Interpreting Bucketed Gamma in a 7Y1Y Payer Swaption

Summary

The document considers why a long 7Y1Y payer swaption might show gamma with different signs at the 7-year and 8-year points on a par yield curve. The answer suggests that the reported bucketed exposures may come from repricing after a parallel curve bump, then measuring how exposure to each individual par point changes relative to the base curve. These curve-point sensitivities are distinct from a single overall gamma measure.

In this account, a parallel rate selloff changes the forward rate underlying the swaption, and the resulting exposure can appear as short 7-year and long 8-year on the par curve. The answer says this is opposite to the signs in the question and raises the possibility of a typo. It is a proposed explanation, not a demonstrated calculation; the exact interpretation depends on the system’s bumping and bucket allocation methodology. It also does not fully explain gamma behavior at option expiry versus swap maturity.

Key ideas

• Bucketed gamma reports sensitivity by curve point, not only the instrument’s overall gamma.
• The proposed interpretation compares exposures after a parallel curve bump with base-curve exposures.
• A 7Y1Y swaption’s curve-point profile may show opposite signs at the 7-year and 8-year points.
• The answer flags a possible sign inconsistency in the question and leaves methodology-dependent details open.

Tags

# Bucketed gamma for swaptions


# Bucketed gamma for swaptions












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.

## Answer by dm63 (score 1, accepted)

https://quant.stackexchange.com/a/41038

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?]

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.