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Show how an interest rate swap works as a string of forward commitments

CFA® Level I · Derivatives · Pricing and Valuation of Interest Rate and Other Swaps · DE.1.c

The idea

A plain vanilla interest rate swap exchanges a fixed rate for a floating rate on a notional that is never itself exchanged. Each payment date can be read as a separate forward contract on the reference rate, and the swap's fixed rate is the single rate that makes the whole strip worth zero at inception. That is why a swap has no value when it is struck and acquires value afterwards as rates move: the package of implied forwards is repriced while the contracted fixed rate stays where it was.

A practice question

From the question bank, with the reason each wrong option is wrong.

What is exchanged on each payment date of a plain vanilla interest rate swap?

  1. The notional principalWhy not: The notional is a reference amount for calculating the payments and never changes hands.
  2. The net difference between fixed and floating interest on the notional — correct
  3. Shares of the underlying issuerWhy not: No securities are exchanged; the swap is a contract over interest flows.

The notional is a reference amount used to compute interest and is not exchanged. Only the net interest difference changes hands.

A harder one

Why is the value of an interest rate swap zero at inception?

  1. Because no payments have yet been madeWhy not: An unstarted contract can still be worth something, if the terms favour one side. Here they are chosen so they do not.
  2. Because the notional has not been exchangedWhy not: The notional is never exchanged, at inception or later, yet the swap acquires value as rates move.
  3. Because the two legs are worth the same — correct

The fixed rate is set so that the present value of the two payment streams is equal. Neither party pays the other to enter, which is only possible if the expected streams are worth the same at the start.

The hardest tier

Interest rates rise sharply after a swap is struck. What happens to the value of the pay-fixed position?

  1. It becomes positive — correct
  2. It becomes negative, because it must pay moreWhy not: The fixed payment does not change when rates rise; that is what makes it fixed. It is the floating receipt that rises.
  3. It stays zero for the life of the contractWhy not: Zero value holds only at inception, when the fixed rate was set against the then-current curve.

The fixed payments it makes are now below the market rate it receives. The pay-fixed party is locked into the old, lower fixed rate while receiving the new, higher floating rate, so the strip of implied forwards has repriced in their favour.

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