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Including Annuity Effects in Swaption Greeks and Risk

Article Quant Q&A · Author: Peaceful
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Summary

The document asks how the annuity should enter swaption risk calculations when a swaption price is expressed as the annuity multiplied by a Black-model price. It focuses on whether the annuity can be treated as fixed when calculating delta, and whether changes in swap rates or the passage of time also change the annuity. It raises a related concern about theta, since shortening time to expiry can alter the annuity as well as the model value.

No answer or derivation is included, so the document does not establish a particular Greek formula. Its useful point is the distinction between differentiating the Black price alone and differentiating the full product when the annuity depends on market variables or time. A practical calculation would need to specify the risk measure, curve and conventions used to define the annuity, and which inputs are held fixed. The text provides no numerical example or evidence to show the size of these effects.

Key ideas

  • A swaption value can be represented as an annuity multiplied by a Black-model price.
  • The document asks whether delta should include changes in the annuity as swap rates move.
  • Theta may also reflect changes in the annuity as time passes.
  • The text poses these questions but does not supply a derivation or definitive formula.

Tags

OptionsFixed incomeDerivatives pricingRisk management
Full text
# When calculating swaption greeks, would annuity need to be considered?


# When calculating swaption greeks, would annuity need to be considered?












we all know that swaption price = annuity * black price. The question is that when calculating risks, should we treat annuity as a constant. i.e. is it correct that swaption delta = annuity * black delta?

Or we need to take annuity into account? In theory, swap rate changes would impact annuity. In particular, for theta, shorten time would certainly change the value of annuity, wouldn't it? in this case, swaption delta = annuity * black theta would not hold.

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.