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Interpolating Implied Volatility Surfaces Across Tenors

Article Quant Q&A · Author: Sebastian Strauss Hansen
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Summary

The document asks how to interpolate implied volatility between listed maturities to construct a volatility surface for a Black–Scholes delta-hedging experiment. It considers bilinear interpolation and seeks guidance on methods that can fill values between observed tenors.

The answer names cubic-polynomial curvature as a simple approach and Gaussian-process interpolation as a more sophisticated alternative used by practitioners. It offers no comparison, implementation details, or evidence about accuracy, stability, or suitability for hedging. The suggestions are therefore starting points; the document does not establish which method best preserves surface behavior or hedge performance.

Key ideas

  • The task is to estimate implied volatility between observed maturities for a delta-hedging experiment.
  • Bilinear interpolation is raised as a possible basic method.
  • Cubic-polynomial curvature is suggested as a simple alternative.
  • Gaussian-process interpolation is presented as a more sophisticated practitioner approach.
  • The document gives no criteria or evidence for choosing between the methods.

Tags

OptionsVolatilityDerivatives pricingStatistics
Full text
# Volatility surface interpolation for Black-Scholes delta hedging


# Volatility surface interpolation for Black-Scholes delta hedging












A general question for interpolation method for implied volatility between tenors. I've recently stumbled accross a dataset from http://www.math.ku.dk/rolf/Svend/, and I would like to interpolate the volatility surface, in order to try and make a delta-hedge expirement. However, I was wondering what interpolation method is best to use. In general I was considering if bi-liniar interpolation is the beth methods, but does anybody have any guidance in what to use?

## Answer by Elyes Mahjoubi (score 1, accepted)

https://quant.stackexchange.com/a/63859

A cubic polynomial curvature would be the most simple one.Otherwise,many practitioners are actually using a Gaussian process interpolation,which is more sophisticated.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.