Since its initial publication the SABR model has gained widespread use across asset
classes and it has now become the standard pricing framework used in the market to
quote interest rate products sensitive to the non flat strike-structure of the market
implied volatility. While very simple, the model’s use has always been based on the
original study of its authors who derive a formula for pricing European options through
a few approximating assumptions which are at times severely violated in the market.
This thesis’ main theoretical goal is to set the path for a generalization of the SABR
model which possesses a closed form solution free from assumptions about the
magnitude of the model’s parameters. We propose such model and derive a closed form
solution for the particular case in which the underlying forward rate and its volatility
are uncorrelated. After using the solution for pricing caplets within a LIBOR Market
Model framework we simplify an approximation for the swap rate developed by
Piterbarg in order to use the same solution for the pricing of swaptions. We conduct the
model’s calibration for short maturities using a computationally efficient approach which
derives an approximation for the model’s implied volatility and uses it to fit the model
to market quotes. Finally, we study the properties of the greeks of our model in
comparison with those of the classical Black model.