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Why a CMS Cap and Floor Can Have Different Vega

Article Quant Q&A · Author: Carmen
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Summary

The document asks why a single-look CMS cap and a CMS floor with the same expiry and at-the-money strike can show different vega exposures. The observation comes from pricing a ten-year-expiry CMS30 cap and comparing it with the corresponding floor. The author suspects the difference may reflect volatility-of-volatility exposure in the CMS index, with the cap and floor carrying different sensitivities, and asks whether that explanation is correct and how it could be formalized.

No answer, valuation method, numerical comparison, or supporting evidence is included. The question highlights that CMS derivatives can have sensitivities shaped by the distribution and convexity of the underlying rate index, but the proposed volatility-of-volatility explanation remains unverified here. A rigorous comparison would depend on the pricing model, calibration, and precise definitions of the cap and floor, none of which the document specifies.

Key ideas

  • The author observes greater vega for a CMS cap than for a same-strike CMS floor.
  • The compared instruments have the same expiry and at-the-money strike.
  • The document proposes volatility-of-volatility exposure as a possible explanation.
  • It supplies no model, derivation, or pricing evidence to confirm that hypothesis.

Tags

Fixed incomeOptionsVolatility
Full text
# CMS cap has more vega exposure than CMS floor for same strike


# CMS cap has more vega exposure than CMS floor for same strike












When I priced a 10y expiry single look CMS30 ATMF CAP, I noticed that the vega exposure is higher than that of the same 10y expiry single look CMS30 ATMF FLOOR. Why is that?

I have a suspicion that it is due to the Vol of Vol exposure of the CMS index where in a cap you are long vol in the cap and long VoV on the CMS index while in a floor you are long vol in the floor but short VoV on the CMS index.

Is that correct/is there a way to formalize this?

Thanks!

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