A
forward contract is an agreement between two parties
to buy or sell an asset (which can be of any kind) at
a preagreed future point in time. Therefore, the trade
date and delivery date are separated. It is used to control
and hedge risk, for example currency exposure risk (e.g., forward
contracts on USD or EUR) or commodity prices (e.g., forward
contracts on oil).
One
party agrees (obligated) to sell, the other to buy, for
a forward
price agreed in advance. In a forward transaction,
no actual cash changes hands. If the transaction is collateralized,
exchange of margin will take place according to a preagreed
rule or schedule. Otherwise no asset of any kind actually
changes hands, until the maturity of the contract.
The
forward price of such a contract is commonly contrasted
with the spot price, which is the price at which the asset
changes hands (on the spot date, usually two business
days). The difference between the spot and the forward
price is the forward premium or forward discount.
A
standardized forward contract that is traded on an exchange
is called a futures contract.
Example
of how the payoff of a forward contract works
Suppose
that Bob wants to buy a house in one year's time. At the
same time, suppose that Andy currently owns a $100,000
house that he wishes to sell in one year's time. Both
parties could enter into a forward contract with each
other. Suppose that they both agree on the sale price
in one year's time of $104,000 (more below on why the
sale price should be this amount). Andy and Bob have entered
into a forward contract. Bob, because he is buying the
underlying, is said to have entered a long forward contract.
Conversely, Andy will have the short forward contract.
At
the end of one year, suppose that the current market valuation
of Andy's house is $110,000. Then, because Andy is obliged
to sell to Bob for only $104,000, Bob will make a profit
of $6,000. To see why this is so, one needs only to recognize
that Bob can buy from Andy for $104,000 and immediately
sell to the market for $110,000. Bob has made the difference
in profit. In contrast, Andy has made a loss of $6,000.
Example
of how forward prices should be agreed upon
Continuing
on the example above, suppose now that the initial price
of Andy's house is $100,000 and that Bob enters into a
forward contract to buy the house one year from today.
But since Andy knows that he can immediately sell for
$100,000 and place the proceeds in the bank, he wants
to be compensated for the delayed sale. Suppose that the
risk free rate of return R (the bank rate) for one year
is 4%. Then the money in the bank would grow to $104,000,
risk free. So Andy would want at least $104,000 one year
from now for the contract to be worthwhile for him  the
opportunity cost will be covered.
Bob,
as any other buyer would, will seek the lowest price he
can for the contract  although as we've seen, there is
an invisible lower limit of $104,000 that Andy will not
go below. As a result, the contract price would be at
least $104,000 or it will not happen at all.
Rational
pricing
If
S_{t}
is the spot price of an asset at time t,
and r is the continuously compounded rate, then the forward
price must satisfy F_{t,T} = S_{t}e^{r(T
âˆ’ t)}.
To
prove this, suppose not. Then we have two possible cases.
Case
1: Suppose that F_{t,T} > S_{t}e^{r(T
âˆ’ t)}. Then an investor can execute
the following trades at time t:
 go
to the bank and get a loan for S_{t} at the continuously compounded
rate r;
 with
this money from the bank, buy one unit of stock for
S_{t};
 enter
into one short forward contract costing 0. A short forward
contract means that the investor owes the counterparty the stock
at time T.
The
initial cost of the trades at the initial time sum to
zero.
At
time T the investor
can reverse the trades that was executed at time t.
Specifically, and mirroring the trades 1., 2. and 3. the
investor
 '
repays the loan to the bank. The inflow to the investor
is âˆ’ S_{t}e^{r(T
âˆ’ t)};
 '
sells the stock for S_{T}. The cash inflow to the investor
is now S_{T}.
 '
settles the short forward contract by receiving S_{T} from the buyer; there is an
inflow of funds to the investor of F_{t,T} âˆ’ S_{T}.
The
sum of the inflows in 1.', 2.' and 3.' equals F_{t,T} âˆ’ S_{t}e^{r(T
âˆ’ t)}, which by hypothesis, is positive.
This is an arbitrage profit. Consequently, and assuming
that the nonarbitrage condition holds, we have a contradiction.
This is called a cash and carry arbitrage because you
"carry" the stock until maturity.
Case
2: Suppose that F_{t,T} < S_{t}e^{r(T
âˆ’ t)}. Then an investor can do the
reverse of what he has done above in case 1. But if you
look at the convenience yield page, you will see that
if there are finite stocks/inventory, the reverse cash
and carry arbitrage is not always possible. It would depend
on the elasticity of demand for forward contracts and
such like.
Extensions
to the forward pricing formula
Suppose
that FV_{T}(X) is the time value
of cash flows X at the contract expiration time T. The forward price is then given by the formula:

The
cash flows can be in the form of dividends from the asset,
or costs of maintaining the asset.
If
these price relationships do not hold, there is an arbitrage
opportunity for a riskless profit similar to that discussed
above. One implication of this is that the presence of
a forward market will force spot prices to reflect current
expectations of future prices. As a result, the forward
price for nonperishable commodities, securities or currency
is no more a predictor of future price than the spot price
is  the relationship between forward and spot prices
is driven by interest rates. For perishable commodities,
arbitrage does not have this
The
above forward pricing formula can also be written as:
 F_{t,T}
= (S_{t} âˆ’ I_{t})e^{r(T
âˆ’ t)}
Where
I_{t}
is the time t value of all cash flows over the life of
the contract.
Theories
of why a forward contract exists
Allaz
and Vila (1993) suggest that there is also a strategic
reason (in an imperfect competitive environment) for the
existence of forward trading, that is, forward trading
can be used even in a world without uncertainty. This
is due to firms having Stackelberg incentives to anticipate
their production through forward contracts.
See
also
References
 John
C. Hull, (2000), Options, Futures and other Derivatives,
PrenticeHall.
 Keith
Redhead, (31 Oct 1996), Financial Derivatives: An Introduction
to Futures, Forwards, Options and Swaps, PrenticeHall
 Abraham
Lioui & Patrice Poncet, (March 30, 2005), Dynamic
Asset Allocation with Forwards and Futures, Springer
Further
reading
 Allaz,
B. and Vila, J.L., Cournot competition, futures markets
and efficiency, Journal of Economic Theory 59, 297308.