Hedging credit derivatives when recovery rates are stochastic

The contributions to the literature on the hedging of credit derivatives in continuous-time financial market models can be classified into two types of models. On the one hand, there exist quite tractable models that yield explicit hedge ratios but impose unrealistic assumptions on the hedging instrument and the quantities the contingent claim to be hedged depends on. In particular, in such models both the interest rate and the default rate are deterministic. Moreover, these models typically assume a deterministic or even constant recovery rate. However, recovery rates of credit derivatives are far away from being deterministic in reality. This motivated Müller (2008) to derive the LRM-hedging strategy when recovery rates are stochastic. On the other hand, there exist models that allow all the relevant quantities to be stochastic but do not yield explicit representations for the hedge ratio. In order to fill the gap between these two classes of models, this work has two main objectives. The first objective is incorporate diffusion risk into the Müller (2008) model and to derive an explicit representation of the LRM-hedge ratio in case of stochastic interest rates and stochastic default rates. The second objective is to replace the junior bond (a defaultable zero coupon bond with total loss in case of default) by a more realistic hedging instrument, e. g. stocks, credit default swaps, a credit index or contingent convertible bonds. A simulation study is conducted in order to investigate the performance of the different hedging instruments.