Keywords VaR；; Bank risk management; Literature review
The real development of VaR benefits from the attention of world-renowned financial institutions to market risk management. Many famous financial institutions, such as JP. Morgan, Banker Trust, Chemical Bank, Chase Manhattan, etc. , has invested a lot of money to develop new market risk management tools, aiming at developing a market risk measurement method that can not only deal with nonlinear options, but also provide overall risk on the basis of accurately identifying and measuring market risks. VaR is developed under this background. It was first used by some financial companies to measure the market risk of tradable securities in the 1980s, and it was widely used. According to the concept of Jorion(200 1), VAR (usually translated as VaR(Value atRisk)) refers to measuring the maximum possible loss of a specific position or portfolio in a certain confidence level and holding period under normal market environment. Compared with traditional risk measurement methods, VaR provides an overall view of portfolio risk considering leverage, correlation and current position, which is called forward-looking risk measurement method. The development of quantitative risk measurement has gone through a process from simplicity to accuracy, from sensitivity to fluctuation, and then to lower measurement. VaR is a downward measure, and it has been proved that the downward measure of risk is a combination of sensitivity and volatility with uncertain adverse results. As a good risk management tool, VaR was formally applied and popularized in the New Basel Accord in 2004, and became the international standard and theoretical basis of modern financial risk management.
1. Research on Value at Risk and Supervision of Commercial Banks
The internal model method (VaR model method) advocated by the new Basel Accord reflects that the regulatory authorities advocate to use market tools and market incentives when possible to improve the supervision level of banks through their policies, behaviors and technologies. Since several global financial crises, the problem of bank risk behavior has been the focus of attention. How to influence banks' risk-taking behavior through different regulatory capital requirements and help banks obtain more accurate risk measurement and appropriate risk incentives has always been the direction of joint efforts of the regulatory authorities and the banking industry. Basel Accord reflects various theoretical and practical achievements of financial supervision. In addition, there are many regulatory documents on bank risk behavior, which are mainly divided into three categories.
The first category is the relevant research results embodied in the Basel series of documents. 1988 the new Basel capital accord puts forward a unified capital requirement for risk-adjusted bank assets, and the total risk is equal to each risk asset multiplied by the corresponding risk weight. At this point, the risk weight mainly aims to reflect the credit risk of specific assets. In the measurement of capital requirements, the capital agreement of 1988 omits many important issues. Short-term account balance and securities held by the government do not include the identification of portfolio, and the exposure calculation of netting agreement in off-balance sheet items is not involved. Because the agreement only considers the capital requirements of credit risk, but not the capital requirements of market risk, with the relative importance of market transaction risk in bank portfolio increasing, regulators are forced to reconsider the capital requirements system of Basel Accord 1988. Therefore, in June 1996 and June 1, the Basel Committee published amendments to the capital accord aimed at incorporating the market risk capital requirements, so as to modify the capital accord in June 1988. The final version of this proposal was officially implemented on 1998 65438+ 10/0/(hereinafter collectively referred to as "amendment 1 996"). The amendment includes the minimum supplementary capital reserve requirement (BIS, 1996a) to cover market risks caused by market price changes. At the same time, two measurement methods are provided for banks to choose: one is to adopt the internal model method (IMA) based on VaR on the premise of meeting the requirements of supervision and audit; The second is to adopt the building block method recommended by the Basel Committee. The specific idea is: first calculate the capital requirements of each risk module separately, and then calculate the overall capital requirements through simple summation. IMA determines the method of calculating bank capital requirements according to the results of internal risk measurement of banks. In order to ensure that the capital requirements of IMA calculation are sufficient, the Basel Committee has formulated the standards for establishing internal models. If the value at risk must be calculated every day; Use the data of at least 12 months to calculate the loss distribution with the holding period of 10 days, and calculate enough capital requirements to cover 99% loss events. In a certain period of time, the minimum capital requirement is equal to the total capital requirement including the whole market risk and credit risk (or special risk), in which the market risk requirement is equal to the multiple of the average biweekly VaR report in the last 60 trading days (≥3), and the credit risk capital requirement is equal to 8% of the risk-adjusted assets. With the rapid development of information technology, the business scale and scope of banks have expanded sharply, and the operational risks of banks are on the rise. Due to the failure of internal control, serious losses and even institutional closures occur frequently. In the proposal for the reform of the New Capital Accord disclosed in June1999, the Basel Committee listed operational risk as the third largest risk after market risk and credit risk. It is suggested that the total income should be taken as the basic index to measure the operational risk of banks, and the capital requirement of operational risk should be the total income multiplied by a proportional index α (≤ 12%, BIS, 200 1). In order to check the accuracy and smooth implementation of IMA, the Basel Committee suggested back testing and comparing the risk measurement results of the internal model with the real transaction results. In order to improve the accuracy of the model, it is suggested that banks develop the ability to use daily loss distribution for posterior testing. Kupiec( 1995) thinks that because the volatility of bank assets is unobservable, the main problem faced by regulators is that they can't rule out the abnormal distribution of incorrect VaR reports and combined reports (such as fat tail, etc.). ), and advocates that posterior inspection must require many observed variables (≥250 trading days). The Basel Committee suggests that banks that fail to meet the accuracy standards of posterior testing will be subject to additional capital requirements. Posterior test and some punishment measures are essentially incentive measures to improve the accuracy of bank enhancement model. Barsac & Shapiro (2001) found that under the constraint of VaR, asset managers can only partially guarantee the loss of their portfolios, especially in the state of non-performing assets. In their model, the value-at-risk constraint must meet a certain period t, allowing bank managers to constantly adjust their portfolios. In order to obtain instantaneous portfolio risk, the regulatory authorities set the VaR posterior test period of active asset trading as one day (Bsael Committee on Banking Supervision, 1996b). However, the above literature does not consider the interactive influence of bank supervision mechanism on the choice of bank risk strategy.
The second category is the banking supervision within the continuous time frame. Merton (1977, 1978) used the option pricing model of Black Scholes( 1973) to obtain the insurance price of time deposits, and put forward the method of random audit by regulators, thus realizing the determination of reasonable deposit insurance price under the assumption of continuous fluctuation of bank assets. Pennachi( 1987) defines risk according to the financial leverage ratio, investigates the motivation of banks to take risks, and puts forward the regulatory importance of preventing banks from bankruptcy to avoid depositors from suffering losses. Kiley (1990), Thomson (1990),
Kaufman (1996) made an analysis and empirical study on how market discipline can improve the efficiency of bank supervision from different levels. The unanimous conclusion is that the full use of market methods can accurately and timely reflect the situation and environment of banking institutions, significantly enhance the supervision of banks by investors and depositors, effectively inhibit the motivation of depositors to transfer risks to the government, and improve the level and efficiency of financial supervision. Rochet( 1992) proved that the limited bank liabilities created an incentive to make risk-averse banks (bank portfolio managers try their best to maximize the expected utility) pursue high-risk investment strategies, and suggested minimizing capital requirements to overcome this risky behavior. Fries et al. (1997) analyzed the optimal bank bankruptcy boundary between social bankruptcy cost and future review cost, and found the incentive reasons for bank managers to take risks. By linearizing the shareholder value function, the incentive policy and equity support scheme to eliminate the risk incentive of banks are obtained, in which risk is defined as the fluctuation of potential state variables, not the leverage ratio. Bhattacharya etal(2002) put forward the optimal bankruptcy boundary to eliminate the risk incentive of banks and the capital needed by banks within this boundary. The model of this paper assumes that the fluctuation of potential state variables is continuous, and the existence of incentives for banks to take risks is only reduced because of the convexity of shareholder value function (for example, the solvency bank value function is convex because most banks' asset values meet the minimum capital requirements), and rarely involves the process of bank risk conversion.
The third category is about the risk conversion of the financial sector in a continuous time. Ericsson (1997); Leland (1998) put forward a model of bank shareholders changing from one risk level to another, aiming at pricing enterprise stocks through the cost of asset replacement and obtaining the best capital structure. However, the factor of deposit insurance is less considered here. Due to the deposit insurance mechanism, bank liabilities can be supported by risk-free interest rates. Therefore, there is a conflict of interest between deposit insurance companies and bank shareholders. In order to reduce the expenses of the deposit insurance system, banks must meet the regulatory constraints imposed through the review mechanism.
Second, the study of VaR and capital management of commercial banks
More reasonable and accurate allocation of capital and risk assets within banks has become the core content of risk management in modern commercial banks. The literature on VaR and bank capital management is mainly divided into three categories.
The first kind of literature is the research on the optimal management of bank capital from a static point of view. Under the analysis framework of static mean square error, Kahane( 1997), Roehn and Santometro( 1980) put forward very strict capital requirements to guide banks to replace higher-risk assets with lower-risk assets, but this may increase the trading risk and default risk of portfolios. Jin & ampSantomero( 1988) established the capital requirements based on risk-weighted assets. Unless the risk weight is directly proportional to the β of assets, capital requirements will lead banks to take more risks. Fudong & Keeley (1990) believes that it is not appropriate to analyze the effect of capital requirements with the mean square error framework under the conditions of deposit insurance and limited liabilities, because limited liabilities lead to limited distribution of return on assets, especially considering the maximization of the value of financial institutions, which shows that stricter leverage restrictions obviously reduce the optimal risk taking. The main reason is that financial institutions choose the portfolio with the greatest risk within the capital requirements, aiming at maximizing the value of deposit insurance. Janot & Pyle (199 1) extended their analysis results, thought that non-zero present value portfolio could be allowed, and indicated that financial institutions would increase asset risk under stricter capital requirements. For static sets, Chan, Greeballm &; Tucker (1992), Giammarino, Lewis & sappington (1993) studied how to guide financial institutions to truthfully reflect their real risks to the regulatory authorities under the condition of providing deposit insurance. Hovakimian & ampKane( 1994) extended Merton's one-phase deposit insurance option model to an indefinite shareholder income model, and based on this, made an empirical analysis on the effectiveness of risk transfer and capital supervision of American commercial banks from 1985 to 1994, which proved that the capital supervision of commercial banks did not effectively prevent the risk transfer of the banking industry. Patrick Jackson, CIA, David J. Maud & William Perraudin (1998) conducted an empirical study based on the application of VaR in bank capital management. Hellmann et al. (2000) established a relatively static game model of capital supervision, which proved that in the market environment of financial liberalization and full competition, if there is no necessary restriction on deposit interest rate, banks will inevitably choose speculative assets, and capital adequacy ratio supervision will not reach Pareto efficiency. Flannery (1998) and Maclachlan (200 1) believe that the supervision mode with capital adequacy ratio as the core has great defects. To improve the effectiveness of capital supervision, it is necessary to cooperate with the corresponding regulatory system arrangement and market restraint mechanism. The Bank Research Bureau of Finland (200 1) combined with the New Basel Accord, analyzed the bank capital slow release based on the VaR method. Philippe Jorion(2002) studied how to use the VaR value to analyze the portfolio risk of banks. Jeremy berkowitz company. Jarmes O'Brien(2003) studied how to improve the accuracy of the VaR model of commercial banks. There are two defects in the above research on the optimal capital requirements of banks under static conditions. First, the transaction cost of banks is not considered; Second, the influence of bank management strategy and risk preference on bank capital management is not considered.
The second kind of literature is about the research of bank capital optimization model under dynamic conditions. Blum (1999) used a two-stage model to prove that in a dynamic portfolio, stricter capital requirements will lead to an increase in portfolio risk. Ju and Pearson( 1999) verified that the amendment of 1996 can encourage financial institutions to reveal their real VaR risks when fines are related to exceptions. Sentanon & Vorst (2001) and Basak & Shapiro (2001) think that traders' investment choices are externally constrained by the trading portfolio VaR, but they do not consider the capital requirements of financial institutions. Cuo, He and Issaenko(200 1) believe that the value function of trading portfolio is limited, and regulators can observe the VaR of financial institutions completely and continuously, and the minimum capital requirement at any time point is simply equivalent to a fixed multiplier of VaR in the same period (with no penalty for exceptions). Because the capital requirement is not exogenous, but the endogenous result of the organization's optimal reporting strategy, binary martingale and binary martingale can be used. Domenico Cuco & Liu Hong (2004) believes that using IMA method to determine capital requirements is very effective in controlling portfolio risks and revealing real risks. Cuoco et al.' s analysis represents the latest achievements in the research of bank capital optimization model based on VaR, which is quite forward-looking. However, their results did not consider the capital requirements of bank operational risk, nor did they further study the situation that if there were exceptions at the end of the reporting period, default might still occur and the bank's capital was insufficient to pay the corresponding fines.
The third kind of literature is the research on the allocation and performance evaluation of bank venture capital based on VaR. Expand the value at risk to risk capital (CaR) and risk-adjusted performance measurement (RAROC). Matten( 1996) introduced various methods for calculating RAROC in detail. Zaik et al. (1996) explained that Bank of America merged the RAROC of various business departments with the banking department.
The motivation for comparing the proportion of East China is that this proportion is the minimum rate of return required by shareholders; Zagst and Kehrbaum( 1998) studied the problem of portfolio optimization under CaR constraints by numerical methods. Stratton & Zechner (1999) discusses the relationship between RAROC and shareholder value SVA; Grouhy et al. (1999) compared the project value methods in detail, and found that under certain conditions, the equity capital cost of RAROC is equal to that of banks. These comparisons also explain the department where RAROC is located. Since then, many literatures on this subject generally discuss the application examples of RAROC. Generally speaking, CaR and RAROC developed with the development of VaR in theory. At present, the research on CaR and RAROC mainly focuses on the application field. In developed countries, the application research of automobile and RAROC has been quite mature. In China, due to the differences in accounting system and the lag of bank risk management technology, it is still in the stage of discussion and experiment.
Three, VaR and commercial bank credit risk and operational risk management research
The application of VaR method has gradually expanded from the initial focus on quantifying market risk to the field of credit risk measurement and management (Basel Committee on Banking Supervision, 200 1). At present, the international representative credit risk management models are: Credit MetricsTM model given by JP Morgan 1997, Credit Risk+ system given by CSFB 1997, and Credit Portfolio ViewTM system given by McKinsey 1998, all of which use VaR to determine the risk value of bank credit portfolio. It can be said that these models are examples of the application of VaR in the field of credit risk management, but these models are mainly aimed at the banking industry in developed countries, and their application scope in China is not very large at present. In addition to the new Basel Accord adopted in June 2004, which reflects the research results of bank credit risk management (mainly reflected in the application of bank internal rating method), In recent years, Gordy & crou hy atal(2000), Frey & McNeil (2001) and Michael B Gordy(2002) have studied the credit risk modeling based on industry default, and found that when only a single credit risk factor drives the debtor's correlation, and any risk exposure in the credit portfolio only accounts for a very small share of the total risk exposure, Although their research only involves the single-factor risk situation, they have proved it. Susan Elmer & ampDirk Tasche(2003) proposed VaR granularity adjustment method and semi-gradual method based on the single factor Vasicek credit portfolio model. At present, the domestic research achievement in this field is mainly the book "Modern Measurement and Management of Bank Credit Risk" by Zhan (2004), but this book is mainly a general summary of the existing achievements abroad. Generally speaking, the research on the subject of bank credit risk management mostly involves only one factor, and rarely involves the specific assets and liabilities of banks.
Since 1980s, a series of financial cases triggered by operational risks have shocked the international banking industry, making bank operators and supervisors generally realize the importance of operational risk management. Duncan Wilson( 1995) first put forward the VaR measurement of operational risk, and thought that operational risk can be measured by VaR as well as market risk and credit risk. Relnhard Buhr(2000) proposed a method to calculate the VaR of financial institutions, which described all the related operation processes in detail. Various internal control methods are regarded as control points, and the maximum loss (MD) and out-of-control probability of each control point are estimated, so the VaR of control points is MDxP. Medova (2000,2001) and Kyriacou(2002) applied VaR and extreme value theory to quantitatively analyze operational risk on the basis of the research on extreme value theory by McNEIL and Alexander J( 1999). Because the probability of low-frequency and high-impact events is very low, the data of losses caused by such events in a single bank is not enough to support the establishment of operational risk model. Generally speaking, at present, the research on VaR operational risk measurement abroad is mainly carried out by financial institutions according to their own business characteristics, and it is still in the exploratory stage, and there is no unified research framework. Compared with the international research, the domestic literature on operational risk is mostly limited to the introduction of the new Basel Capital Accord, and there is little quantitative analysis of operational risk, let alone the corresponding database construction.
The above is the research status of foreign scholars. At present, the application research of VaR in China is still in its infancy. VaR method and its application in financial risk management were first studied by Chinese scholar Zheng 1997. The representative research on this topic in China is Financial Market Risk Management (200 1) written by Wang Chunfeng, which systematically introduces the relevant theoretical basis of VaR. Generally speaking, the domestic research on VaR is mostly a summary or imitation of foreign literature, focusing on the application in the securities market, lacking theoretical analysis and empirical research on risk management of China banking industry based on VaR.
Four. Concluding remarks
In the new Basel II (adopted in June 2004 and implemented in 2006), the design of capital (or venture capital) calculation formula and the determination and testing of related parameters all draw lessons from the ideas and methods of VaR. Because of its simple concept and easy communication, VaR method has become a standard tool for risk measurement and information disclosure in international banking. It can be said that the New Basel Accord reflects many research results of VaR in risk management of commercial banks, but the Accord itself mainly reflects the capital management requirements of banks in developed countries, and it only provides a very broad analytical framework for diversified banking systems in various countries. VaR method has a unique perspective in observing and dealing with risks. Although some of them have completely exceeded the current situation of financial research and practice in China, it is our only way to establish a modern bank risk management system that is in line with international standards. Under the condition of open economy, it is only a matter of time before the new Basel Accord with VaR as the core is implemented in China. Based on the characteristics of China's banking industry, we should take precautions and strengthen the theoretical and applied research of VaR method in the field of bank risk management in China in view of the shortcomings of the existing research and application of VaR in the above analysis.
hope this helps