Measurement model at counterparty or issuer level
(1) Risk measurement model based on option pricing technology.
Merton found that banks get the same payment by discounting loans with face value D and selling put options with strike price D. Therefore, the value of risk loan is equivalent to the value of non-default risk loan with face value of D plus put option. The value of the loan's selling right depends on five variables, namely, the market value of the enterprise assets, the fluctuation of the market value of the enterprise assets, the face value of the discounted loan, the remaining term of the loan and the risk-free interest rate.
Based on the market value of an enterprise and the unobservability of its fluctuation, KMV Company of the United States developed KMV model in 1995, also known as expected default frequency (edf). This model uses the structural relationship between the market value of enterprise equity and the market value of assets to calculate the market value of enterprise assets. The structural relationship between the volatility of enterprise assets and the volatility of enterprise equity is used to calculate the volatility of enterprise assets, and the bankruptcy ratio of companies with a certain standard deviation in one year is counted to measure the default probability of companies with the same standard deviation.
This model is one of the most widely used credit risk models in practice. The theoretical basis of this model is similar to Blake-Scholes (1973), Merton (1974) and Herwhite (1995) in many aspects. The basic idea is that when the company's value drops to a certain extent, the company will default on its debts. According to the correlation analysis, KMV found that the most common breakpoint is when the company's value is equal to 50% of current liabilities plus long-term liabilities. With the expected value of the company in the future and the default point at this time, we can determine how much the company's value will drop to reach the default point. To reach the default point, the ratio of the percentage of asset value to the standard deviation of asset value is called the default distance. Default distance = (expected value of assets-default point)/expected value of assets × volatility of asset value. This method has a relatively sufficient theoretical basis and is especially suitable for the credit risk of listed companies.
The advantage of KMV model is that it links the default with the characteristics of the company rather than the initial credit rating of the company, making it more sensitive to the changes in the quality of the debtor; At the same time, it measures the expected default probability of listed companies through the stock price, so the market information can also be reflected in the model, which makes it forward-looking and has strong forecasting ability. Moreover, because the variables used in this model are all market-driven, showing greater time variability, the choice of holding period is more flexible than the credit measurement model.
(B) var-based credit measurement model.
Var refers to quantifying the maximum value loss that financial assets may suffer in a certain period of time under normal market conditions and a given level of confidence. When calculating the risk value of financial instrument market risk, the main input variables are the current market price and volatility of financial assets. Due to the lack of liquidity of loans, it is impossible to observe the market value and volatility of loans.
JP Morgan (1997) bank has developed a credit index system (credit metrics? ) system to solve the valuation and risk calculation of non-trading assets such as loans and private placements. Based on the borrower's credit rating, credit transfer matrix, the recovery rate of default loans and the credit risk spread in the bond market, this method calculates the market value and volatility of loans, infers the var of individual loans or portfolios, and thus evaluates loans and non-trading assets and credit risks.
The advantage of the credit measurement model is that the credit grade transfer, default rate, default recovery rate and default correlation are brought into a unified framework for the first time to measure credit risk. This model is suitable for risk measurement of credit asset portfolios such as commercial credit, bonds, loans, loan commitments, letters of credit and market instruments (swaps, forwards, etc.). However, there are the following problems in the application of this model: the default rate is directly taken from the average value of historical data, but empirical research shows that the default rate is directly related to the macroeconomic situation and is not fixed. Assume that the return on assets obeys normal distribution, but empirical research shows that the actual distribution is mostly characterized by thick tail; The hypothesis that the correlation between the returns of enterprise assets is equal to the correlation between the returns of company securities needs to be verified. The calculation results of this method are highly sensitive to this assumption.
(3) credit risk+ system based on actuarial science.
The leading idea of Credit Risk Plus system developed by CSFB (1997) Bank of Credit Suisse comes from actuarial science, that is, the loss depends on the frequency of disasters and the degree of loss or damage caused by disasters. It doesn't analyze the reasons of default, and the model only focuses on the default risk, and does not involve the transfer risk, which is especially suitable for the credit risk analysis of loan portfolios containing a large number of small and medium-sized loans.
This method is based on some assumptions: whether any single loan in the loan portfolio defaults is random; The default probability of each loan is independent, so this method assumes that the default probability distribution of each loan in the loan portfolio obeys Poisson distribution. The advantage of the credit risk additional model is that it only needs limited input data, basically only needs the loan default rate, default rate volatility and risk exposure of each group in the loan portfolio, so the loan loss is easy to calculate.
(4) Credit portfolio view system based on macro simulation.
The credit portfolio viewpoint system is developed by McKinsey & Company (Wilson, 1997), and it is a macroeconomic simulation system of default risk. Because the business cycle factor affects the probability of default, McKinsey & Company brings the cyclical factor into the measurement model. Based on credit indicators, the system deals with cyclical factors and systematizes the relationship between rating transfer matrix and macroeconomic variables such as economic growth rate, unemployment rate, interest rate, exchange rate and government expenditure. Monte Carlo method is used to simulate the "influence" of periodic factors to measure the change of rating transfer probability, analyze the relationship between macroeconomic situation change and credit default probability and transfer probability, and then analyze the credit risk degree of borrowers with different credit ratings in different industries or departments.
The advantage of this model is that all kinds of macro factors affecting the probability of default and the change of credit rating are brought into its own system, and the specific loss distribution is given, which can describe the uncertainty of recovery rate and the losses caused by national risks; All risk exposures adopt the mark-to-market method, which is more suitable for measuring the credit risk of a single debtor and a group of debtors. It is mainly suitable for measuring the credit risk of speculative debtors who are sensitive to changes in macroeconomic factors.
Measurement model of asset portfolio level
Modern modern portfolio theory (MPT) shows that proper use of the correlation between assets can effectively reduce risks and improve the risk-return situation of portfolio. However, the loan and bond portfolios with poor liquidity have some problems, such as the non-normality of returns and the unobservability of returns and correlation coefficients, which make it impossible for modern portfolio theory to simply apply these portfolios. Due to the non-normality of returns, the modern portfolio theory based on two moments (mean and variance) can only be better described by adding skewness and kurtosis. The lack of historical price and transaction data makes it extremely difficult to calculate the correlation coefficient between yield, variance and covariance and income by using historical time series data. The credit risk measurement model at portfolio level is developed by overcoming these problems. This kind of model can be roughly divided into two categories: one is to seek to calculate the risk-return alternation relationship of all securities portfolios, such as KMV's portfolio management model; The other is the var calculation of centralized risk dimension and portfolio, such as the Creditmetrics portfolio model.
Credit risk measurement model of derivatives
Derivatives can be divided into interest rate derivatives and credit derivatives. The former can be divided into symmetrical derivatives according to its risk-return characteristics, mainly referring to forwards, futures and swaps, while options belong to asymmetric derivatives, and their risk-return characteristics show typical nonlinearity. The latter mainly changes the overall risk characteristics of assets by adopting decomposition and combination technologies such as credit swap, credit option and credit forward.
There are many differences between credit risk of derivatives and on-balance-sheet business. First of all, the non-default value of the contract must be negative for the counterparty; Secondly, the counterparty must be in financial difficulties; Thirdly, under any level of default probability, derivatives are generally settled by net, and the losses suffered by default are often lower than those of loans with the same amount; Finally, banks and other financial institutions use many other mechanisms to reduce the probability and loss of default. In view of this, researchers put forward many econometric models, but mainly focused on swaps and options.
The pricing of credit derivatives is a difficult problem in the research field of credit risk management. At present, there are three main methods for pricing credit derivatives in academic and practical circles: pricing based on insurance theory, pricing based on replication technology and pricing based on stochastic model. In the pricing method based on insurance theory, the insurance company bears the credit risk of the insured, so it must get a certain premium as compensation. This pricing method is a statistical method based on the historical default database of insurance companies, which has a narrow scope of application and can only provide insurance for credit derivatives with historical default data. Pricing based on replication technology needs to determine the value of all positions in the portfolio one by one, which is difficult to achieve for credit derivatives with complex structure. Pricing based on stochastic model is the mainstream direction at present, in which strength model and mixed model are widely used.