Research Of Basket Credit Default Swaps Pricing Model Based On The Mixed Copula

Credit default swap is a kind of off-balance sheet derivative financial instruments for financial institutions which are used to manage credit risk. Credit default swaps have become the largest trading volume products of credit derivatives. The pricing models for Credit default swaps have become the focus of the scholars. In2010, the Chinese version of the credit default swap-credit risk mitigants (CRM) has been introduced in the markets, but after3years of development, the transactions of CRM has been light. The imperfect pricing model becomes one of the bottleneck to the development of CRM market.With basket credit default swaps(BDS), a number of assets are managed as a portfolio aimed to risk management. BDS can effectively reduce the cost of risk management and transaction cost, and is helpful to improve the level of portfolio risk management, have become one of the fastest growing credit derivatives in the recent derivatives market. In this paper, a mixed copula function connect the joint distribution of the default time, and then build the pricing formula for basket credit default swap based on the mixed copula function.The main work:(1) To build and estimate the mixed copula function model. First, estimate the parameters of a single copula function:non-parametric kernel estimation which is used to estimate the marginal distribution functions; the great maximum likelihood method which is used to estimate copulas connect function parameters. Second, estimate the mixed Copula function parameters with the minimum distance method based on experience copula function. Though two steps, the mixed copula model has been builded which is more accurate for the default distribution tail.(2) To build pricing model for BDS based on mixed copula function, and give simulation steps for the joint distribution of the multiple assets default time based on the monte carlo simulation method. Based on random number simulation method for copula function, in the case of known copula function parameters, we can get N simulated future defaults possible, and then get the numerical solution for BDS of the k-th time of default.The main features and innovations:(1) Construction of mixed Copula to measure the nonlinear dependency structure of the asset. We build a linear combination of three types of Archimedean Copula-based function which is a mixed copula function. This paper aims to build a mixed Copula function which is relatively simple to calculate, based on three commonly used Archimedes Copulas. This paper uses the mixed copula function to measure the default correlation of multiple assets, not only avoid the linear correlation coefficient can’t measure nonlinear related defects, but also avoid using elliptical copulas function which may lead to small tail correlation.(2) The parameter estimation of mixed Copula is divided into three steps, the use of the minimum distance method and experience Copula to fit the best mixed copula, can reduce the difficulty of multiple parameters estimation.