Forward and Futures Prices
A
forward contract
on a security is an agreement to exchange the security at a
particular time in the future, known as the
delivery date
, at a price that is fixed at the
contract initiation date
.
The price that is fixed at the contract initiation date is called the
forward price
.
As an investor can take a long position or a short position in the forward
contract, it thus follows from the
principle of no arbitrage
that we determine the forward
price from the requirement that the cost to enter the forward contract is zero.
For
t
<
T
, let
F
t
,
T
(
S
) denote the time
t
forward price
for time
T
delivery of a share
of the stock
S
.
(
t
is the contract initiation date and
T
is the delivery date.)
By the
Fundamental Theorem of Asset Pricing
,
F
t
,
T
(
S
) is the quantity that satisfies the equation
0
=
()d
E[
T
t
rs s
t
e
{
S
(
T
)
F
t
,
T
(
S
)}]
=
T
t
t
e
S
(
T
)]
T
t
t
e
F
t
,
T
(
S
)]
=
T
t
t
e
S
(
T
)]
T
t
t
e
]×
F
t
,
T
(
S
),
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This note was uploaded on 04/01/2012 for the course 22S 175 taught by Professor Tang,q during the Spring '08 term at University of Iowa.
 Spring '08
 Tang,Q

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