B481/S98/NOTES/Grabbe-5 FORWARDS, SWAPS, AND INTEREST ...

First, consider borrowing dollars. We have the following:
Sa = US$ .4438/DM
Fb = US$.4450/DM
ia = 10 13
= ( 10. 8125) percent
ib* = 5 7
16
8
( = 5 . 875) percent
1
If we borrow
= 1
dollars, convert them
[ 1 + ia( T / 360] [ 1 + . 108125( 30 / 360) ]
at the spot rate Sa = US$.4438/DM, place them at the interest rate ib* =
5 7
8
percent, and convert the DM back to US$ at Fb = US$.4450/DM, then we
will receive [ 1 + ib∗ ( T / 360) ]
[ 1 + ia( T / 360]
Fb( t , T )
Sa( t )
=
[ 1 + . 05875( 30 / 360) ]
[ 1 + . 108125( 30 / 360) ]
. 4450
. 4438 = $.9986.
Since this is less than the US$1 that we owe, there are no profits in
arbitrage via borrowing US$.
Now, consider borrowing foreign currency. We have the following:
Sb = US$ .4428/DM
Fa = US$.4460/DM
ib = 10 11
( = 10. 6875) percent
16
ia* = 6 percent
If we borrow
1
[ 1 + ia * ( T / 360] = 1
[ 1 + . 06( 30 / 360) ]
DM, convert them at the
spot rate Sb = US$.4428/DM, place them at the interest rate ib = 10 11
percent, and convert the US$ back to DM at Fa = US$.4460/DM, then we will
[ 1 + ib( T / 360) ] Sb( t ) [ 1 + . 106875( 30 / 360) ] . 4428
receive =
[ 1 + ia ∗ ( T / 360] Fa( t , T ) [ 1 + . 06( 30 / 360) ] . 4460 = DM.9966.
Since this is less than the DM1 that we owe, there are no arbitrage profits
in arbitrage via borrowing DM.
Therefore, there are no arbitrage profits in the setting described by the
data given here.
16
14