Interest Rate Gamma

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?

Comments (4)

 
Mar 3, 2016 - 3:16pm

What you are refferring to is more commonly known as "convexity" on a vanilla swaps desk. A rec fixed position has the same profile as a long bond position whereby when rates rally (yields decrease) you get longer duration (make more money when rates fall) and when rates selloff you get shorter duration (loose less). Therefore a rec fixed position has a positive convexity profile. This is more pronounced in longer dated swaps as this effect is larger - one reason why very long dated swap rates (say 50y) are lower than 30y rates. This is also very pronounced for off market swaps (deeply in the money) - eg a 30y rec fixed swap struck at 5% when rates are at 2%. Hence when valuing off market swaps desks have to tweak the curve by large amounts to get a sense for the convexity profile - you wouldnt want to pay fixed on a swap like the one mentioned without getting "[email protected] to do so. This should be clear if you look a a simple price yield graph for a bond (if rates are very low the slope is very steep.

 
Mar 4, 2016 - 5:08am

So a swap is commonly assumed to be a linear instrument, which ignores the second order effects, such as convexity. This is more or less justified for a short-dated swap, since the impact of convexity there is relatively small. Therefore, most of the time people would not talk about gamma in the context of swaps. The PNL effect you're describing is simply a function of delta.

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