Present value for a FP 133
Suppose you want to close out a FP at time
t, t0<t<T.
At time
t
: close out a FP by adding a FS for the same
T
At time
T:
Payoff from FP:
ST
-F
t0,T
You will buy one unit of the underlying and pay
Ft0,T
for it.
Payoff from FS:
Ft,T
-S
T
You will sell one unit of
the underlying and receive
Ft,T
for it.
Sum of the payoffs:
ST
-F
t0,T
+F
t,T
-S
=FT
t,T
-F
t0,T
Discounting with the risk-free rate
gives the present value for a FP:
Note:
(
)
rT
T
t
Tt
t
e
F
F
PV
−
−
=
, 0
,
()
T T t T T t T T T
rT
T
t
T
t
t
CF
F
S
F
F
PV
e
F
F
PV
=
−
=
−
=
=
−
=
−
, 0
, 0
,
, 0
, 0
0
0
Derivative securities: Forwards - Introduction