Example

Commodity Futures Options

Crude oil April 2018 implied vol surface fitted with C9 vs strike, second expiry — bias-free fit across all listed strikes
Crude oil April 2018 implied vol surface fitted with C9 vs strike, fourth expiry — bias-free fit across all listed strikes
Crude oil April 2018 implied vol surface fitted with C9 vs strike, fifth expiry — bias-free fit across all listed strikes
Crude oil April 2018 total variance plot in log moneyness — curves non-intersecting, confirming no calendar arbitrage

Just like for equity and index options, our robust fitter allows easy and fast calibration of tradable volcurves for futures options. In fact, one of our first clients has been trading crude options off our volcurves since early 2016.

Here we show fits for a couple of expiries on a snapshot of the market. Note that there are a lot of strikes and all expiries can be fitted well with the C9 curve.

The volsurface is, off course, completely free of butterfly and calendar arbitrage. The latter is illustrated by the total variance plot.