Why Forward Contract Value Is Discounted Before Maturity

Summary

The exchange explains the discount factor in the value of a forward contract on an asset that pays no income. The contract’s delivery price is fixed when the agreement is initiated, while the forward price can change over time. Their difference represents the contract’s payoff at the delivery date, not an amount received immediately.

To express that future payoff as a value at an earlier time, discount it at the risk-free rate over the remaining life of the contract. The response’s central point is about timing: comparing the current forward price with the agreed delivery price gives a maturity-date amount, and present valuation requires converting that amount to today’s value. The brief answer assumes the stated no-income asset setup and does not discuss other contract features, such as interim cash flows, credit risk, or market frictions.

Key ideas

• The forward price and fixed delivery price determine a payoff at the contract’s maturity.
• A maturity-date payoff must be discounted to express its value at an earlier date.
• The discount period is the time remaining until delivery.
• The explanation assumes a non-income-paying asset and omits credit risk and market frictions.

Tags

# Why is the value of a forward contract discounted to the present value?


# Why is the value of a forward contract discounted to the present value?












I'm not sure if this question has been asked before, but it's a simple one. Let's consider a Forward contract on a non-income paying investment asset. We know that the Forward price on such an asset is given by:

$K=S_oe^{rT}$

which we can get through no-arbitrage arguments. Suppose this contract were entered into today, at $t=0$ and is concluding at time $t=T$. Then, the value of the Forward contract at any time $t$ between $t=0$ and $t=T$ is given by:

$f=(F_o-K)e^{-r(T-t)}$

What I don't understand is why the $e^{-r(T-t)}$ part is included into the equation? Since $K$ of the forward contract is a fixed price that was negotiated when the contract was entered into (i.e at time $t=0$), shouldn't we just compare it with the Forward Price of the asset (and not discount it)?

## Answer by dm63 (score 3)

https://quant.stackexchange.com/a/40358

Because the amounts $F_0$ and $K$ are both paid at time $T$. So you know this contract will be worth $F_0 - K$ at time $T$, but if you want to know what it is worth at time $t$ you have to discount it.

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