Delta and Gamma Exposure of a Receive-Fixed Interest Rate Swap

Summary

The document discusses the rate sensitivity of a receive-fixed interest rate swap, using a two-year swap as context. One response characterizes the position as long delta: receiving fixed benefits when rates fall. It also argues that the position has positive gamma because its delta exposure grows as rates decline and shrinks as rates rise, describing the swap as slightly convex despite its common classification as a linear derivative.

A second response agrees that receiving fixed has long delta but disputes the presence of gamma, reasoning that an interest rate swap is linear and describing its duration as the difference between the fixed and floating legs. The document therefore presents conflicting claims rather than a complete derivation or settled treatment. It provides no equations, numerical example, curve-shift assumptions, or discussion of swap valuation conventions. Readers should distinguish the direction of first-order rate exposure from curvature and specify how rates or the curve are parameterized before applying the claims to risk measurement.

Key ideas

• Receiving fixed is described as a position that benefits when interest rates decline.
• One response characterizes the receive-fixed position as having positive delta and gamma.
• Another response agrees on positive delta but argues that the swap has no gamma because it is linear.
• The document does not resolve the disagreement with a derivation or stated curve-shift assumptions.

Tags

# Interest Rate Risk - The Greeks


# Interest Rate Risk - The Greeks












IR Delta and Gamma. Can someone please explain if my understanding is accurate as relates to a 2yr interest rate swap? You are considered to be long Delta in an interest rate swap if you are receiving the fixed rate. As for gamma, which is the rate of change of your delta, suppose the short end of the curve rallies and you are receiving the fixed rate, would this mean you are long gamma? If the curve rallies, bond prices go up and yields go down, therefore receiving a fixed rate is good for you, therefore long gamma?

## Answer by dm63 (score 5)

https://quant.stackexchange.com/a/42577

Receiving fixed on an IRS is both long delta and long gamma. The delta is obvious. The gamma is because the long position in delta increases as rates go down, and decreases as rates go up. Swaps are indeed sometimes called linear derivatives, but are in fact slightly convex as a function of rates, just like bonds.

## Answer by Abhinav Saxena (score 0)

https://quant.stackexchange.com/a/42567

Since Interest Rate Swap is a Linear derivative , I dont believe there will be Gamma on a IRS. If Duration of Swap is considered, it will be Duration of Fixed minus Duration of Floating which will be Positive. Hence , receiving Fixed will have Long Delta.

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