Swaps: Interest Rate and Currency Swaps for Actuaries

Interest Rate Swaps

In a plain vanilla interest rate swap, two parties exchange interest payments on a notional principal: one pays a fixed rate and receives a floating rate, and the other does the opposite. No principal is exchanged. The fixed rate (swap rate) is set so the swap has zero value at inception.

The swap rate R satisfies: R * sum(v^t) = sum(f_t * v^t), where f_t are the forward rates and v^t are discount factors. Equivalently, R = (1 - v^n) / sum(v^t for t = 1 to n). On Exam FM, you may be asked to compute the swap rate given a term structure of spot or forward rates.

Valuing a Swap

After inception, as rates change, the swap acquires positive value for one party and negative value for the other. The value of the fixed-rate payer's position is the present value of floating payments minus the present value of fixed payments. A swap can be decomposed into a portfolio of forward contracts (forward rate agreements) or into a long position in a floating-rate bond minus a short position in a fixed-rate bond.

Currency Swaps

A currency swap exchanges principal and interest payments in two different currencies. Unlike interest rate swaps, the principal amounts are exchanged at inception and at maturity. The exchange rate at inception is the current spot rate. On Exam FM, currency swaps combine interest rate calculations with exchange rate conversions. The key principle is the same: the swap rate is set so the initial value is zero, which requires computing present values in each currency using the respective interest rates.