Forward Contract Value Versus Forward Price in a Binomial Model
Summary
The document clears up a common binomial-pricing confusion: a forward’s market price and the value of an existing forward contract are different quantities. A binomial calculation that discounts expected future payoffs is valuing a contract with specified terms; its result does not mean a newly entered forward requires an upfront payment. At inception, the delivery price is set so the contract’s value is zero.
The explanation uses a simple example: agreeing to buy an asset for 100 has zero value if the market forward price remains 100, but becomes valuable to the buyer if the market price rises to 110. The buyer can purchase for less than the asset’s then-current forward price. This illustrates how contract value changes after inception. The post does not provide a full derivation of the binomial model or discuss practical complications such as dividends, financing conventions, or differences between forwards and futures.
Key ideas
- A forward price specifies the agreed delivery price for a future transaction.
- The value of a forward contract depends on its terms relative to current market prices.
- A newly initiated forward is structured to have zero initial value.
- An existing long forward gains value when the market forward price rises above its agreed delivery price.
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# Confusion in forward contract pricing on a stock using the binomial model
# Confusion in forward contract pricing on a stock using the binomial model
In the financial engineering course I am taking we are studying how to use the binomial model to price derivatives, one of which is the forward. For this question it is related to a forward contract on a stock.
At time $t = T$ the forward contract is equal to the value of the underlying at time $T$. From there we can work backwards using the following formula:
$F_t = \frac{1}{R}[q * F_u + (1 - q) * F_d]$
Where $R$ is the interest rate, $Q = {q, 1-q}$ are the risk-neutral probabilities, and $F_u$ and $F_d$ are the next period's up and down price for the forward, respectively.
If we work this back in the lattice to $T = 0$ we get a price of some kind. See the example image below:
This is the pricing for a futures contract on an underlying stock that is priced using the binomial model.
Where I am confused is that in order to derive the price of a forward or a future we know that at $t = 0$ the contract must be worth $0$. Intuitively this is because you don't "purchase" a forward. You just agree to be beholden to it. This is unlike an option, where the counterparty will get some kind of premium for taking on the risk.
But this binomial model clearly shows at $t = 0$ it's worth something! What does the number at $t = n$ represent here in the binomial pricing model?
## Answer by AlRacoon (score 2)
https://quant.stackexchange.com/a/38540
You are confusing forward price and valuation of the forward contract. If you agree to buy something at 100 sometime in the future, the forward or future price is 100. If the future price is still 100, the value of that forward is 0 to you. If the future price goes to 110, the value of the forward to you is 10--since you and your counterparty agreed to transact at $100, you will get something worth 110 for 100.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.