Pricing and Valuation of Interest Rates and Other Swaps

How an interest rate swap relates to a series of forward rate agreements, how its price (the par swap rate) is solved from zero rates and implied forward rates, why issuers and investors prefer swaps, and how a swap's value starts at zero and then moves with periodic settlements, the passage of time and changes in expected forward rates.

1. 1. Swaps versus a series of forward rate agreementsAn interest rate swap is like a strip of FRAs on consecutive periods, except that every period uses one constant fixed rate instead of a different implied forward rate for each period.Free12 min
2. 2. Pricing a swap: the par swap rateThe swap's price is the par swap rate: the single fixed rate at which the present value of the fixed payments equals the present value of the expected floating payments, with floating payments expected at the implied forward rates.Video · 5 min14 min
3. 3. Why issuers and investors use swapsSwaps let issuers transform the interest rate profile of their debt and let investors change portfolio duration without trading bonds, because a receive-fixed swap behaves like a long fixed-rate bond and a pay-fixed swap like a short one.12 min
4. 4. Swap price versus swap valueA swap's price is its fixed swap rate, set once at inception; its value starts at zero and, on any settlement date, equals the current settlement plus the present value of all remaining expected settlements.Video · 5 min13 min
5. 5. How swap values change: time, rates and credit exposureAfter inception a swap's value drifts as settlements are made along a sloped forward curve and jumps when expected forward rates change: higher forwards help the fixed payer, lower forwards help the fixed receiver.13 min
6. 6. Integrated cases: a treasury desk's futures and swap hedgesA treasury case chains a pricing step to a risk step: price the futures contract with its storage cost and locate the margin call, then choose and size a forward-starting swap, then say what can and cannot be known about a swap's value.15 min