Smile-Consistent Analysis of Crude Oil Spread Options

We present an empirical study of the Bachelier implied volatility smile for spread options on crude oil futures. It is known that the at-the-money (ATM) spread implied volatility is simply related to the futures prices and volatilities and their correlation. Assuming that the underlying futures prices follow correlated local volatility models, it was shown recently that a similar relation holds for the ATM spread skew. Using market data from CME Group, we present tests of the spread skew predictions for WTI 1M Calendar Spread Options (CSO) and WTI–Brent crude oil spread options. The predictions are in good qualitative agreement with market data for strikes sufficiently close to the ATM point.