  Risk management is an important practice in the banking industry. In this
paper we develop a new methodology to estimate and predict the probability of
default (PD) based on the rating transition matrices, which relates the rating
transition matrices to the macroeconomic variables. Our method can overcome the
shortcomings of the framework of Belkin et al. (1998), and is especially useful
in predicting the PD and doing stress testing. Simulation is conducted at the
end, which shows that our method can provide more accurate estimate than that
obtained by the method of Belkin et al. (1998).
