【作者】 么向华；

【导师】 詹原瑞；

【作者基本信息】 天津大学 ， 金融工程与金融管理， 2007， 博士

【摘要】 贷款是商业银行的核心业务。在我国利率市场化以及巴塞尔新资本协议实施的双重背景下,应用国际上先进的信用风险定价技术,研究贷款定价模型,是当前商业银行经营决策中面临的一项重大挑战。由于贷款所面临的信用风险的基本要素——违约概率、违约损失率、贷款暴露和年期等因素存在着不确定性和相关性,以及贷款客户历史违约数据稀缺、我国间接融资比例高等现实因素,加之研究的主要工具——随机分析和鞅方法需要较为艰深的数学知识,使得这一问题的研究具有重要的理论和现实意义。本文采用了金融工程学的研究方法,在风险中性的研究环境和简化型模型的框架下,运用随机分析和鞅方法的有关技术,数学推导出在不同假设背景下商业银行贷款的定价模型,建立了三大类、共七个贷款定价模型。本文的核心内容及研究成果,可以概括为:采用扩散过程刻画无风险利率过程以及违约强度过程的运动趋势。数学推导出了无风险利率过程和违约强度过程独立,无风险利率过程与违约强度过程相关,无风险利率过程与违约强度过程和回收率过程三者相关,三种假设条件下的定价模型,解释了模型的经济含义和应用范围。研究两个贷款客户违约相关条件下的贷款定价模型。将研究背景设定为两种情况,一种是两个贷款客户在风险中性测度下违约相关,另一种情景是两个贷款客户在真实测度下违约相关。解释了在两种情景下,模型的现实意义和应用范围。数学推导出了推导出了两个贷款客户在真实测度和风险中性测度下的联合违约分布和密度函数,并推导出了定价模型,解释了模型的经济含义。按照信用等级细分贷款客户的无违约状态,利用离散状态空间的连续时间G -Markov链,以及离散状态空间的连续时间F -条件的G -Markov链,刻画贷款客户信用等级迁移过程。假设无风险利率过程与信用等级迁移过程独立,以及无风险利率过程与信用等级迁移过程两者相关两种情景,数学推导出了贷款定价模型,解释了模型的现实意义和应用范围。列举了实际的分析算例,运用Monte Carlo随机模拟的方法,计算出了风险价差和商业银行盈亏平衡利率,分析了模型中参数的变动对风险价差的影响。更多还原

【Abstract】 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 BaselⅡ, 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.更多还原