Pricing of Embedded Options: Implementing Stochastic Interest Rates & Stochastic Spread

Abstract: Given the current market climate, in an era of negative interest-rates, the Hull-White model has regained popularity in the eyes of investors. This thesis aims to extend this model to incorporate credit risk, to allow the modelling of credit derivatives such as diff swaps, defaultable corporate bonds and credit default swaps. This process can be achieved in a number of ways, by utilising either two one-factor models or one two-factor model. Additionally, notable generalisation procedures are outlined to extend the modelling framework to incorporate popular one-factor short rate alternatives such as Black-Karasinski. Finally, calibration methods of the input variables are discussed as well as determining sensitivity metrics directly from the lattice trees themselves, used in hedging these derivatives which is of particular interest in practical applications.