Research on BDS pricing with variable structure of default correlation

The pricing of CDS has become a hot issue after the U.S. subprime mortgage crisis erupted. For BDS with different reference assets, it is important to define the default correlation between the assets. Using copula functions to describe the dependent structure between the assets has some advantages and becomes popular recently. In the paper, we develop a BDS pricing model using the copula function with variable structure to describe default correlation. Considering the influence of economy situation change on BDS pricing, we introduce the Markovian regime shift to default density and default correlation change along with economy situation and make comparison by Monte Carlo simulation. The study finds that the BDS price obtained from the model with variable structure is located between BDS prices from the model without variable structure under different initial conditions. As default density is directly proportional to BDS price and default correlation is inversely proportional to BDS price, the influence of economy situation change on BDS pricing results from the comprehensive effect of default density and default correlation. Generally speaking, the influence of default density will exceed that of default correlation, thus, the BDS price in times of prosperity is low than that in times of depression.