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?
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.