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Autorregresive conditional volatility, skewness and kurtosis

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  • León, Angel
  • Serna, Gregorio
  • Rubio Irigoyen, Gonzalo
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    Abstract

    This paper proposes a GARCH-type model allowing for time-varying volatility, skewness and kurtosis. The model is estimated assuming a Gram-Charlier series expansion of the normal density function for the error term, which is easier to estimate than the non-central t distribution proposed by Harvey and Siddique (1999). Moreover, this approach accounts for time-varying skewness and kurtosis while the approach by Harvey and Siddique (1999) only accounts for nonnormal skewness. We apply this method to daily returns of a variety of stock indices and exchange rates. Our results indicate a significant presence of conditional skewness and kurtosis. It is also found that specifications allowing for time-varying skewness and kurtosis outperform specifications with constant third and fourth moments.

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    File URL: https://addi.ehu.es/bitstream/10810/6759/1/wp2002-06.pdf
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    Bibliographic Info

    Paper provided by University of the Basque Country - Department of Foundations of Economic Analysis II in its series DFAEII Working Papers with number 2002-06.

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    Date of creation: Dec 2004
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    Handle: RePEc:ehu:dfaeii:200206

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    Postal: Dpto. de Fundamentos del Análisis Económico II, = Facultad de CC. Económicas y Empresariales, Universidad del País Vasco, Avda. Lehendakari Aguirre 83, 48015 Bilbao, Spain
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    Keywords: skewness and kurtosis; conditional volatility; Gram-Charlier series expansion; stock indices;

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    References

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    1. David Backus & Silverio Foresi & Liuren Wu, 2002. "Accouting for Biases in Black-Scholes," Finance, EconWPA 0207008, EconWPA.
    2. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, Elsevier, vol. 31(3), pages 307-327, April.
    3. Das, Sanjiv Ranjan & Sundaram, Rangarajan K., 1999. "Of Smiles and Smirks: A Term Structure Perspective," Journal of Financial and Quantitative Analysis, Cambridge University Press, Cambridge University Press, vol. 34(02), pages 211-239, June.
    4. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-43.
    5. Lamoureux, Christopher G & Lastrapes, William D, 1993. "Forecasting Stock-Return Variance: Toward an Understanding of Stochastic Implied Volatilities," Review of Financial Studies, Society for Financial Studies, Society for Financial Studies, vol. 6(2), pages 293-326.
    6. Amin, Kaushik I & Ng, Victor K, 1997. "Inferring Future Volatility from the Information in Implied Volatility in Eurodollar Options: A New Approach," Review of Financial Studies, Society for Financial Studies, Society for Financial Studies, vol. 10(2), pages 333-67.
    7. Jarrow, Robert & Rudd, Andrew, 1982. "Approximate option valuation for arbitrary stochastic processes," Journal of Financial Economics, Elsevier, Elsevier, vol. 10(3), pages 347-369, November.
    8. Heston, Steven L & Nandi, Saikat, 2000. "A Closed-Form GARCH Option Valuation Model," Review of Financial Studies, Society for Financial Studies, Society for Financial Studies, vol. 13(3), pages 585-625.
    9. Harvey, Campbell R. & Siddique, Akhtar, 1999. "Autoregressive Conditional Skewness," Journal of Financial and Quantitative Analysis, Cambridge University Press, Cambridge University Press, vol. 34(04), pages 465-487, December.
    10. Engle, Robert F & Ng, Victor K, 1993. " Measuring and Testing the Impact of News on Volatility," Journal of Finance, American Finance Association, American Finance Association, vol. 48(5), pages 1749-78, December.
    11. Angel León & Juan Mora, 1999. "Modelling conditional heteroskedasticity: Application to the "IBEX-35" stock-return index," Spanish Economic Review, Springer, Springer, vol. 1(3), pages 215-238.
    12. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," Review of Financial Studies, Society for Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
    13. Peiro, Amado, 1999. "Skewness in financial returns," Journal of Banking & Finance, Elsevier, Elsevier, vol. 23(6), pages 847-862, June.
    14. Corrado, Charles J & Su, Tie, 1996. "Skewness and Kurtosis in S&P 500 Index Returns Implied by Option Prices," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, Southern Finance Association;Southwestern Finance Association, vol. 19(2), pages 175-92, Summer.
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