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Title: A Stochastic Volatility LIBOR Market Model with a Closed Form Solution
Author: Nada, Hazim
ISNI:       0000 0004 2672 527X
Awarding Body: Imperial College London
Current Institution: Imperial College London
Date of Award: 2008
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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 modelÂ’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 thesisÂ’ 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 modelÂ’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 modelÂ’s calibration for short maturities using a computationally efficient approach which derives an approximation for the modelÂ’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.
Supervisor: Christofides, Nicos ; Meade, Nigel Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral