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Strip Cap Quotes into Caplet Volatilities Before SABR Calibration

Article Quant Q&A · Author: Hasek
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Summary

This discussion addresses whether SABR should be calibrated directly to cap quotes or to the individual caplets that compose those caps. Its proposed workflow is to first strip market cap quotes into a caplet volatility surface, then calibrate SABR separately for each caplet expiration. This produces a set of expiration-specific model smiles rather than treating each multi-period cap as a single option.

A cap is then valued as the sum of its constituent caplet prices, each using its own spot volatility. The flat volatility quoted for a cap is described as the single volatility that reprices the whole cap when applied to every caplet. The answer supports this distinction conceptually but provides no stripping algorithm, calibration objective, market data, or comparison of fit quality. Results therefore depend on the stripping method, market conventions, and model assumptions, none of which are detailed in the exchange.

Key ideas

  • A cap consists of multiple caplets, so its quote reflects a portfolio of options.
  • Strip cap market quotes to infer caplet volatilities before fitting expiration-specific SABR smiles.
  • Price a cap by summing the prices of its caplets using their respective spot volatilities.
  • A flat cap volatility is a common repricing quote applied across all constituent caplets.

Tags

Fixed incomeOptionsVolatilityDerivatives pricing
Full text
# Should one calibrate SABR model on caps or caplets?


# Should one calibrate SABR model on caps or caplets?












I want to build a volatility surface for caps on a 3M index implied from SABR model. I have a set of cap normal volatilities for a range of strikes (4%, 6%, 8%, 10% and ATM) and maturities (1, 2, 3, 4 and 5 years) as an input data.

However I'm confused what instruments should I use for calibration -- caps or caplets? Can I directly fit SABR model to given caps data even though caps aren't options bur rather a portfolios of options? Should I first obtain a caplet volatility surface, i.e. do what is known as a spot volatility stripping from given flat volatilities, and then calibrate SABR on caplets since these are the "real" options?

I would be very grateful for any clarifications and explanations. I also asked a related question recently because I got some seemingly strange results while trying to do a volatility stripping.

## Answer by Hasek (score 0, accepted)

https://quant.stackexchange.com/a/70533

Let me post an answer to my own question in case someone would need it...

> Should I first obtain a caplet volatility surface, i.e. do what is known as a spot volatility stripping from given flat volatilities, and then calibrate SABR on caplets since these are the "real" options?

This is the right approach. First things first one should obtain a caplet volatility surface (see this paper for more details) from market caps quotes. It allows for independent calibration of SABR model on different caplet expirations and hence one have a set of separate model smiles. A cap then priced as a sum of prices of constituent caplets, each with its own model spot volatility, and quoted in terms of a flat volatility which is the volatility repricing the cap when assigned to all constituting caplets.

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.