Study and Calibration of a LIBOR Forward Swap Model with Stochastic Volatility

The topic of this master thesis is the study of a LIBOR forward swap model with stochastic volatility and its calibration based on the market European swaption implied volatility surface. The first part of the thesis will briefly review the most common short rate models; it will introduce the Heath-Jarrow-Morton framework and it will describe the LIBOR swap Market Model (LMM). The topic of the second part will be the extension of the LMM including a stochastic term in the forward rate volatility. In particular the thesis will follow the approach described by Wu and Zhang 2006. This approach allows a calibration of the LMM parameters to an European swaption implied volatility surface making it particularly interesting for applications in the financial industry. In the third part, the numerical implementation of the model will be described and the calibration procedures and results will be discussed. The conclusions will summarize the key features of the stochastic volatility LMM and will discuss the main results