Study In Tail Saddlepoint Approximation Of Portfolio Credit Risk

Recently, as the the phenomenon of bank bankruptcy growing rapidly in theworldwide, credit risk has become the focus of financial problems. Banks haveto prepare more capital for credit risk than that for market risk. So it is of greatimportance of doing insight research on credit risk. In 1950s, market risk port-folio model was first time introduced by economists and then, some academicstudies and applications was proposed. However, the theory and application ofportfolio credit risk have got the widespread attention after 1990s. And thensome important models corresponding to portfolio credit risk were proposed bysome large financial companies. This paper focuses on the research of tail sad-dlepoint approximation of portfolio credit risk based on CreditRisk~+ model ofdefault loss rate to both fixed value and random variable.The main content of this paper can be summarized as follows:1. In the first chapter, I introduce the background of the topics and itssignificance. In the following section, the literature of portfolio credit risk modeland basic knowledge were summarized. And then the comparisons of differentportfolio credit risk models were introduced.2. In the second chapter, the building CreditRisk~+ models were introduced,By defining the probability generating function, the CreditRisk~+ model of thedefault probability to both fixed value and random variable was discussed.3. In chapterⅢ, the detailed derivation of tail saddlepoint approximation ofthe portfolio credit risk when the default loss rate to a fixed value is discussed. Bybuilding portfolio credit risk probability generating function and the cumulativeproduction function, and using Lugannani-Rice saddlepoint approximation. Wecome to the tail distribution function of portfolio credit risk when default lossrate of fixed value.4. In chapterⅣ, The tail saddle point approximation of the portfolio creditrisk when the default rate for the random variable is researched. In this part, weassume that the rate of default losses obeys Beta distribution through buildingmoment generating function, probability generating function and the cumulativeproduction function, Using the same approximate Lugannani—Rice with chapter Ⅲ, we can obtain portfolio credit risk tail distribution function when default lossrate obeys Beta distribution.5. In chapterⅤ, a new method, distortion risk measurement, was introduced.I proved that a concave distortion function is a necessary and sufficient conditionfor coherence. And then comparison between this method with VaR and Tail-VaR was presented, at last, We got the conclusion that this method is-betterthan VaR and Tail-VaR in risk measurement.