Pricing Barrier Options on Forwards and Commodity Futures

# Valuation of FX vs. Commodities Barrier Options


# Valuation of FX vs. Commodities Barrier Options












With reference to my previous question about the computation of a barrier option delta, @LocalVolatility referenced a nice closed form solution to value barrier options on a stock paying a dividend yield. Out of curiosity, I wonder wether this model could "be abused" to value a similar barrier option on a commodities future? To value an FX option I would simply exchange the dividend yield with the foreign exchange rate.

Let's say I want to value an option on some commodites future, I understand that for a Vanilla option I could use the Black model (which is related to the Garman Kohlhagen model). The thought was, could I possibly "abuse" the model above to value a respective barrier option on a commodities future? My "idea of abusal" here would be, given the future, to extract the spot from the future via the interest rate parity relation and use this as input to the model. I know this is really vague, especially since it ignores things like storage costs in the cost of carry, just wondering?

EDIT

As mentioned in a comment below, I wonder wether I could also just exchange the dividend yield for the risk free rate and then price on the future. Intuitively, I got the idea from the derivation of the Black model, but I'm not sure at all.

## Answer by LocalVolatility (score 1, accepted)

https://quant.stackexchange.com/a/32704

If I understand your question correctly, then you have a barrier option pricer for spot model dynamics of the form

\begin{equation} \mathrm{d}S_t = (r - \delta) S_t \mathrm{d}t + \sigma S_t \mathrm{d}W_t. \end{equation}

Now you are wondering whether you can abuse the input parameters in a way such as to use the same model to price options on a forward contract. Normally, the forward dynamics under the Black-Scholes model are given by

\begin{equation} \mathrm{d}F_t = \sigma F_t \mathrm{d}W_t. \end{equation}

You could thus set $S_0 = F_0$ and $\delta = r$ in your model and get the correct price.

## Answer by Nivel Egres (score 1)

https://quant.stackexchange.com/a/32702

I assume you mean a barrier option on a futures contract? It's not a straight forward thing to do analytically because of the Samuelson effect (futures tend to ramp up in volatility as they approach maturity). Most people build a dedicated vol surface for the futures contract and use a local vol based solution.