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Seize the Moments: Approximating American Option Prices in the GARCH Framework

  • Jin-Chuan Duan

    (University of Toronto)

  • Genevieve Gauthier

    (HEC Montreal)

  • Caroline Sasseville

    (HEC Montreal)

  • Jean-Guy Simonato

    (HEC Montreal)

This paper proposes an efficient approach to compute the prices of American style options in the GARCH framework. Rubinstein's (1998) Edgeworth tree idea is combined with the analytical formulas for moments of the cumulative return under GARCH developed in Duan et al. (1999, 2002) to yield a simple recombining binomial tree for option valuation in the GARCH context. Since the resulting tree is univariate, the proposed approach represents a convenient approximation of the bivariate GARCH system. Numerical analyses are used to demonstrate the speed and accuracy of the proposed approximation.

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File URL: http://128.118.178.162/eps/fin/papers/0206/0206005.pdf
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Paper provided by EconWPA in its series Finance with number 0206005.

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Length: 15 pages
Date of creation: 30 Jun 2002
Date of revision:
Handle: RePEc:wpa:wuwpfi:0206005
Note: Type of Document - PDF; pages: 15
Contact details of provider: Web page: http://128.118.178.162

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  1. Jin-Chuan Duan & Jean-Guy Simonato, 1995. "Empirical Martingale Simulation for Asset Prices," CIRANO Working Papers 95s-43, CIRANO.
  2. Jan Kallsen & Murad S. Taqqu, 1998. "Option Pricing in ARCH-type Models," Mathematical Finance, Wiley Blackwell, vol. 8(1), pages 13-26.
  3. Robert F. Engle & Victor K. Ng, 1991. "Measuring and Testing the Impact of News on Volatility," NBER Working Papers 3681, National Bureau of Economic Research, Inc.
  4. Jarrow, Robert & Rudd, Andrew, 1982. "Approximate option valuation for arbitrary stochastic processes," Journal of Financial Economics, Elsevier, vol. 10(3), pages 347-369, November.
  5. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
  6. Broadie, Mark & Detemple, Jerome, 1996. "American Option Valuation: New Bounds, Approximations, and a Comparison of Existing Methods," Review of Financial Studies, Society for Financial Studies, vol. 9(4), pages 1211-50.
  7. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  8. Duan, Jin-Chuan & Simonato, Jean-Guy, 2001. "American option pricing under GARCH by a Markov chain approximation," Journal of Economic Dynamics and Control, Elsevier, vol. 25(11), pages 1689-1718, November.
  9. Peter Ritchken & Rob Trevor, 1999. "Pricing Options under Generalized GARCH and Stochastic Volatility Processes," Journal of Finance, American Finance Association, vol. 54(1), pages 377-402, 02.
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