Lévy LIBOR model and credit risk

In this thesis, we extend the LIBOR market model (LMM) by allowing the underlying LIBOR to follow a Lévy process, which can be viewed as a generalized Brownian motion that allows jumps in its path. In our framework we also model swaprates using the freezing coefficient technique. For pricing purpose, we adopt the efficient FFT method, which is later used in the calibration procedure. In the calibration, we found that the major bottleneck lies in the calculation of the implied volatility by solving Black's formula. Next, we extend the model to single-name credit risk market, and we are able to back out the implied hazard rate and recovery rate from corporate bond prices and CDS rates. Finally, we further extend it to multiple name credit risk model, and focuses on the correlation sensitive CDO. We find that there are two types of correlation, the spread and default correlation, and the first type has a much smaller effect than the second does on the pricing of CDO. Also, we find that a flat term structure assumption for individual CDS rate may be an over-simplification for the CDO tranche rate because it generates a non-smooth implied correlation structure