The Credit Risk Metric Research Of KMV Reduced Model Based On The Business Cycle

We theoretically explore the effects of macroeconomic conditions on credit risk metric model in a Lucas-type economy. Under Lucas-type exchange economy, unlike most other structural models, our model explicitly incorporates equilibrium macroeconomic dynamics including the volatility rate and growth rate of the aggregate output. In the mean time, we also consider the relative risk aversion coefficient of a representative investor who has CRRA utility. It models the asset value of the corporation following the stochastic procedure which is directly impacted by the aggregate output dynamics. Through the Black-Schole method we deduce a differential equation, and then solving the equation we deduce e pricing model of the value of enterprise. According to the definition of Huang and Huang (2003), Default occurs when the asset value of enterprise reach default point that can be fixed or determined the model stochastically. The definition of default probability adopts the cumulate probability definition of Huang and Huang (2003). Through the strict deducing, we get the default probability equation finally. Our structural model allows us to examine how default probability is affected by the interaction of macroeconomic conditions and firm characteristics. We calibrate the model to match the historical default experience. Our model produces the following predictions: (i) default probability is positively correlated with interest rate, the risk aversion coefficient of the representative investor, and the volatility of the aggregate output; (ii) firm characteristics including asset growth rate and volatility have significant effects on default probability and these effects also vary with economic conditions. These predictions are consistent with the available empirical evidence and generate implications for further empirical investigation.