Why Forward Contract Value Converges to Spot at Delivery
Summary
The document asks why a forward contract’s value at delivery is not simply the spot price minus the contracted delivery price. It describes the holder’s apparent ability to buy at the agreed price and immediately sell at the market price, then questions a textbook arbitrage argument that futures prices converge to spot as delivery approaches.
The key distinction is between the contract’s value and the price of the underlying asset: at delivery, the forward’s payoff to its long is the spot price less the delivery price, while the asset itself trades at spot. The question highlights how cash flows from opening or holding the contract, purchasing the asset, and making delivery must be tracked consistently. It does not include a complete resolution, worked arbitrage calculation, or discussion of contract settlement conventions, so readers should treat it as a conceptual question rather than a full derivation.
Key ideas
- At delivery, the long forward’s payoff is the difference between spot price and the agreed delivery price.
- The asset’s spot price and the value of the forward contract are distinct quantities.
- An arbitrage argument about futures and spot convergence requires consistent accounting of contract cash flows and delivery obligations.
- The document raises the pricing question but does not provide a complete resolution.
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# Why does forward price equal spot price at delivery? # Why does forward price equal spot price at delivery? Disclaimer: I understand this is a basic question that gets addressed in most 101 textbooks. Yet I have reviewed many of them not finding a satisfactory answer. Please bear with my ignorance. Suppose a forward contract enforces the parties to exchange an asset with price $K$ at the delivery date $t=T$, and suppose the spot price of that asset at $t=T$ is $L$ (so both $K$ and $L$ are constant). Then the possessor of the forward contract at $t=T$ is forced to buy the asset at price $K$, and the possessor can also sell the asset immediately to obtain $L$. That means, the possessor at time $t=T$ can immediately earn $L-K$. Therefore anyone who are to buy that future contract at $t=T$ must obviously pay $L-K$. This means that the forward contract at $t=T$ should be of price $L-K$. However, all textbooks and resources I've seen claim that the forward contract at $t=T$ should be of price $L$ instead of $L-K$. Why so? What is wrong in my argument? Another attempt I made to understand this point is by reading [1]. In section 2.3, it provides a more detailed argument: > As the delivery period for a futures contract is approached, the futures price converges to the spot price of the underlying asset. When the delivery period is reached, the futures price equals—or is very close to—the spot price. To see why this is so, we first suppose that the futures price is above the spot price during the delivery period. Traders then have a clear arbitrage opportunity: Sell (i.e., short) a futures contract Buy the asset Make delivery. But when I carry the cash flow out, I can't make that balance. First, selling a future contract yields a flow `(-1 * future) + (+1 * future-price-at-time-T)`. Second, buying the asset yields a flow `(+1 * asset) + (-1 * spot-price-at-time-T)`. Third, making delivery yields a flow `(-1 * asset) + K`. The net balance of three flows is ``` + 1 * future-price-at-time-T - 1 * spot-price-at-time-T - 1 * future + K ``` I can't tell why if `+ 1 * future-price-at-time-T - 1 * spot-price-at-time-T > 0` then there is an arbitrage opportunity. Thanks for your patience and sharing. #### Reference - [1] Options, Futures, and Other Derivatives by John C. Hull
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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.