The thesis consists of three parts. In the first part, we establish a dual-curve market model. The new model accounts for the evolution of interest market after the 2007 credit crisis. The model can capture the spreads of swap rates between different tenors, and it can price caps, floors and swaptions in closed forms. In addition, we incorporate the stochastic volatility to the dual-curve market model, which allows us to capture volatility smiles or skews carried by interest rate caps and floors....[ Read more ]

The thesis consists of three parts. In the first part, we establish a dual-curve market model. The new model accounts for the evolution of interest market after the 2007 credit crisis. The model can capture the spreads of swap rates between different tenors, and it can price caps, floors and swaptions in closed forms. In addition, we incorporate the stochastic volatility to the dual-curve market model, which allows us to capture volatility smiles or skews carried by interest rate caps and floors.

In the second part, we create a market model for inflation rates using a Lévy process as driving process. An arbitrage-free condition is derived, which allows us to unite existing inflation-rate models developed under the approach of “foreign currency analogy”. Pricing formulae for inflation-linked swaps and options are developed, using moment generating function and fast Fourier transforms.

In the third part, we develop two approximated option pricing formulas for Heston model. The first is based on generalized Hull-White pricing formula, while the second is obtained through weak Taylor expansions. The two methods can be utilized as well in time-dependent Heston model, where closed-form pricing is not available.