For a long 7Y1Y payer swaption, I understand that the overall gamma will be positive. I see gamma to be positive in 7Y tenor and negative in 8Y - why would that be the case?

Intuitively, how would gamma behave (long/short) at option expiry (7y) vs swap maturity (8y point)?

Many Thanks.

  • $\begingroup$ That doesn't sound right. To calculate the gamma in different tenors, what exactly are you bumping and what exactly are you keeping constant ? $\endgroup$
    – dm63
    Jul 31, 2018 at 11:28
  • $\begingroup$ Actually I used an in-house pricer, would need to check what's its doing exactly to calculate gamma Sens. But intuitively if I want to understand how gamma would behave (long/short) at option expiry (7years) vs swap maturity (1y). What would be the explanation? $\endgroup$
    – babaji
    Jul 31, 2018 at 11:39
  • $\begingroup$ Hi babaji, what @dm63 is trying to say is that it depends on how you calculate Gamma. First you need to explain if you compute it by bumping a) the discount yield curve only without impact on the fwd par swap rate b) Or the same curve as (a) but recomputing the fwd par rate c) Or bumping forwards projection curve, d) Or swap rates.... (z) any thing with curve in it. Unfortunately there is no standard definition to the gamma in rates world $\endgroup$
    – Jiem
    Jul 31, 2018 at 16:52
  • $\begingroup$ hello Jiem, its the same yield curve i am bumping $\endgroup$
    – babaji
    Aug 1, 2018 at 3:20

1 Answer 1


I think the likely explanation is as follows: the gammas with respect to different parts of the curve are being calculated by asking: if I bump the whole yield curve in parallel (up and down by a standard amount such as 1bp), what is the convexity with respect to various par points on the yield curve. So, the "7yr gamma" is: the exposure of the swaption to the 7yr par point (after whole curve is shifted up 1bp ) - exposure of swaption to 7yr par point (using base curve). Similarly for the 8yr point. Using this method will show that when rates sell off by parallel 1bp, the 7yr1yr payer swaption will get shorter the 7y1yr forward rate, which will be shown as short 8yr/long 7yr on a par curve. Thus, the structure is long 8yr gamma/short 7yr gamma on a par curve. [This is opposite to what you said- was there a typo?]

  • $\begingroup$ Thanks a lot. If I understand correctly : for this payer swaption the underlying is 7y1y forward rate, so if I bump the whole yield curve 1bps, the 7y1y fwd is also bumped 1bps, since this is a payer, we get MtM gains; delta is positive (short) for 7y1y so short in 8y (+ve) and long in 7y (-ve). As far as gamma is concerned, since we are long an option on 7y1y underlying, we should be long (positive) in 8y vs short (negative) in 7y? $\endgroup$
    – babaji
    Aug 1, 2018 at 3:16

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