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?
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$\begingroup$ What did Google reveal to you? Do you have an understanding of the absolute basiscs of the quantitative theory of financial markets? $\endgroup$– Dr_BeCommented Feb 18, 2016 at 7:30
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$\begingroup$ Hi Akop88, welcome to Quant.SE! I concur with @BerndH, this is either too basic or too broad. $\endgroup$– Bob Jansen ♦Commented Feb 18, 2016 at 8:33
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$\begingroup$ wallstreetoasis.com/forums/interest-rate-gamma $\endgroup$– nbbo2Commented Nov 11, 2018 at 2:42
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2 Answers
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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.
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$\begingroup$ Totally agree. I have a follow-up question, as the swap has Gamma, does it have Theta? So we end up with an instrument that longs Gamma but has no Theta offset. How to interpret and hedge the Gamma risk then? Would it be better to redefine the Greeks for interest rates derivatives as sensitivity against curve instrument prices not the rates? $\endgroup$– JUWCommented Oct 4 at 9:36
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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.
