# Up-front settlement of forward contract

One has entered a forward contract to purchase oil at $F_{t,T} = S_{t}e^{(r_f + s - c)(T-t)}$. The contract is entered at time $t$ and executed at time $T$.

Where:
$S_{t}$ is the spot price at time $t$
$r_{f}$ is the risk free rate
$s$ are the storage costs
$c$ is the convenience yield

How would one calculate the price at which one would settle the forward upfront (at time $t$)?

The question: at what rate would you discount the forward price to determine the "upfront settlement price" i.e. the price settled today to take future delivery of the oil.

I initially thought of using a CAPM model to determine the risk of the underlying. However in both the classic forward and the "upfront settled" forward one is exposed to changes in the oil price, so this wouldn't make sense.

I then thought you could discount at the forward rate, but then one would settle at spot at time $t$ and I suppose one would rather then just buy the underlying?

Any ideas on the best approach would be much appreciated!