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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.

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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.

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