Lesson 2 of 6 · All lessons in this module
- Arbitrage and the law of one priceVideo lesson
- Replicating a forward commitmentVideo lesson
- Exploiting a mispriced forward, and the role of r and T
- The cost of carry: income and costs of owning the underlyingVideo lesson
- Commodities, convenience yield and carry by asset classVideo lesson
- FX forwards: carry as an interest rate differential
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 at T only if : 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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