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FRM Part II · FRM Exam Part II · VaR Mapping

A firm holds a USD 50 million notional pay-fixed, receive-floating swap just after a floating reset, so the floating leg is priced like a bond that resets to par. The remaining fixed leg is a 3-year coupon bond. For VaR mapping, which representation is most appropriate?

A pay-fixed receive-floating swap maps to a short position in a fixed-rate coupon bond and a long position in a floating-rate note. Just after a reset, the floating note behaves like a short-maturity zero near par, so its interest rate risk is small compared with the fixed leg.

  1. AShort the fixed-coupon bond and long a floating-rate note, where the floating note behaves like a very short-maturity zero until next resetCorrect
  2. BLong the fixed-coupon bond and long a floating-rate note with 3-year maturity
  3. CShort both the fixed-coupon bond and the floating-rate note
  4. DLong a 3-year zero for the full notional only

Explanation

Paying fixed is equivalent to being short a fixed-coupon bond. Receiving floating is equivalent to being long a floating-rate note, which just after reset has duration near the reset interval, so it maps to a short-maturity zero. Using a 3-year floating exposure would overstate risk.

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