Credit Risk Theory, Model, And Applied Research

Credit risk is one of the major risks in front of the financial institutions (banks, in particular). It directly influences the various aspects of economic life in modern society, also a country's macro economic policy-making, and the stability and coordinated development of global economy at large. With the frequent occurrences of crises in international banking, the international banking industry and the academic society are fully aware of the increasingly important role of credit risk model research in asset price setting and risk management. A large number of credit risk models are thus produced. The ever deepening method of credit risk management in New Barsell Agreement is the most striking example. Meanwhile, with the change of financial market environment and the development of credit spin-off, credit risk has acquired new connotation. Research into credit risk models has become one of the most challenging topics in the financial field. In recent years, the banking industry in China has developed very fast. But the credit risk management techniques are still backward in comparison with the economic developed countries due to the historical and systematic reasons. The research and application of credit risk models are still at the beginning stage. With the further opening of the financial market in our country, the promotion of interest rate marketing process, and the fast pace of financial product innovation, the credit risk in our banking industry has gradually taken shape, and may bring about big crisis. For the above reasons, the study of credit risk theory, model and application in this paper has considerate theoretical significance as well as practical value.Credit risk measure has great significance in credit risk operation and supervision. For this reason, this paper gives a systematic exposition of its theoretical foundation, components, risk price setting models based on the extensive reading of relevant literature at home and abroad. In the mean time, this paper makes research into the in-risk value calculation of some commercial credit risk models, and carries out some experimental and analytical study. The whole paper falls into three parts: Part I is the credit risk theory and components; Part II is the credit risk price-fixing models, including structural and intensity forms; Part III discusses the modern commercial credit risk models and the calculation application of the in-risk value as well as its experimental and analytical research. To be specific, the content is as follows:Chapter I is the introduction part. The author exposits the significance of the current topic, literature review, the framework of the whole paper, the research methods, the innovation points of the paper and the further research topics.Chapter II mainly discusses the theoretical knowledge of risk: the theory of mean-variance. To begin with, this paper introduces the risk property, risk measure, and risk decentralized. The criterion of mean-variance introduction is: to minimize the portfolio variance in given expected revenue rate, to maximize the expected revenue of portfolio in given variance, and to use Largrange multiplication to construct functions and get the variance of the portfolio. It clarifies the portfolio mean-variance theory which was first proposed by Harry Markowitz: How to minimize risk in given expected revenue? How to maximize revenue in given variance?Chapter III analyzes the components of credit risk models. It gives a definition of credit risk and points that credit risk includes default probability, default exposure, default loss and annual period as the basis components. It mainly discusses two elements: the default probability that measures credit risk input parameter, and the default recovery rate. This chapter systematically illustrates the default probability models such as logical regression model and the default probability model based on Merton model and default evaluation. It also makes research into the Logit model and applies it into the loan clients of the commercial bank. And it discusses the dimidiate dependent variable model given that the assumed condition probability complies with normal distribution: the Probit model. The author gives the mathematical formulae of the margin default rate, history default rate and mean default in certain period respectively. Then the author uses the Bayes approach to estimate the transition matrix, and discusses the transition matrix with Markov chain discrete time condition. According to the Markov property andtime homogeneity, the author then gets the n·τyear transition matrix using n time transition matrix, that is, Tr(n·τ) = Tr(τ)~n . From this the company defaultprobability based on Merton model is deduced, and constant default probability model and time variation default probability model based on default intensity is deduced. The author gives a definition of recovery rate, and illustrates that recovery rate level is a random variable. In given default condition, we can determine the risk neutral recovery rate, and thus reveal the increasing influence of risk dislike on risk neutral default probability. Accordingly, the author further investigates the default bond price setting in random recovery rate condition, and discusses the hidden recovery rate model and the model based on Merton model, exposits the relevance between intensity and recovery rate. However, due to the date reasons, the author still cannot make experimental research and factor adjustment to the recovery rate model, which remains to be done in future research.Chapter IV researches the structure form credit risk price setting model. The models proposed by Black and Scholes(1973) and Merton (1974) are the earliest ones that discuss the credit risk price setting models. Therefore, they are considered to be the milestone in the establishment of credit risk model. The development of option price setting techniques and the research and application of company debt form the foundation of credit risk structure form model. This chapter researches the basic analysis framework of CCA, and makes some basic assumptions of the framework. Merton model is to analyze the price setting model in a market condition with constant business without attrition based on the standard Black-Scholes model. It assumes that the company value comply with geometrical Brownian motion, and uses the equavalent martingale probability measure to generate the structural models of stock price setting, bond price setting and credit risk price setting. Based on this, the author gives an example of the application of Merton model. Using numeraire technique, equavalent martingale probability measure and Ito's Lemma, the author makes deep investigatin into the Merton model with random interest rate. The strok equity price generated from this model differs from the Merton model only in terms of random interest rate, the author makes preliminary investigation into the first-passage model. We assume that the default wall is a constant within a certain span, the default time is a random variable, then we can generate the default probability and company value model.Chapter 5 constructs reduced form credit models. Reduced form credit models play a very important role in studying default risks, and work as a bridge between credit risk and default pricing models. It firstly introduces related knowledge concerning Reduced form credit models, such as point process, intensity process, duality random and ranking shift intensity. Then it studies Jarrow,Lando and Turnbull model in discrete state. Jarrow and Turnbull has proven that if there exists the only Risk-neutral probability measure and Equavalent Martingale Measure, risk bond value can be represented by the discount expectancy of Risk-neutral probalility measure. Jarrow and Turnbull model hypothesizes that the rate of amortization and default intensity are two exogene contants, and uses binary tree to deduce default risk pricing model. Developed from the study of Jarrow and Turnbull model Jarrow,Lando and Turnbull model is a Markov model of credit spread term structure, which takes default process as an absorbing state of discrete state in credit ranking, and default as a exogene process, deduce Zero-coupon bonds price model by way of long-term interest rather than company's potential assets. This chapter also studies the Cox process with time single jump structure, explores the question of risk premium based on reducde models, and makes a preliminary study on Reduced form models with imperfect information.Chapter 6 systematically clears up the basic concepts of VaR risk evaluation and the evaluation methods and so on. VaR is a general number, which can show possible loss considering all the risk factors, and can directly show the magnitude of risks. To have a VaR caculation, three items are required, dimension of confidence interval, length of holding time and expected loss. This chapter states caculation method of numerical VaR, parameter VaR and quantile and so on. It studies VaR tools, i.e. margin VaR, increment VaR and component VaR, which are often used in risk management. This studies also expounds various methods for VaR measurement, such as the easily applicable Delta-normal approach,the experience-based history simulation approach and the more precise and trustworthy Monte carlo simulation approach. Among these methods, this paper makes an indepth study on monovariant Monte carlo simulation and multivariable Monte carlo simulation, which provides a multi-methods method for VaR caculation. Finally, the writer chooses one fund as a example to illustrate VaR caculating process and how to analyze with the results.Chapter 7 systematically states modern commercial credit risk models. Four kinds of representative commercial credit risk modes are highlighted in this paper, i.e CreditMetrics, KMV, CreditRisk+ and Credit Portfolio View, which are emphasizes in commercial application of credit risk modes. It firstly studies CreditMetrics model which is from Morton Company's value model. CreditMetrics is one of the important models in international financial credit risk management in recent years and it marks that great progress has been achieved in precision and initiativeness of risk management. The writer put more emphasis on the study on method and application of credit risk evaluation of CreditMetrics' uni- bond or loan, compound bonds or loans, which is a very important reference for our commercial bank's risk management. Secondly, it studies the KMV model which is from double pricing theory, and makes a demonstrative analysis. This model has been applied in commerce in more than 50 countries. This chapter studies its basic framework, asset value and fluctuation ratio, calculating method of distance to default, and deduces default probability and Risk-neutral expected default probability. The emphasis is on the demonstrative analysis of our country's listed companies's credit risks based on KMV. The writer has chosen 28 different types of listed companies to demonstrate their credit risk. The results show that the well-performed stocks' distance to default is larger than that of bad-performed stocks, hi-teck stocks's distance to fault larger than that small and medium-sized companes's stocks. These results have a instructive effect in making credit loan policy, adjusting credit loan structure and instructing the delivery of credit loans. Both the two models mentioned above are based on Morton model theory, i.e. the default of company is related to the capital structure of the company and when the company's asset value fall below certain critical value, default will happen. Thirdly, it expounds deeply the CreditRisk+ model,which applies the framework of actuarial science into the analysis of loss distribution of liabilities assets including stocks and loans. But in this model, it only takes default risk into consideration and neglects the risk of downgrading of the debtor's credit level. The frame stated by the writer in this paper, mainly concerns four parameters, i.e.default ratio, exposure, default fluctuation and rate of amortization. Suppose the default event submit to Poisson distribution, the default loss ratio can be deduced and then the diversified portfolio loss ratio can also be deduced. CreditRisk model divides loss into several small groups, with each group's expourse level nearly a round figure. This model introduces a very important concept, i.e. probability generating function, and systematically states and deduces each default event, default event distribution and default loss under fixed default ratio condition and changeable default ratio condition respectively, then expands the one year term default probability model to a multi-year model. Fourthly, this paper makes an in-depth analysis of CPV model. CPV model is a multiple factor model. It only measure default risk, and the default probability depends on macro-economic variable. The application of this modes shows that credit cycle and economic cycle are a unity. Relating state macro-economic multiple factors analysis and lagged marco variable to establish default forecasting model, deducing accumulation and transfer probability distribution from condition transfer matrix, and getting credit risk value measurement from transfer probability distribution, and working out relative historical average ratio by way of simulated default probability, from this ratio, we can judge that the economy is on uprising or waning stage.