Linkage between risk-free rates and Libor rates broke down during the financial crisis as LIBOR-OIS spreads and basis swap spreads exploded. Nowadays, the multi-curve modeling and has become the new norm of LIBOR derivatives modeling. The majority of multi-curve modeling approaches, however, are at odd with the stylized pattern of basis swap curves: smooth and monotonically decreasing in terms (or maturities), which cannot be retained if forward rates of different tenors were driven by different random factors in any usual way. In this thesis, we decompose a LIBOR rate into an OIS forward rate and an “discrete loss rate”, which represent the risk-free component and the default-risk component, respectively, and model them simultaneously using some popular dynamics for interest...[ Read more ]

Linkage between risk-free rates and Libor rates broke down during the financial crisis as LIBOR-OIS spreads and basis swap spreads exploded. Nowadays, the multi-curve modeling and has become the new norm of LIBOR derivatives modeling. The majority of multi-curve modeling approaches, however, are at odd with the stylized pattern of basis swap curves: smooth and monotonically decreasing in terms (or maturities), which cannot be retained if forward rates of different tenors were driven by different random factors in any usual way. In this thesis, we decompose a LIBOR rate into an OIS forward rate and an “discrete loss rate”, which represent the risk-free component and the default-risk component, respectively, and model them simultaneously using some popular dynamics for interest rates. In particular, we adopt the lognormal and CEV dynamics with stochastic volatility and establish the dual-curve versions of the LIBOR market model and the SABR model, respectively. Unlike multi-curve modeling approaches, we only model one Libor curve with a particular tenor and link it with Libor of other tenors by taking into account the effect of Libor panel review. After these model specifications, we provide a fast way of pricing vanilla options i.e., caps/floors, swaptions by using the heat kernel expansion method. It will be used in the calibration procedure in order to capture market information of interest rates. After that, we will show you how this dual-curve modeling approach can also be used to price and risk-manage exotic oprions. And due to high dimensionality of this dual-curve model, in this part, we adopt approaches to pricing and greeks calculations of exotics under the framework of Monte Carlo simulation.