Choosing Volatility for Options on Commodity Futures

# Commodity Option Pricing - Which implied volatility to use?


# Commodity Option Pricing - Which implied volatility to use?












I am trying to value a simple european option on ICE Brent - and I'm struggling with understanding which implied volatility to use when option expiry differs from the maturity of the underlying.

I have an implied volatiltiy surface where the option expiry lines up with maturity of the underlying (more or less). I.e. the implied volatilities in DEC26 is for the DEC26 contract etc.

For instance, say I want to value a european option on the underlying DEC26 ICE Brent contract - but with option expiry in FEB26. Which volatiltiy do I then use in practice? The one of the DEC26 (for the correct underlying contract) or do I need to calculate an adjusted one using forward volatiltiy of FEB26-DEC26 even though the FEB6 is for a completely different underlying?

## Answer by Rylan (score 0)

https://quant.stackexchange.com/a/82428

In general you'll need a model and to make assumptions. A popular assumption I've seen is to model commodity forwards as a mean reverting process, which accounts for the Samuelson effect. With this, you can have an estimate of the early expiry vol for every day from now until expiry of the Dec26 contract, and it can be completely unaffected by the Feb26 implied vol.

## Answer by QuantCalc.net (score 0)

https://quant.stackexchange.com/a/85417

We consider a European option with expiry $T_{\mathrm{opt}}=\mathrm{Feb\ 2026}$ written on the ICE Brent DEC26 futures contract, whose delivery date is $T_{\mathrm{fut}}=\mathrm{Dec\ 2026}$, with $T_{\mathrm{opt}}<T_{\mathrm{fut}}$.

Under the Black (1976) model for options on futures, the option price at time $0$ is \begin{equation} V_0 = DF(0,T_{\mathrm{opt}}) \,\mathbb{E}^{\mathbb{Q}} \!\left[ \big(F^{\mathrm{DEC26}}_{T_{\mathrm{opt}}}-K\big)^+ \right], \end{equation} where $F_t^{\mathrm{DEC26}}$ denotes the price of the DEC26 Brent future at time $t$.

The volatility input required by the model is \begin{equation} \sigma_{\mathrm{DEC26}}(0,T_{\mathrm{opt}}) = \sqrt{ \frac{1}{T_{\mathrm{opt}}} \operatorname{Var}^{\mathbb{Q}} \!\left( \ln F^{\mathrm{DEC26}}_{T_{\mathrm{opt}}} \,\big|\, F^{\mathrm{DEC26}}_0 \right) }. \end{equation} Hence the relevant quantity is the distribution of the DEC26 futures price at the option expiry.

Using the implied volatility of FEB26 futures options is incorrect, since it corresponds to a different underlying process $F_t^{\mathrm{FEB26}}\neq F_t^{\mathrm{DEC26}}$.

Using forward volatility over $[T_{\mathrm{opt}},T_{\mathrm{fut}}]$ is also incorrect. Forward volatility measures \begin{equation} \operatorname{Var} \!\left( \ln F^{\mathrm{DEC26}}_{T_{\mathrm{fut}}} - \ln F^{\mathrm{DEC26}}_{T_{\mathrm{opt}}} \right), \end{equation} which does not enter the option payoff, since the payoff is fixed at $T_{\mathrm{opt}}$.

In practice, one should use the implied volatility quoted for the DEC26 futures contract with option expiry in Feb 2026. If this volatility is not directly available, one fixes the underlying futures contract (DEC26) and interpolates the implied volatility term structure in option expiry to $T=T_{\mathrm{opt}}$.

The delivery date of the futures contract affects pricing only through the futures price itself. For a European option expiring at $T_{\mathrm{opt}}$, only the distribution of $F^{\mathrm{DEC26}}_{T_{\mathrm{opt}}}$ matters.