Effects Of Complete And Incomplete Information On The Structural Model

This paper is an overview.Credit risk,generally speaking, means that in a contract one party,at least,cannot follow the items as promised previously for a certain reason so that other party or parties have to be exposed to the risk of suffering from losses.Usually, credit risk is equivalent to default risk in finance.Since the globalization in economy and finance is well accelerated nowadays, with advancement in financial markets changing with each passing day,and financial innovations emerging in endlessly,different kinds of technologies and methods for managing and controlling credit risk are invented and renewed continually.Particularly,a large amount of bankruptcies of enterprises and banks and worldwide financial crisis triggered by subprime mortgage crisis in USA currently lead people's eyes to focus on the prevention and management for credit risk.However,the traditional techniques and ways for managing credit risk have remarkable shortcomings.For example,the traditional methods are simple and lack of flexibility;furthermore,it depends upon individual,subjective judgment too much and there exists no quantitative analysis either.Therefore,mathematical models for measuring credit risk are explored and developed.Some models belonging to this kind are structural model,KMV,Creditmetrics, Creditrisk+and Creditpotforlioveiw.These models have disadvanrages respectively,although they improve the traditional methods for credit risk management in a way.Especially,in the structural model,it is implicitly assumed that investors are able to know complete information about company's financial statement which is obviously unpractical in reality.So in this paper,some studies by Kay Giesecke are reviewed on structural model and pricing zero bond issued by a defaultable company with incomplete information.First,background knowledge about credit and credit risk is briefly expounded in the part of Introduction,including the definitions and characteristics,especially the significance and necessity of studying and managing credit risk.Then concise introductions and remarks are followed of four modern mathematical models for managing and measuring credit risk:KMV,Creditmetrics,Creditrisk +and Creditpotforlioveiw.In chapter 2,Merton's structural model is specifically explained, which was developed by Robert C.Merton,the 1997 Nobel Prize winner in economics,one year later after option pricing method with no-arbitrage was invented.The model essence is that basing on theory of option pricing with no-arbitrage and its classical premises, and assuming the simple case that the capital construction of the company just consists of stocks and bonds,the company's assets can be regarded as the underlying assets of a European option,price of which is identical with the reasonable one of the company bonds. Thus the bond pricing formula is able to be derived through solving some type of PDE.The model is called structural model since the results of the model are of much concern with capital structure of the company.Although the structural model is simple and its premises are difficult to satisfy in practice,the model is the original and ini- tial research on credit risk studies with mathematical methods and therefore a cornerstone for later development in modern credit risk research.In the sequel,quite a lot models which are more complex and practical have their origins from structural model.Nevertheless, the model disadvantages are evident.On the one hand,it only considers the simplest case about the company's capital structure, and at the same time the definition of default in the model is not practical.It assumes that default could happen only at bond maturity. Instead,the content of default in modern credit risk model belongs to a mark-to-market pattern,which is more practical.On the other hand,it is implicitly assumed that investors can master complete financial information about the company.But a real financial market can never be complete,and financial scandals frequently happen,so investor information is limited for certain and cannot be guaranteed its truth.In view of shortcomings of structural model,Kay Giesecke introduced a set of a-algebras called filtration which are generated by variables about financial information of companies to describe investor information and thus developed structural model with incomplete information.In chapter 3,detailed and systematic explanations are made over the incomplete default model.In this part, a first passage default model is introduced at the beginning.The model modifies the definition of default in Merton's model and assume that default could happen when the value of company asset moves to values below a certain default barrier for the first time, even if bonds are still not mature.What is more,a general filtration is defined,of which different kinds of investor information flow are examples.In the ideal financial market,investor could own all the information about the company,especially the information about values of company asset and default barrier.Then the model is a complete information one,and the model filtration is generated by variables of company asset value and default barrier value,in which the short credit spread of bonds tends to be zero.Cases where investors cannot obtain complete information are as follow:only information about company asset is available;only information about default barrier is available;neither company asset information nor default barrier information is available.Respective information flow is generated by the variables mastered by investors,through which bond price and credit spread are expressed in certain formulae.In the final part,the common and different between default model with incomplete information and reduced-form model are briefly expounded,which concludes to the end of this paper.