This thesis presents a tractable and flexible LIBOR market model with multi-factor stochastic volatilities is well developed. This model takes the following form: multi-stochastic factors are adopted for forward-rate volatilities, and each factor follows a square-root process (CIR process), and correlations between the forward rates and the stochastic factors. The forward LIBOR market model is extended to a cross-currency setting. Foreign caps and floors, and cross-currency swaps are studied in detail in the framework of cross-currency LIBOR market model with stochastic volatilities. Approximate closed-form pricing formulas based on moment generating function are derived. Lastly, the stochastic volatility LIBOR market model is calibrated to USD caps market....[ Read more ]

This thesis presents a tractable and flexible LIBOR market model with multi-factor stochastic volatilities is well developed. This model takes the following form: multi-stochastic factors are adopted for forward-rate volatilities, and each factor follows a square-root process (CIR process), and correlations between the forward rates and the stochastic factors. The forward LIBOR market model is extended to a cross-currency setting. Foreign caps and floors, and cross-currency swaps are studied in detail in the framework of cross-currency LIBOR market model with stochastic volatilities. Approximate closed-form pricing formulas based on moment generating function are derived. Lastly, the stochastic volatility LIBOR market model is calibrated to USD caps market.

Keywords: multi-factor stochastic volatility LIBOR market model, caps and floors, cross-currency LIBOR market, cross-currency swaps, calibration