Research On Pricing Of Basket Credit Default Swaps Based On Kmv-Combined Copula Model

Since 2014,default events have occurred frequently in China's bond market,and investors are faced with a certain risk of bond default.Therefore,how to reduce the probability of bond default and the loss to investors caused by bond default is an important problem that needs to be solved quickly in the current financial market.Credit default swaps contract is a kind of credit derivatives with the function of credit risk mitigation.By signing a contract,the credit risk bearers transfer the credit risk in the market to those who are willing to take credit risk and obtain return income.Credit default swap products are widely used in overseas financial markets,and have become one of the main credit derivatives.However,the development speed of credit risk mitigation tools in the domestic credit market is relatively slow.The first credit risk mitigation tool was launched in 2010,and the product transaction is not active enough,and the pricing system is not perfect.Therefore,the pricing of credit default swap products in China has become one of the hot issues in academic circles.This paper makes a detailed analysis and in-depth discussion on the pricing mechanism and pricing model of credit default swap to help promote the introduction and development of credit risk mitigation tools in China,which is conducive to the risk management in China's financial market.The basket credit default swaps(BDS)is a credit derivative product with multiple reference assets.The one who wants to avoid credit risk can transfer the default risk of multiple assets by signing the basket credit default swap contracts.Based on the existing academic research,this paper studies and discusses the pricing of the basket of credit default swap contracts based on the market data in China.And the paper also makes an empirical study on the corporate bonds issued by small and medium-sized enterprises(SME)listed on the SME board to provide reference for the pricing of BDS contracts of SMEs.The research work of the whole paper is as follows:(1)This paper research the pricing formula of the basket of credit default swap contracts.On the basis of a detailed overview of the basket credit default swaps,this paper first expounds the trading mechanism of the basket credit default swaps,and then according to its trading mechanism and the principle of no arbitrage in the market,establishes a pricing model of the basket credit default swaps,and gives the calculation formula of the fair spread of the contract.(2)We construct the distribution function of asset default time.Combined with the core idea of KMV model,the KMV model is established based on the stock data and the company's relevant financial index data to solve the default probability.Then,the marginal distribution function of default time is constructed on the premise that the asset default intensity remains unchanged.(3)Constructing combined Copula model to connect the marginal distribution of default time and simulate the default time.Firstly,using the maximum likelihood estimation method to estimate the parameters of three single copula models;then introducing GIOWA operator,and sort the three single copula models according to the order of minimum square deviation,second square deviation and maximum square deviation,and established model which taking minimum absolute value of deviation with the once power as the optimal criterion to solve the weight of induced Copula series.Then,according to the simple weighted average method,we obtained the weights of three single Copula functions and the combined Copula model.Finally,using Monte Carlo simulation method to simulate the default time of three single Copula models and combined Copula models.(4)Calculating the contract price and make a comparative analysis under different conditions.Firstly,Sorting the simulated default time from small to large,and get the default time of the reference assets.Then,Using the formula of fair spread of contract,the contract price of the first default contract are obtained.This paper calculates and compare the contract prices of different default times by using single Copula model and combined Copula model based on GIOWA operator,and compares the prices of different contract periods,different number of reference assets.Finally,the paper compares contract price based on GIOWA operator combination Copula model which with different parameter values.The results of modeling and comparative analysis show that:(1)It is feasible to introduce GIOWA operator into the application of combined copula model to estimate the model weight.Compared with the price of the basket credit default swap contracts solved by Gumbel Copula model,Clayton Copula model and Frank Copula model,the price solved by Combined Copula model is in the middle.It will not set the price too high or too low.(2)Using different GIOWA operators to establish a combined Copula model to describe the correlation structure of data,the results will be different.When the parameter? of GIOWA operator is 1,the combined Copula model has the highest pricing for the first default and the second default of BDS contracts;when the parameter ? of GIOWA operator is 0,the combined Copula model has the lowest pricing for the first default contracts;when the parameter ? of GIOWA operator is-1,the combined Copula model has the lowest pricing for the second default contracts.(3)For the basket credit default swaps contracts,there is a big difference in the pricing of different default times.And for the reference entity selected in this paper,increasing the number of reference entities in the basket credit default swaps contracts will increase the contract price accordingly.In addition,the different duration of basket credit default swaps contracts will also have an impact on the contract price.