- Introduction: A Simple Market Model 11
1.5 Forward Contracts........................................
Aforward contractis an agreement to buy or sell a risky asset at a specified
future time, known as thedelivery date,forapriceF fixed at the present
moment, called theforward price. An investor who agrees to buy the asset is
said toenter into a long forward contractor totake a long forward position.If
an investor agrees to sell the asset, we speak of ashort forward contractor a
short forward position. No money is paid at the time when a forward contract
is exchanged.
Example 1.5
Suppose that the forward price is $80. If the market price of the asset turns out
to be $84 on the delivery date, then the holder of a long forward contract will
buy the asset for $80 and can sell it immediately for $84, cashing the difference
of $4. On the other hand, the party holding a short forward position will have
to sell the asset for $80, suffering a loss of $4. However, if the market price of
the asset turns out to be $75 on the delivery date, then the party holding a
long forward position will have to buy the asset for $80, suffering a loss of $5.
Meanwhile, the party holding a short position will gain $5 by selling the asset
above its market price. In either case the loss of one party is the gain of the
other.
In general, the party holding a long forward contract with delivery date 1
will benefit if the future asset priceS(1) rises above the forward priceF.If
the asset priceS(1) falls below the forward priceF, then the holder of a long
forward contract will suffer a loss. In general, the payoff for a long forward
position isS(1)−F (which can be positive, negative or zero). For a short
forward position the payoff isF−S(1).
Apart from stock and bonds, a portfolio held by an investor may contain
forward contracts, in which case it will be described by a triple (x, y, z). Here
xandyare the numbers of stock shares and bonds, as before, andzis the
number of forward contracts (positive for a long forward position and negative
for a short position). Because no payment is due when a forward contract is
exchanged, the initial value of such a portfolio is simply
V(0) =xS(0) +yA(0).At the delivery date the value of the portfolio will become
V(1) =xS(1) +yA(1) +z(S(1)−F).