Futures: Convergence of Spot and Futures Prices at Expiration

This lesson is part 9 of 15 in the course Derivatives Part 1

Given that futures contracts are standardized modifications on forward contracts, the same pricing formula and arbitrage relationship applied.

Futures Price: f₀(T) = [S₀ – PV(CF)](1+r)^T

Futures Price (alternative formula): f₀(T) = S₀(1+r)^T – FV(CF)

A lower case “f” notation distinguishes futures from forwards (“F”).

At the expiration of a futures contract, the futures contract price must equal the spot price of the underlying; if this is not the case then an arbitrage opportunity exists.
If the futures contract is less than the spot price of the underlying at expiration, then a trader can buy the future and sell the spot.
If the futures contract is greater than the spot price of the underlying at expiration, then a trader can buy the spot and sell the futures contract.