At the end of the three years, the two firms swap their notional principals.

The two firms have set the exchange rate at the current spot rate of 0.60USD/1CD for the initial swap of the notional principals and for the swap back in three years.

The only certain gain was a known currency exchange rate for the initial and final swap of the notional principals. Whether or not this was a financial gain over what could have been attained in the foreign currency markets is unknowable.

On each of the payment dates, t, the contract calls for the fixed-rate payer to pay the notional principal multiplied by a fixed proportion (1 + [pi]) H(t) to the floating-rate payer and to receive in return the notional principal multiplied by S(t).

The second enters into a portfolio of k annual survivor forward contracts, each of which requires payment of the notional principal multiplied by (1 + [[pi].sub.n]) H(n) and the receipt of the notional principal multiplied by S(n), n = 1,2,...

First, consider two parties wishing to exchange the notional principal (7) multiplied by the actual survivorship of cohorts j and k.

from which it follows that the fair value in a floating-for-floating basis swap requires one party to make payments determined by the notional principal multiplied by [S.sub.j](n) and the other party to make payments determined by the notional principal multiplied by [kappa][S.sub.k](n); [kappa] is determined at the outset of the basis swap and remains fixed for the duration of the contract.

Thus, in the case of a floating-for-floating cross-currency basis swap, on each payment date, n, one party will make a payment of the notional principal multiplied by [S.sub.j](n) and receive in return a payment of [[kappa].sub.FX] [S.sub.k](n).

Thus, if the notional principal were $1 million and the time frame were 1 year, a long position in a December futures contract at a price of [pi] = 3 percent would notionally commit the holder to pay $1.03 million multiplied by the expected size of the cohort surviving and to receive $1 million multiplied by the actual size.