How Cap Volatility Prices a Cap’s Caplets

Summary

The document explains how a quoted cap volatility is used to value a cap made up of multiple caplets. Under the market convention described, one cap volatility is applied across the cap’s caplets so that their combined valuation matches the market price of the cap. This addresses whether the same six-month Libor cap volatility can be used for each caplet in an 18-month cap.

The key distinction is between the cap’s single quoted volatility and the individual implied volatilities that would result if each caplet were priced separately. Those individual values need not be equal to one another or to the quoted cap volatility. The explanation is brief and gives no pricing equations, market data, or discussion of calibration conventions, so it does not establish that one volatility fits every caplet across different caps or market conditions.

Key ideas

• A cap volatility is defined so that applying it across the caplets reproduces the market price of the full cap.
• Individually priced caplets can have different implied volatilities.
• The quoted cap volatility should be understood as a cap-level convention, not necessarily as each caplet’s standalone implied volatility.

Tags

# Use of cap volatilities


# Use of cap volatilities












I have a cap volatility surface for the 6 months Libor.

Can I use the same cap volatility for every cap's caplet to valuate the full cap?

Example: Valuate a 18M cap (Libor 6M) by valuating 3 6M caplets using the same 180days 6M-Libor cap vol for the 3 caplets.

## Answer by dm63 (score 4)

https://quant.stackexchange.com/a/38402

Yes, because by definition, a "cap volatility" is a volatility that when used for all caplets, gives the market price. However, if the caplets were priced independently, they would have different implied volatilities.

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.