Fitting Sparse Commodity Option Volatility Surfaces

Summary

The document describes a practical challenge in fitting an oil options volatility surface when market data are uneven across maturities. Near-dated contracts are liquid and screen-based, while longer-dated quotes are broker-based. At-the-money levels toward the back of the curve are relatively accessible, but skew observations are sparse and inferred mainly from structures such as spreads, ratios, and fences. The author asks how to incorporate those observations for vanilla options without modeling volatility dynamics.

The proposed intuition is to regularize the fit with market-shape assumptions, including a flattening skew at longer maturities, and smoothness constraints; a two-stage procedure is also considered. The document supplies no fitted surface, algorithm, empirical comparison, or evidence that these constraints guarantee an arbitrage-free result. Any implementation would need to address quote quality, instrument conventions, and consistency constraints, which are not detailed here.

Key ideas

• Oil option volatility data are more liquid near term than at longer maturities.
• At-the-money levels are easier to estimate at the back end than volatility skew.
• Spreads, ratios, and fences provide sparse information about longer-dated skew.
• Smoothness and a flattening-skew assumption are proposed as possible fitting constraints.
• The document asks about a two-stage fitting approach but does not specify or validate one.

Tags

# Volatility surface fitting, interpolation and extension from sparse data


# Volatility surface fitting, interpolation and extension from sparse data












There are some nice papers about constrained spline fitting essentially giving you a smoothing and arb free surface. I am focusing on the oil market here: The market is essentially split in a very liquid screen based front part (about 1yr out) and a broker based back end. Far end atm prices are fairly easy to get/guess, but the skew less so. Skew information comes mainly through spreads, ratios and fences giving you spares data there. I was wondering if there is an elegant way to make use of that data? This is purely about vanillas, so no fancy vol dynamic required.

Intuitively, you'd probably have to force a fit using stylised facts like a flattening skew and smoothness constraints. Maybe a two step procedure would be best? Any suggestions welcome.

Thank you

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