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Volatility, Momentum, and Time-Varying Skewness in Foreign Exchange Returns

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  • Johnson, Timothy C

Abstract

This article tests a stochastic volatility model of exchange rates that links both the level of volatility and its instantaneous covariance with returns to pathwise properties of the currency. In particular, the model implies that the return-volatility covariance behaves like a weighted average of recent returns and hence switches signs according to the direction of trends in the data. This implies that the skewness of the finite-horizon return distribution likewise switches sign, leading to time-varying implied volatility "smiles" in options prices. The model is fit and assessed using Bayesian techniques. Some previously reported volatility results are accounted for by the fitted models. The predicted pattern of skewness dynamics accords well with that found in historical options prices.

Suggested Citation

  • Johnson, Timothy C, 2002. "Volatility, Momentum, and Time-Varying Skewness in Foreign Exchange Returns," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 390-411, July.
    • Handle: RePEc:bes:jnlbes:v:20:y:2002:i:3:p:390-411
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    Citations

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    Cited by:

    1. Iseringhausen, Martin, 2020. "The time-varying asymmetry of exchange rate returns: A stochastic volatility – stochastic skewness model," Journal of Empirical Finance, Elsevier, vol. 58(C), pages 275-292.
    2. Gordon R. Richards, 2004. "A fractal forecasting model for financial time series," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 23(8), pages 586-601.
    3. Wang, Jianxin & Yang, Minxian, 2009. "Asymmetric volatility in the foreign exchange markets," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 19(4), pages 597-615, October.
    4. Carr, Peter & Wu, Liuren, 2007. "Stochastic skew in currency options," Journal of Financial Economics, Elsevier, vol. 86(1), pages 213-247, October.
    5. Chernov, Mikhail & Graveline, Jeremy & Zviadadze, Irina, 2018. "Crash Risk in Currency Returns," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 53(1), pages 137-170, February.
    6. Xu, Weidong & Wu, Chongfeng & Li, Hongyi, 2011. "Accounting for the impact of higher order moments in foreign equity option pricing model," Economic Modelling, Elsevier, vol. 28(4), pages 1726-1729, July.
    7. Liu, Zhenya & Lu, Shanglin & Wang, Shixuan, 2021. "Asymmetry, tail risk and time series momentum," International Review of Financial Analysis, Elsevier, vol. 78(C).
    8. Carpinteyro, Martha & Venegas-Martínez, Francisco & Martínez-García, Miguel Ángel, 2018. "Modeling Returns of Stock Indexes through Fractional Brownian Motion Combined with Jump Processes and Modulated by Markov Chains," MPRA Paper 90549, University Library of Munich, Germany.
    9. Federico Gatta & Fabrizio Lillo & Piero Mazzarisi, 2024. "CAESar: Conditional Autoregressive Expected Shortfall," Papers 2407.06619, arXiv.org.
    10. Chernov, Mikhail & Graveline, Jeremy & Zviadadze, Irina, 2012. "Sources of Risk in Currency Returns," CEPR Discussion Papers 8745, C.E.P.R. Discussion Papers.
    11. Carpinteyro, Martha & Venegas Martínez, Francisco & Martínez García, Miguel Ángel, 2019. "Modelado de rendimientos de índices bursátiles mediante movimiento fraccional browniano combinado con procesos de saltos y modulado por cadenas de Markov / Modeling Returns of Stock Indexes through Fr," Estocástica: finanzas y riesgo, Departamento de Administración de la Universidad Autónoma Metropolitana Unidad Azcapotzalco, vol. 9(2), pages 163-180, julio-dic.
    12. Reyes-García, Nallely Jacqueline & Venegas-Martínez, Francisco & Cruz-Aké, Salvador, 2018. "Un análisis comparativo entre GARCH-M, EGARCH y PJ-RS-EV para modelar la volatilidad de Índice de precios y cotizaciones de la Bolsa Mexicana de Valores [A Comparative Analysis among GARCH-M, EGARC," MPRA Paper 84304, University Library of Munich, Germany.
    13. David Feldman, 2007. "Incomplete information equilibria: Separation theorems and other myths," Annals of Operations Research, Springer, vol. 151(1), pages 119-149, April.
    14. A. Balakrishnan & Nirakar Barik, 2021. "Do select macroeconomic factors drive momentum returns?," Future Business Journal, Springer, vol. 7(1), pages 1-12, December.
    15. Xu, Weidong & Wu, Chongfeng & Li, Hongyi, 2011. "Foreign equity option pricing under stochastic volatility model with double jumps," Economic Modelling, Elsevier, vol. 28(4), pages 1857-1863, July.

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