Arbitrage, Replication, and the Cost of Carry in Pricing Derivatives

Why no-arbitrage pins a forward price to the spot price, how a forward can be rebuilt from the underlying plus borrowing or lending, and how the cost of carry (the risk-free rate, storage costs, dividends, coupons, convenience yield or a second currency's interest rate) decides whether the forward price sits above or below spot.

1. 1. Arbitrage and the law of one pricePrices must leave no riskless profit on the table: identical cash flows must cost the same, and an asset with a known future price must trade at that price discounted at the risk-free rate.Video · 5 minFree11 min
2. 2. Replicating a forward commitmentA 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.Video · 5 min13 min
3. 3. Exploiting a mispriced forward, and the role of r and TIf a quoted forward price differs from $S_0(1+r)^T$, one replication strategy is cheaper than the other and the gap can be locked in as riskless profit.11 min
4. 4. The cost of carry: income and costs of owning the underlyingThe forward price is the spot price plus the net cost of carrying the asset to delivery: financing and other costs push it up, income and other benefits push it down.Video · 6 min13 min
5. 5. Commodities, convenience yield and carry by asset classPhysical commodities carry storage and insurance costs that raise the forward price, while a convenience yield from holding scarce stock can pull it back down.Video · 5 min11 min
6. 6. FX forwards: carry as an interest rate differentialFor currencies, the cost of carry is the gap between the two interest rates, so the FX forward rate is the spot rate grown at the price currency's rate minus the base currency's rate.12 min