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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:

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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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  • $\begingroup$ Is theta left out on purpose? $\endgroup$
    – emot
    Commented Jan 7, 2023 at 23:23
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    $\begingroup$ For the gamma, you can have an NxN matrix for all pairs of fitting instruments. You're just looking at its diagonal. But it's an overkill for a vanilla IR swap. You can use one gamma figure for a swap, a risk-weighted sum of the matrix. If done correctly, it should help your P&L ezplanation a little bit if the swap is 20+ years, not be a lot under 20Y. Can you please post your swaps T&C, all the market data and risk numbers, ideally the QL code that we can run? $\endgroup$ Commented Jan 8, 2023 at 0:11
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    $\begingroup$ The key observation you make is that the second order term needs to include all the cross gamma terms and not just the individual partial gammas. $\endgroup$
    – dm63
    Commented Jan 8, 2023 at 14:33
  • $\begingroup$ For certain products, it also helps to include the cross-gammas between interest rates and the time. $\endgroup$ Commented Jan 9, 2023 at 1:07

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