Forward and Future Implied Volatility

28 Pages Posted: 9 Jul 2010 Last revised: 23 Jul 2011

See all articles by Paul Glasserman

Paul Glasserman

Columbia Business School

Qi Wu

City University of Hong Kong (CityUHK)

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Date Written: July 7, 2010


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 {Wu10} 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 Implied Volatility, Implied vol Surface, Time-dependent SABR model, FX options

Suggested Citation

Glasserman, Paul and Wu, Qi, Forward and Future Implied Volatility (July 7, 2010). International Journal of Theoretical and Applied Finance, Vol. 14, No. 03, 2011, Available at SSRN:

Paul Glasserman

Columbia Business School ( email )

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Qi Wu (Contact Author)

City University of Hong Kong (CityUHK) ( email )

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Hong Kong

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