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Using Delta and Gamma to Explain Swap P&L Across a Rate Curve

Article Quant Q&A · Author: SIMO
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Summary

The document describes an attempt to explain a swap’s profit and loss using sensitivities to instruments across a rate curve, including money-market rates, futures, and swaps. The author applies separate one-basis-point shocks to the curve instruments and compares an explanation using delta alone with one that also includes gamma.

The reported result is counterintuitive: adding gamma makes the explanation fit worse, while delta alone performs better. This raises a useful diagnostic question about how sensitivities and curve shocks are constructed and combined. However, the document is only a question; it provides no answer, supporting calculations, market data, or diagnosis. It therefore identifies a P&L attribution problem but does not establish why the gamma terms degrade the explanation or whether the issue lies in the bump method, curve representation, or another implementation detail.

Key ideas

  • The author attempts to explain swap P&L using sensitivities to multiple rate-curve instruments.
  • The approach applies separate one-basis-point shocks to curve instruments.
  • Including gamma reportedly worsens the explanation compared with using delta alone.
  • The document poses the problem but provides no diagnosis or evidence beyond the reported behavior.

Tags

Fixed incomeDerivatives pricingRisk management
Full text
# P&L explain for swap?


# P&L explain for swap?












I try to make a P&L explanation of a swap from the delta, gamma, to the N instruments of the rate curve (money market, futures and swap). I use a perturbative shock of 1bp for each instrument of my rate curve used in the pricing:

the result I get is strongly degraded if I integrate the gamma in the P&L explanation (the P&L explain is better with Just delta Effect !) which is counter intuitive

Do you see a mistake in my approach ?

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