International Finance: Putting Theory Into Practice

4.7. APPENDIX: THE FORWARD FORWARD AND THE FORWARD RATE AGREEMENT 161

Figure 4.6:Spot and Forward Money Markets (with International Links)

HCT 2 FCT 2

HCT 1 FCT 1

HCt FCt

1

1+rt,T 1 1 +rt,T^1

1

1+r∗t,T 1 1 +r

t,T∗

1

1

1+rft,T 1 ,T 2 1 +r

f

t,T 1 ,T 2

1

1+rf,t,T∗ 1 ,T 2 1 +r

f,∗

t,T 1 ,T 2







?

6 6

?

?

6 6

?

?

6 6

?

1

1+rt,T 2 1 +rt,T^2

1

1+r∗t,T 2 1 +r

t,T∗

2

As in the case of currency forwards, no causality is implied by our way of express-
ing Equation [4.48]. The three rates are set jointly and have to satisfy Equation
[4.48], that’s all. As in Chapter 4, one could argue that causality, if any, may run
from the forward interest rate towards the spot rate because the forward rate reflects
the risk-adjusted expectations about the future interest rate. We shall use Equation
[4.48] when we discuss eurocurrency futures, in the Appendix to Chapter 6.

There is an obvious no-arbitrage version of this. In Figure 4.6 we combine two of
our familiar spot-forward currency diagrams, one for future dateT 1 and the other
for dateT 2. The focus, this time, is not on the exchange markets, so the horizontal
lines that refer to currency deals are made thinner. The forward deposits and
loans are shown as transactions that transformT 1 -dated money intoT 2 money (the
deposit) or vice versa (the loan), and the multiplication factors needed to compute
the output from a transaction, shown next to the arrows, are (1 +rf) and 1/(1 +rf),
respectively. This diagram shows that every spot or forward money-market deal can
be replicated, which helps you in shopping-around problems. The diagram also helps
identifying the no-arb constraints.

DoItYourself problem 4.9
We have already shown how to replicate thet-to-T 2 deposit. In the table below, add