These are contracts where the buyer/ holder of the contract agrees to purchase while the seller / writer of the contract agrees to deliver a specified asset at some future specified time (the exact delivery date is not specified only the delivery month) for a predetermined delivery price. As in the case of forward contracts both parties to the contract are obligated to perform on the transaction.
These contracts are standardized and tradable on organized exchanges. Also, they are subject to daily settlements (marked to market) and margin requirements that help to minimize the contract’s exposure to credit risk.
Margins are amounts that are deposited with the broker by both parties. There is an initial margin that is kept with the broker at the origination of the contract and a maintenance margin which is lower than the initial margin. If this latter margin is breached a margin call is generated that requires the given party to deposit additional margin (known as the variation margin) to restore it to the initial level. If the party does not comply his position in the contract and account with the broker could be terminated.
All gains and losses to the account are charged to the parties’ margin accounts on a daily basis which in effect is the daily settlement or marked to market process of the contract.
Future contracts are usually used to hedge an company’s exposure to the price of an asset.
The price on a futures contract is equal to the price on a forwards contract if the risk free rate is constant and same for all maturities and both contracts have the same delivery date.
In theory, when interest rates fluctuate a lot this relationship breaks down. For example if the underlying asset is positively correlated with interest rates, a forward contract would be unaffected by any short term fluctuations in interest rates since there is no daily settlement. However a long future contract would move with the interest rates (rates go up, asset goes up, the resulting daily gains will be invested at a higher interest rate hence the value of the future contract goes up and vice versa). As a result, when the price of the underlying asset is positively correlated with interest rates, future prices are higher than forward prices. When the price of the underlying asset is negatively correlated with interest rates, future prices are lower than forward prices.
In practice, differences between the two prices arise because of taxes, transaction costs, margin treatment, varying degrees of counterparty default risk, liquidity and marketability of the contract, etc.
Stock Index futures
These futures are used to offset the exposure to a well diversified equity portfolio, in particular the systemic risk associated with the portfolio.
The futures price of stock indices with known yield is as follows:
Futures contracts on currencies
The futures price a currency is as follows:
Where F0 is the futures price in local currency of one unit of foreign currency
S0 is the current spot price in local currency of one unit of foreign currency
r is the domestic risk free rate
rf is the foreign risk free rate
Futures contracts on commodities
The futures price of a commodity with no storage cost or income is as follows:
The futures price of a commodity with storage cost and income is as follows:
Where U is the discounted value of the storage costs net of income during the life of the futures contract.
Interest Rate Futures
Treasury Bond Futures
The US government bonds delivered under this futures contract should have more than 15 years to maturity on the first day of the delivery month and should not be callable for 15 years from this date with par value of $100,000.
Treasury Note Futures
The US government bonds/ notes delivered under this futures contract should have between 6.5 to 10 years to maturity with par value of $100,000.
5-year Treasury Note Futures
The US government bonds/ notes delivered under this futures contract should have between 4 to 5 years to maturity with par value of $100,000.
Treasury Bill Futures
The US government Treasury bills delivered under this futures contract have 3-months left to maturity with a face value of $1 million.
Futures Price for Treasury Bond futures contracts
Where I is the present value of the coupons during the life of the contract discounted at the risk free rate.
The underlying instrument on these contracts is the 3-month Eurodollar Certificate of Deposit which earns a fixed interest rate related to the US LIBOR. The face value of the contract is $1 million. These futures allow the investor to lock into an interest rate for a future period. Unlike the other future contracts mentioned above the settlement doesn’t involve delivery of the underlying instrument but cash. Also unlike forward rate agreement the Eurodollar contract is settled daily and the settlement amount reflecting the observed interest rate is made at the beginning of the period but without discounting.