Upfront Valuation of a Forward Contract with Funding and Credit Risk

Summary

The post asks how to price an oil forward that requires payment at inception rather than following the usual zero-value-at-entry convention. The stated forward price incorporates spot, the risk-free rate, storage costs, and convenience yield. The reply distinguishes a standard forward, whose delivery price is set to the current forward price and therefore requires no upfront payment, from a contract that has an initial value because its delivery terms differ, such as a zero strike.

For a contract with a future cash flow and nonzero initial value, the response says to discount that cash flow to today. It does not prescribe a universal discount rate: the relevant rate depends on the trader’s funding cost and the price of credit risk. This frames the issue as valuation of a specific contract cash flow rather than applying CAPM to the underlying commodity’s price risk. The answer is concise and provides no numerical worked example or detailed treatment of collateral, counterparty exposure, or commodity delivery conventions, so those details require separate specification.

Key ideas

• A standard forward is commonly entered at zero value by setting its delivery price to the current forward price.
• A contract with nonzero initial value requires valuing its future cash flow at inception.
• Discounting should reflect funding costs and the price of credit risk.
• Commodity price exposure alone does not determine the appropriate discount rate.

Tags

# Up-front settlement of forward contract


# 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!

## Answer by Bram (score 1, accepted)

https://quant.stackexchange.com/a/35300

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.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.