Bootstrapping Caplet Volatilities from Cap Volatility Quotes

Summary

The note explains how to recover interval caplet volatilities from a term structure of at-the-money cap volatilities. A quoted cap volatility is a flat volatility that prices the cap as a whole, combining the values of its component optionlets; it is not necessarily the volatility of each individual caplet.

The proposed approach strips the volatilities one maturity at a time. First use the shortest-maturity cap quote to determine its caplet volatility. For the next maturity, hold the previously identified caplet volatility fixed and solve for the new interval’s volatility so the combined optionlets match the longer cap’s market price. Repeat this procedure for successive maturities. The note gives a conceptual recipe rather than calculations or market data, and does not discuss model choice, instruments’ detailed conventions, or numerical solution methods.

Key ideas

• A quoted cap volatility is a flat input that reproduces the market price of the full cap.
• Caplet volatilities can be inferred sequentially by matching cap prices across maturities.
• At each step, retain the previously stripped caplet volatilities and solve for the new interval’s volatility.
• The note outlines the method but does not provide numerical examples or implementation details.

Tags

# Find the caplet volatilities for LIBOR fixings at each interval, given the ATM implied cap volatility term structure


# Find the caplet volatilities for LIBOR fixings at each interval, given the ATM implied cap volatility term structure












anyone can provide solution or some idea to the following question? thanks

## Answer by David Duarte (score 4, accepted)

https://quant.stackexchange.com/a/54758

Cap vols are normally quoted as a flat black or bachelier volatility that when used to price all the optionlets, will give the correct market price of the cap.

In your case, you will have to strip the caplet volatilities.

Example: you have the vol for the 1y cap and you have the vol for the 2y cap. Using the 1y vol for the caplets expiring the first year, find the vol for the caplets expiring in the second year that give you a market price equal to the 2y cap with a flat vol of the 2y vol.

Then use the same procedure for the 3y cap, with the 1y vol and the vol you found for the caplets expiring in the second year. Then same for 4th years and so forth...

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