Lesson 2 of 6 · 13 min

Replicating a forward commitment

A forward can be rebuilt from the underlying plus risk-free borrowing or lending, so its price must equal the spot price grown at the risk-free rate.

In short

Replication recreates a derivative's cash flows with the underlying and borrowing or lending at the risk-free rate.
Long forward = borrow the spot price at r and buy the asset. Short forward = short-sell the asset and lend the proceeds at r.
Both routes give $S_T - F_0(T)$ at T only if $F_0(T) = S_0(1+r)^T$ : the no-arbitrage forward price for an asset with no other costs or benefits.
Long asset + short forward = a risk-free position that earns exactly r. Financed with a loan at r, it earns zero.
Replication is used when the law of one price holds: to price, mirror or offset a derivative position.

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