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Pricing bivariate option under GARCH processes with time-varying copula

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  • Zhang, J.
  • Guégan, D.

Abstract

This paper develops a method for pricing bivariate contingent claims under General Autoregressive Conditionally Heteroskedastic (GARCH) process. As the association between the underlying assets may vary over time, the dynamic copula with time-varying parameter offers a better alternative to any static model for dependence structure and even to the dynamic copula model determined by dynamic dependence measure. Therefore, the proposed method proves to play an important role in pricing bivariate options. The approach is illustrated with one type of better-of-two-markets claims: call option on the better performer of Shanghai and Shenzhen Stock Composite Indexes. Results show that the option prices obtained by the time-varying copula model differ substantially from the prices implied by the static copula model and even the dynamic copula model derived from the dynamic dependence measure. Moreover, the empirical work displays the advantages of the suggested method.

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Bibliographic Info

Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

Volume (Year): 42 (2008)
Issue (Month): 3 (June)
Pages: 1095-1103

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Handle: RePEc:eee:insuma:v:42:y:2008:i:3:p:1095-1103

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Web page: http://www.elsevier.com/locate/inca/505554

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References

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  1. 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.
  2. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  3. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
  4. 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.
  5. 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.
  6. 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.
  7. U. Cherubini & E. Luciano, 2002. "Bivariate option pricing with copulas," Applied Mathematical Finance, Taylor & Francis Journals, vol. 9(2), pages 69-85.
  8. 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.
  9. 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.
  10. Jin-Chuan Duan, 1995. "The Garch Option Pricing Model," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 13-32.
  11. 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-.
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Cited by:
  1. Branger, Nicole & Muck, Matthias, 2012. "Keep on smiling? The pricing of Quanto options when all covariances are stochastic," Journal of Banking & Finance, Elsevier, vol. 36(6), pages 1577-1591.
  2. ROMBOUTS, Jeroen J. K & STENTOFT, Lars, 2010. "Multivariate option pricing with time varying volatility and correlations," CORE Discussion Papers 2010020, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. Aloui, Riadh & Hammoudeh, Shawkat & Nguyen, Duc Khuong, 2013. "A time-varying copula approach to oil and stock market dependence: The case of transition economies," Energy Economics, Elsevier, vol. 39(C), pages 208-221.
  4. ROMBOUTS, Jeroen V. K. & STENTOFT, Lars & VIOLANTE, Francesco, 2012. "The value of multivariate model sophistication: an application to pricing Dow Jones Industrial Average options," CORE Discussion Papers 2012003, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).

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