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Why Swaption Greeks Use the Annuity Measure

Article Quant Q&A · Author: Nope
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Summary

The document addresses whether differentiating a Black-style swaption valuation while treating the swap annuity as independent of the swap rate gives meaningful Greeks. Its answer points to the swaption, or annuity, measure: pricing is expressed using a matching annuity as the unit of account, which explains why the usual calculation does not add the proposed correlation adjustment in that framework.

The explanation offers a concise conceptual correction to an intuition about rates and discount factors moving together. It gives no derivation, numerical example, or comparison with other pricing setups, so it is an introduction rather than a full account of measure changes or the assumptions behind standard swaption analytics.

Key ideas

  • Swaption pricing commonly uses the swaption or annuity measure.
  • The matching swap annuity serves as the unit of account under that measure.
  • The answer says the suggested annuity and swap-rate correlation adjustment is unnecessary in this framework.
  • The brief explanation does not derive the pricing measure or detail its assumptions.

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# How is this greek calculation meaningful?


# How is this greek calculation meaningful?












For a swaption, the "Pricing And Hedging Of Swaptions" paper by Akume et al (2003) says:

I get that he's just taking the derivative of the swaption valuation formula (which is N * A * BLACKSCHOLES), but he's assuming A (the annuity) is independent of the underlying swap rate. Surely if we live in a world where swap rates triple, then discount rates are also affected, so A and S aren't independent. Or am I wrong?

## Answer by dm63 (score 2)

https://quant.stackexchange.com/a/76877

Yes, you are actually wrong. The pricing of swaptions is done in the ‘swaption measure’, or ‘annuity measure’, where the unit under consideration is a 1% per annum annuity matching the life of the underlying swap. Because of this, there is no need to consider the correlation you mention. This is quite hard to believe initially, but it is standard swaption pricing analytics.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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