Extrapolating Implied Volatility Beyond the Market Surface

Summary

The note describes a volatility surface calibrated with singular value decomposition, comparing current implied volatilities with a previous surface. For maturities without market quotes, the author extrapolates at-the-money volatility using forward variance. This can amplify the movement seen in the last observable maturities: a decline there may produce a larger move at an intermediate long maturity before regularization pulls the surface back toward its initial state.

The author reports that this can create uneven maturity patterns, while disabling extrapolation when consensus data is available gives better results. The evidence is a practical observation rather than a quantified comparison. The note does not specify the calibration objective, regularization strength, or alternative extrapolation methods, and it poses a question about other approaches rather than recommending a settled method.

Key ideas

• Forward variance can be used to extrapolate at-the-money implied volatility where longer-dated quotes are unavailable.
• The extrapolation may amplify recent volatility moves at some maturities before regularization draws the surface back toward its initial shape.
• The resulting maturity profile can be uneven, with larger changes at an intermediate tenor than at shorter or longer tenors.
• The author observes better results when consensus data is available and extrapolation is turned off.

Tags

# Best way to extrapolate on implied volatility


# Best way to extrapolate on implied volatility












I am doing some standard svd calibration to mark market implied vols in difference to a previous volatility surface.

For longer term maturities where there is no market data, I am extrapolating ATM using forward variance which leads to very high moves compared to consensus data. Exact behavior will be: if my last observable vols are peaking down, I will have an amplification of that move before eventually coming back to the init volatility surface thanks to regularization constraints. So I can have small moves on the first 2Y big move on 3Y and small moves again on 5Y.

When there is consensus data available I usually shut down the extrapolation and the results are much better. Have any of you used different methods for extrapolating volatilities ?

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