Bond Default Risk Measurement Based On Improved KMV Model

Default is an inevitable product of the maturity of the bond market.The size of the default risk can be used as an objective yardstick to measure the market default situation and credit risk,which has important reference significance for all participants in the bond market.In mature bond markets abroad,a relatively complete default risk measurement system has been developed and widely used by all parties in the market.China’s bond market started late and is in a period of development and growth.The measurement of bond default risk has been paid more and more attention by investors,entrepreneurs and market regulators.The KMV model is based on the BSM option pricing theory,and the latest expected default probability can be obtained in real time through market transaction data.Because of its strong theoretical foundation,comprehensive analysis,real-time quantitative analysis,and wide application range,this model is widely used in the default risk measurement system of China’s bond market.This paper aims to use KMV model to measure the default risk of Bonds in China,and explore the optimization and improvement by using genetic algorithm and nonlinear expectation,in order to get better results.The article is divided into five parts:The first part is the introduction.It mainly studies the development of China’s bond market and the process of default,consults the relevant literature on the study of credit bond risk at home and abroad,and expounds the development process of the risk measurement model system.The second part is an overview of the theory.The KMV model theory,genetic algorithm theory and nonlinear expectation-related theory are introduced in detail,providing theoretical support for later empirical analysis and risk measurement model exploration and innovation.The third part is the modeling process and empirical analysis of the KMV model.The sample takes listed companies that have defaulted on bonds as the default group,and a large number of normal companies as the control group.The parameters of the KMV model are adjusted according to the bond market in China,and the empirical results are roughly equivalent to the previous research and analysis results.The fourth part is the empirical analysis of the improved KMV model.Through the statistical analysis of a large number of historical default data in the US bond market,KMV company finally determined the default point formula as:DP=Ds+0.5DL,where,DS and DL respectively represent the short-term and long-term debt of the enterprise.This paper attempts to redefine the default point through genetic algorithm,and calculates the unique default point of my country’s bond market by using the data of my country’s bond market.However,because my country’s bond market started late and has a short development time and there are few bond samples,ST companies are used instead of default bond samples.And select a considerable scale of the normal operation of listed companies as a control sample,use the genetic algorithm to determine the optimal default point of China’s financial market:DP=4.3DS+1.7DL,The empirical effect of the KMV model under the new default point is ideal in predicting whether the company is ST.The improved default point is used in the KMV model,and the empirical results are compared with the original KMV model results,and the improved genetic algorithm is obtained.The accuracy of the KMV model has been improved,but the effect is still somewhat insufficient due to the use of ST company samples to replace bond data.In addition,considering that the KMV model is derived from the BSM option pricing model,and the BSM model is established under complete market conditions,which cannot describe the uncertainty of the market,this paper tries to put forward a further improvement of the KMV model based on uncertain market.Using the nonlinear expectation correlation theory,the European option pricing formula under uncertain market is derived,and the fuzzy coeficient k is introduced to extend the linear measure under the complete market to a family of probability families with uncertainty.And then the improved KMV model based on nonlinear expectation is derived.Find the appropriate value of k for different industries so that the default distance of the default group is lower than the average value of the control group.According to the empirical results,when k is greater than or equal to 0.1,the default distance of the default group becomes smaller,while the default distance of the control group becomes relatively stable or sharply larger and then becomes smaller.The change trend of the k value corresponding to different companies in different industries is different,but all of them reflect the effectiveness of the introduction of the k value.It also proves that the market has uncertainty,and the uncertainty of different companies in different industries is also different,which more strongly proves the effectiveness and superiority of the improved KMV model based on nonlinear expectation.Finally,the work and conclusions of this paper are summarized.Based on the improved KMV model,some suggestions are given to the bond market risk measurement system,which provides a reference template for future bond default risk measurement.The deficiency of the model and the direction of how to improve the bond default risk measurement mechanism in the future are pointed out.Look into the future of the bond market and give some suggestions to the participants of the bond market.