Investments, tenth edition

A: Two forward contracts, each

priced independently

$1.992

$1.955

£1

£1

B: Two-year swap agreement

$1.974

$1.974

£1

£1

 Figure 23.8 

Forward contracts versus swaps  

820

P A R T   V I

  Options, Futures, and Other Derivatives

where  y  

1

  and  y  

2

  are the appropriate yields from the yield curve for discounting dollar cash 

flows of 1- and 2-year maturities, respectively. In our example, where we have assumed a 

flat U.S. yield curve at 5%, we would solve   

1.992

1.05

1

1.955

1.05

2

5

F*

1.05

1

F*

1.05

2

 

which implies that  F *   5  1.974. The same principle would apply to a foreign exchange 

swap of any other maturity. In essence, we need to find the level annuity,  F *, with the same 

present value as the stream of annual cash flows that would be incurred in a sequence of 

forward rate agreements. 

 Interest rate swaps can be subjected to precisely the same analysis. Here, the forward 

contract is on an interest rate. For example, if you swap LIBOR for a 7% fixed rate with 

notional principal of $100, then you have entered a forward contract for delivery of $100 

times LIBOR for a fixed “forward” price of $7. If the swap agreement is for many periods, 

the fair spread will be determined by the entire sequence of interest rate forward prices 

over the life of the swap.