Research On The Pricing Of Collateralized Debt Obligation Based On Copula

As a structurized credit derivative product, collateralized debt obligation is very complex in structure and Transaction flow, exploring its pricing method have become one of numerous scholars'matters concerning. In the CDO property pond,each kind of property faces credit risks event is not mutually the independent relations, but one kind of misalignment relations,which has enlarged the difficulty of pricing.Through the mathematical theory analysis, we may be clear about joint distribution function of various properties in the base property pond. This article introduces one kind of method-Copula function,and it is very simple and fast method to construct joint distribution function method.This function is used to describe asymmetrical nonlinear correlation relations between the variable specially.Therefore,it is very appropriate to estimate joint distribution between various assets in the CDO property.In recent years, along with our country economy's fast development, the finance market also obtained develops quickly, and financial systems and the laws and regulations consummated unceasingly, the financial products innovated increase fast, emerging of large quantities of finance derivative product has provided the advantageous condition for our country's property securitization. In 2005, collateralised loan obligation of the National Development Bank and asset backed securities by mortgaging individual house of China Construction bank have opened collateralised loan obligation of our country. Because of CDO's function that transfer risk and increase financial organization and investor's investment channel and so on, we may estimate that our country's collateralised loan obligation market will be stronger and stronger. Therefore,it is necessary to know deeply this product's structure, the function and the risk and to studys the reasonable pricing method, while understanding and reducing the risk can also promote the development of our country's collateralised loan obligation market.This article first describe the CDO's concept, the classification and the domestic and foreign market development condition,which made us know the CDO's essential characteristic. Then in view of our country credit product's characteristic, utilizing the KMV model estimates each debtor's default probability among property pond.KMV-the Merton model is the classical model of the credit risks domain, which bases on the hypothesis that the undering asset value follows geometry Brown's motion. Next, using the Copula function (Gaussian copula, Student's t-copula and Clayton n-copula) portrays the dependence between the debtors in the property pond, and using the Monte Carlo method simulates each debtor's default time according to default probability which has calculated, and estimates the CDO's fair credit spread applying the CDO's pricingformula.For better understanding this pricing process, this article constructs a CDO to show the price process above through the example. We discovery:The CDO's fair credit spreads reduce from equity tranch to senior tranch to every copula, which accords with the risk which undertakes respectively. The bigger the risk is, the bigger the fair credit spread credit; Moreover, the fair credit spreads which are calculated with Student-t Copula are higher than Gaussion Copula and Clayton Copula roughly. This is because Student-t Copula has portrayed the extremum influence, the higher debtor's default dependence is, the bigger the risk is. therefore the fair credit spreads the investor requests is also higher. Moreover,we discovered by analyzing the deadline and recovery rate:for any kind of Copula, the deadline is longer, the corresponding series's spread is bigger. This is because the deadline is longer, the uncertainty will be bigger, then the risk the investor will undertake is also bigger, and the spread is bigger; Moreover the credit spread reduces with the recovery rate getting bigger.This is because, the recovery rate is bigger, the risk is smaller, the spread is also naturally small. Except the simulation example analysis, this article also uses Gaussion Copula and t Copula to research a CLO-08 zhaoYuan, and discover Gaussion Copula underestimates A1 and B tranches, but overestimation A2 tranch.The error is in 5 basic points, which is acceptable. Therefore this method can apply in pricing of CLO, and may estimate the level due returns ratio of senior tranch.