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Forward And Future Implied Volatility

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  • PAUL GLASSERMAN

    ()
    (Columbia Business School, USA)

  • QI WU

    ()
    (Department of APAM, Columbia University, 200 S.W. Mudd Building, New York, NY 10027, USA)

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    Abstract

    We address the problem of defining and calculating forward volatility implied by option prices when the underlying asset is driven by a stochastic volatility process. We examine alternative notions of forward implied volatility and the information required to extract these measures from the prices of European options at fixed maturities. We then specialize to the SABR model and show how the asymptotic expansion of the bivariate transition density in Wu (forthcoming) allows calibration of the SABR model with piecewise constant parameters and calculation of forward volatility. We then investigate empirically whether current option prices at multiple maturities contain useful information in predicting future option prices and future implied volatility. We undertake this investigation using data on options on the euro-dollar, sterling-dollar, and dollar-yen exchange rates. We find that prices across maturities do indeed have predictive value. Moreover, we find that model-based forward volatility extracts this predicative information better than a standard "model-free" measure of forward volatility and better than spot implied volatility. The enhancement to out-of-sample forecasting accuracy gained from model-based forward volatility is greatest at longer forecasting horizons.

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    Bibliographic Info

    Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Journal of Theoretical and Applied Finance.

    Volume (Year): 14 (2011)
    Issue (Month): 03 ()
    Pages: 407-432

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    Handle: RePEc:wsi:ijtafx:v:14:y:2011:i:03:p:407-432

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    Related research

    Keywords: Forward volatility; implied volatility surface; time-dependent SABR model; currency options; volatility forecasting;

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    Cited by:
    1. Fernández, J.L. & Ferreiro, A.M. & García-Rodríguez, J.A. & Leitao, A. & López-Salas, J.G. & Vázquez, C., 2013. "Static and dynamic SABR stochastic volatility models: Calibration and option pricing using GPUs," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 94(C), pages 55-75.

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