The log-normal LIBOR market model, mathematically established by Brace, Gatarek and Musiela (1997), Jamshidian (1997) and Miltersen, Sandmann and Sondermann (1997), has historically grown to be the standard tool for the description and pricing of many prominent (structured) interest rate products. Yet, with respect to the model?s inherent incapability to cope with the implied volatility smile and skew phenomena as recently observed in all major fixed income markets around the world, academics and practitioners alike continuously strive for improvements of the original setup. This thesis takes up one end of research in an extension as suggested by Wu and Zhang (2003). Specifically, we develop a general stochastic volatility framework by introducing an additional correlated multiplicative stochastic component to the deterministic volatilities of all underlying spanning forward LIBORs. By virtue of this construction, skews and/or smiles naturally evolve. Several suitable approximations facilitate equivalent semi-closed form pricing relations for plain-vanilla caplets and European swaptions in terms of Fourier integrals that have to be evaluated numerically by standard quadrature. We reproduce the essentially required and important theory of conditional characteristic transforms and associated inversion techniques and also discuss two alternative Fourier methods to the historically classic approach, which are promising in light of increased computational efficiency of the valuation algorithm as they enable and advocate an application of the Fast Fourier Transform (FFT) technology. Explicit analytic solutions within the framework to a square-root diffusion variance factor and an Ornstein-Uhlenbeck stochastic volatility component are generated and illustratively examined. Owing its practical motivation the thesis also highlights issues arising with a numerical implementation and presents extensive empirical findings.     «

The log-normal LIBOR market model, mathematically established by Brace, Gatarek and Musiela (1997), Jamshidian (1997) and Miltersen, Sandmann and Sondermann (1997), has historically grown to be the standard tool for the description and pricing of many prominent (structured) interest rate products. Yet, with respect to the model?s inherent incapability to cope with the implied volatility smile and skew phenomena as recently observed in all major fixed income markets around the world, academics an...     »