Present value for a FS 134
Suppose you want to close out a FS at time
t, t0<t<T.
At time
t
: Close out a FS by adding a FP for the same
T
.
At time
T:
Payoff from FP:
ST
-F
t,T
You will buy one unit of the underlying and pay
Ft,T
for it.
Payoff from FS:
Ft0,T
-S
T
You will sell one unit of
the underlying and receive
Ft0,T
for it.
Sum of the payoffs:
ST
-F
t,T
+F
t0,T
-S
=FT
t0,T
-F
t,T
Discounting with the risk-free rate
gives the present value for a FS:
Note:
(
)
rT
Tt
T
t
t
e
F
F
PV
−
−
=
,
, 0
()
T T T t T T T t T
rT
T
t
T
t
t
CF
S
F
F
F
PV
e
F
F
PV
=
−
=
−
=
=
−
=
−
, 0
,
, 0
, 0
, 0
0
0
Derivative securities: Forwards - Introduction