Credit default swap spreads modeling under stochastic recovery rate

There are many studies on development of models for analyzing some derivatives such as credit default swap (CDS). A continuous-time autoregressive moving average (CARMA) driven by L´evy process is applied for modeling the CDS premia. It is based on the stochastic recovery rate which is time-varying during the maturity stage and makes the model suitable for evaluating the premium leg. We show that this model is a class of affine term structure model. By simulating the CARMA(2,1) process the effectiveness of this model in determining the most appropriate parameters are illustrated. Also a comparison of the Bayesian information criterion between two models is given