FORWARD AND FUTURE IMPLIED VOLATILITY

Paul Glasserman () and Qi Wu ()
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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

International Journal of Theoretical and Applied Finance (IJTAF), 2011, vol. 14, issue 03, 407-432

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.

Keywords: Forward volatility; implied volatility surface; time-dependent SABR model; currency options; volatility forecasting (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (8)

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DOI: 10.1142/S0219024911006590

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