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Forecasting volatility and option pricing for exchange-rate dynamics: a comparison of models

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  • Kaehler, Jürgen
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    Abstract

    This paper explores the applicability of static and dynamic models to capture the stylized facts of exchange-rate dynamics. The static models (mixture of distributions, compound Poisson process, generalized Student distribution) are compatible with leptokurtosis and can be characterized as scale-compounded distributions. The dynamic models (GARCH, GARCH-t, EGARCH, Markov-switching model), on the other hand, are compatible with both leptokurtosis and heteroskedasticity. In a comparison of the candidate models, it is found that the dynamic models do indeed achieve a better fit to the data than the static models. However, in forecasting experiments the dynamic models can outperform a 'naive' model of constant variances only with respect to unbiasedness but not with respect to precision. Furthermore, the paper examines the implications of the static and dynamic models for the pricing of foreign-currency options by simple simulations. Static models show significang option-price effect only when the maturity is short. GARCH and EGARCH models, on the other hand, imply options prices which are higher than Black-Scholes prices for the full range of moneyness. Only the Markov-switching model is compatible with the observed 'smile effects' on option markets. --

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    Paper provided by ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research in its series ZEW Discussion Papers with number 93-19.

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    Date of creation: 1993
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    Handle: RePEc:zbw:zewdip:9319

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    1. 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, Elsevier, vol. 52(1-2), pages 5-59.
    2. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, Econometric Society, vol. 59(2), pages 347-70, March.
    3. Bollerslev, Tim, 1987. "A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return," The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 542-47, August.
    4. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, Econometric Society, vol. 50(4), pages 987-1007, July.
    5. L. Wade, 1988. "Review," Public Choice, Springer, Springer, vol. 58(1), pages 99-100, July.
    6. Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, University of Chicago Press, vol. 36, pages 394.
    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. Meese, Richard A. & Rogoff, Kenneth, 1983. "Empirical exchange rate models of the seventies : Do they fit out of sample?," Journal of International Economics, Elsevier, Elsevier, vol. 14(1-2), pages 3-24, February.
    9. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, American Finance Association, vol. 42(2), pages 281-300, June.
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