A Study On Pricing The Loan For The Commercial Bank Based On The Reduced Form Models

The loan business is the core of operations in the commercial banks. Under the circumstances of interest rate adopted of the market principle and the implementation Baselâ…¡, it is an important challenge for the commercial bank to study the pricing models by using advanced credit risk pricing technology. Since the basic credit risk elements of the loan : default probability, recovery rate, exposure and term are uncertain and correlated, and historic default data of the borrowers are scarce, and indirect financing plays an important role, and stochastic analysis and martingale methods are difficult to be learnt , which have made it being meaningful to study the questions both in theory and reality.The paper uses the research approaches in financial engineering. In the framework of the risk neutral measures and reduced form models, by applying the technology of stochastic analysis and martingale methods, the mathematic models of pricing the loan are deduced under the circumstances of different assumptions in this paper. Seven models belonging to three classes are built in the paper.The core and achievements of the paper can be generalized as follows:The processes of risk-free interest rate and hazard rate are drawn by the diffusion process. The mathematic models of pricing the loan are deduced on the circumstance of the risk-free interest rate process and the hazard rate being independent, the risk-free interest rate process and the hazard rate being dependent, the risk-free interest rate process and the hazard rate and recovery rate being dependent. The economic meaning and application of the model are illustrated.The paper builds the two pricing models considering the correlated defaults. The study backgrounds are set as follow: one is the two clients are default correlated on the physical measurement, the other is the two clients are default correlated on the martingale measurement. The real meaning and the field of application are explained. The joint default distribution function and the density function of the two clients are deduced under the physical measurement and the neutral-risk measurement. The models of pricing the loan are deduced.The states of default-free of the client are divided by credit classes. By adopting continuous time G -Markov chains and F -conditioned G -Markov chain in the discrete state space, the migration process of credit classes are drown. The study backgrounds are set as follow: one is the risk-free interest rate is correlated with the migration process of credit classes, the other is the two processes are independent. The economic meaning and application of the model are illustrated. The models of pricing the loan are deduced.Some examples are given. Through the Monte Carlo simulation the break-even interest rate and risk premium are calculated. The paper analyses the influence on the risk premium by changing parameters in the model.