Practical Uses and Limits of Calibrated SABR Models

# SABR applications once calibrated


# SABR applications once calibrated












Spend some time writing a script for calibrating SABR to market swaption quotes. I have managed to now get a good fit. My question out of interest is; what is the SABR model actually used for in practice once fitted? I would like to go a bit further and explore its applications to pricing etc.

Thanks!

## Answer by David (score 1)

https://quant.stackexchange.com/a/78727

It is widely used for parameterising the rates volatility surfaces for caps/floors and swaptions.

One of the main advantages SABR has over non-model based volatility surface parameterizations, is that it prescribes dynamics for the movement of the surface as the underlying forward moves. Its dynamics are argued to be more realistic than for example a pure local volatility model.

It is sometimes used for cms spread options and midcurve options.

## Answer by Jesper Tidblom (score 0)

https://quant.stackexchange.com/a/78748

I have also reflected over this question at times. Things are not so clear as they first might seem, not to me at least. So I want to add some things to Davids answer.

As David says, the SABR model is often used as a way of parametrizing a volatility surface. However, a problem is that this often is seen as the same as calibration and parametrization using the well known "Hagan formula" for obtaining the Black volatilities given the parameters of the SABR model. This formula is analytical and therefore very practical and fast to use. However, this formula has well known shortcomings. It is an approximative formula that can get quite bad for more extreme strikes or longer maturities. This might lead to problems like negative volatilities in extreme cases.

So typically one needs to somehow "fix" the distribution for more extreme strikes in various ways (or rather, fix the error in the Hagan formulas). This is not straightforward and quite a bit of research have been devoted to the issue. So the value of the model for volatility surface interpolation has known problems. But it can still be useful.

Also, as David says, the SABR model is a stochastic vol model that typically mimics the volatility of an asset better than the pure local volatility model. One shortcoming here is that the model only has four parameters, which limits the quality of the fit to a larger number of market option prices.

Sometimes the SABR model is combined with other models like the Libor Market Model (or its spiritual successor Forward Market Model) to compensate for its shortcomings and give better result when used in Monte Carlo pricing. Then one can calibrate SABR parameters for each market maturity separately and connect them in time using the LMM/FMM model. This gives more flexibility to match market option prices and we still preserve the desired stochastic behavior.