Swaps Swaptions

Section: Swaps and Swaptions Estimated study time: 60 minutes Content: An interest rate swap is an agreement between two counterparties to exchange a series of fixed cash flows for a series of floating cash flows (or vice versa) based on a notional principal amount. The notional is not exchanged — only the net interest differential is paid. In a plain vanilla interest rate swap, one party pays a fixed rate (the swap rate) and receives a floating rate (such as SOFR), while the counterparty does the opposite. The fixed rate that makes the swap have zero net present value at initiation (fair market value = 0) is called the par swap rate. At Level 2, candidates must price swaps by equating the present value of the fixed payments to the present value of the floating payments using the current spot rate curve. Swap pricing uses the no-arbitrage principle. The floating leg of a swap has a known present value — the first floating payment is set in advance (the current reference rate), and because the notional is returned (hypothetically) at the end, the floating leg's value always equals par at each reset date. Therefore: PV(fixed leg) = PV(floating leg) = par (at initiation). The fixed swap rate (c) is determined by: Sum [c / (1+z_t)^t] + [1/(1+z_T)^T] = 1, where z_t are the spot rates for each payment period. Solving: c = (1 - 1/(1+z_T)^T) / Sum[1/(1+z_t)^t]. This is analogous to setting a bond's coupon so it prices at par, where the coupon rate equals the par yield (which equals the swap rate for equivalent maturities). After initiation, a swap's value changes as interest rates change. The value of…