in Discrete Time Models," Journal of Finance, American Finance Association, vol. 34(1), pages 53-68, March.
- Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
- Margrabe, William, 1978. "The Value of an Option to Exchange One Asset for Another," Journal of Finance, American Finance Association, vol. 33(1), pages 177-86, March.
- van den Goorbergh, Rob W.J. & Genest, Christian & Werker, Bas J.M., 2005. "Bivariate option pricing using dynamic copula models," Insurance: Mathematics and Economics, Elsevier, vol. 37(1), pages 101-114, August.
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