# Futures: Convergence of Spot and Futures Prices at Expiration

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.

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LESSONS

- CFA Level 2: Derivatives Part 1 – Introduction
- What are Forward Contracts?
- Equity Forward Contracts
- Fixed Income Forward Contracts
- Currency Forward Contracts
- Forward Rate Agreements (FRA)
- Credit Risk and Forward Contracts
- Introduction to Futures Contracts
- Futures: Convergence of Spot and Futures Prices at Expiration
- Futures Prices vs. Forward Prices
- Contago and Backwardation
- Pricing Stock Index Futures
- Pricing Interest Rate/Treasury Bond Futures
- Pricing Currency Futures
- Eurodollar Futures

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