BOND MATH: The Theory Behind the Formulas

Interest Rate Swap Duration and Convexity

We know from the numerical example above that when the swap fixed rate falls, the fixed-rate payer loses market value and the fixed-rate receiver gains. Therefore, the swap has negative duration to the long position (the “buyer”) and positive duration to the short (the “seller”). We'll see in Chapter 10 that adding a pay-fixed swap to a fixed-income investment portfolio reduces average portfolio duration while adding a receive-fixed swap increases average duration. How much of an increase or decrease depends on the duration of the swap and the amount of notional principal.

The duration of a plain vanilla interest rate swap is derived in practice (e.g., on Bloomberg) by recognizing that the net settlement ...