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!

1 Answer

Normally you enter a forward with strike equal to the current forward price, there is no upfront settlement. If the contract does have an initial value (e.g. because the strike is zero) you do settle upfront, you discount the future cash flow to today. The discounting rate depends on your cost of funding and the price of credit risk.

• Thank you for your reply, much appreciated! The scenario sketched in the question may seem a bit arbitrary (apologies), but the question is trying to determine at what rate would you discount if you were to settle the full forward price at inception of the contract. Not the difference between the market price and the forward (the initial value is zero for the forward). In other words the question is asking what discount one should received on the forward price for a "paying now to receive the oil later" deal. Perhaps discounting at risk free due to the opportunity cost? Commented Jul 26, 2017 at 23:40
• The textbook answer here used to be the riskfree rate, which comes up from replication arguments. However, things have evolved to take things like credit risk and cost of funding into account. E.g. suppose I'm a bank and we enter into a forward with strike zero and we don't have any csa in place. That's like me extending you a loan. And banks typically don't extend loans that at the risk free rate...
– Bram
Commented Jul 27, 2017 at 20:52