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Option pricing using EGARCH models

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  • Schmitt, Christian
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    Abstract

    Various empirical studies have shown that the time-varying volatility of asset returns can be described by GARCH (generalised autoregressive conditional heteroskedasticity) models. The corresponding GARCH option pricing model of Duan (1995) is capable of depicting the smile-effect which often can be found in option prices. In some derivative markets, however, the slope of the smile is not symmetrical. In this paper an option pricing model in the context of the EGARCH (Exponential GARCH) process will be developed. Extensive numerical analyses suggest that the EGARCH option pricing model is able to explain the different slopes of the smile curve. --

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    Bibliographic Info

    Paper provided by ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research in its series ZEW Discussion Papers with number 96-20.

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    Date of creation: 1996
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    Handle: RePEc:zbw:zewdip:9620

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    1. Gallant, A Ronald & Rossi, Peter E & Tauchen, George, 1992. "Stock Prices and Volume," Review of Financial Studies, Society for Financial Studies, vol. 5(2), pages 199-242.
    2. Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394.
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    4. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
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    7. Christie, Andrew A., 1982. "The stochastic behavior of common stock variances : Value, leverage and interest rate effects," Journal of Financial Economics, Elsevier, vol. 10(4), pages 407-432, December.
    8. Johnson, Herb & Shanno, David, 1987. "Option Pricing when the Variance Is Changing," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(02), pages 143-151, June.
    9. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
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    18. Engle, Robert F. & Mustafa, Chowdhury, 1992. "Implied ARCH models from options prices," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 289-311.
    19. 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.
    20. 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.
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    22. Chesney, Marc & Scott, Louis, 1989. "Pricing European Currency Options: A Comparison of the Modified Black-Scholes Model and a Random Variance Model," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 24(03), pages 267-284, September.
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    Cited by:
    1. Zhu, Ke & Ling, Shiqing, 2014. "Model-based pricing for financial derivatives," MPRA Paper 56623, University Library of Munich, Germany.
    2. Liu, Heping & Shi, Jing, 2013. "Applying ARMA–GARCH approaches to forecasting short-term electricity prices," Energy Economics, Elsevier, vol. 37(C), pages 152-166.

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