Fitting SVI Volatility Surfaces Across Commodity Futures Expiries

Summary

The document raises a modeling question about fitting SVI-family implied volatility surfaces to options on commodity futures. Standard SVI fitting often imposes constraints intended to prevent calendar-spread and butterfly arbitrage. The concern is that options tied to different delivery months can reference futures contracts with materially different seasonal fundamentals, as illustrated by winter and summer natural gas contracts.

The author asks whether a calendar-arbitrage constraint should link such expiries and whether fitting each expiry slice separately might be more appropriate. No answer, implementation, or empirical comparison is provided, so the document serves as a statement of a surface-construction problem rather than a resolved method. It highlights that arbitrage conditions and cross-expiry smoothing need to be considered in light of the underlying contracts’ distinct delivery exposures; it does not establish which constraints are correct for a particular commodity or dataset.

Key ideas

• SVI-family parameterizations can impose constraints aimed at avoiding calendar-spread and butterfly arbitrage.
• Commodity futures for different delivery months may have distinct seasonal fundamentals and behavior.
• The document questions whether calendar constraints should link options on different delivery contracts.
• It proposes fitting expiry slices separately as a possibility but gives no conclusion or empirical evidence.

Tags

# Vol surface fitting to options on commodity futures


# Vol surface fitting to options on commodity futures












Trying to fit variants of SVI (Zeliade method, SSVI etc) to options on futures price data. One of the core ideas of the SVI parameterization is the absence of calendar spread arbitrage.

I think the SVI fitting procedure kind of makes sense in the context of financial futures (where the basis between delivery months is mostly a function of the risk free rate). However, in commodity futures there can be a massive difference in the fundamentals/behavior along the futures curve. E.g. Natural gas in winter vs summer

Examples of fitting SVI to options on futures (see here) seem to build the forward curve using options on futures of different delivery months (because in futures there typically exists one options expiry per futures contract traded, as opposed to equities which have many expiries every month). And parameterizing SVI by penalizing for existence of calendar spread arbitrage and butterfly arbitrage.

So assume we are looking at Natural gas futures options and fitting SVI using March and April natural gas futures options. Delivery of natural gas in March is still considered a "winter" month, whereas delivery of natural gas in April is summer. Does it make sense to assume no calendar spread arbitrage between the March and April expiries (two fundamentally different underlyings) when fitting SVI? If not, then how does one fit surfaces to commodity futures options (perhaps the answer is just only fitting one slice at a time)?

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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