Var model of var model

Main researchers: Huang Shifu, Yang, Yang Cangsong.

introduce

In the 1990s, with the standardization and expansion of the international financial market, the competition among financial institutions has also undergone fundamental changes, especially the innovation of financial products, which has transformed financial institutions from the past resource exploration into internal management and innovation competition, thus leading to profound changes in the management of financial institutions. Banks, securities companies and other financial institutions in developed countries actively participate in the innovation and trading of financial products (tools), making financial risk management a modern financial institution. With China's entry into WTO, domestic financial institutions are facing the challenge of global financial integration, and financial risk management is particularly important.

Traditional asset-liability management relies too much on the analysis of financial institutions' statements and lacks timeliness. Asset Pricing Model (CAPM) can't be integrated into new financial derivatives, and measuring risk with variance and β coefficient only reflects the fluctuation range of the market (or assets). These traditional methods are difficult to accurately define and measure the financial risks existing in financial institutions. 1993, G30 Group published the report "Practice and Rules of Derivatives" on the basis of studying derivatives, and put forward the VaR( Value-at-Risk) model ("risk valuation" model) for measuring market risk. See you later, JP. Morgan introduced RiskMetrics risk control model to calculate VaR. On this basis, the CreditMetricsTM risk control model for calculating VaR is introduced, the former is used to measure market risk; CreditmetricsTM technology released by JP. Morgan successfully extended the application scope of standard VaR model to credit risk assessment and developed it into "credit risk value" model. Of course, the model for calculating credit risk assessment is more complicated than the market risk assessment model. At present, VaR-based financial risk measurement has become a widely used financial risk measurement method in most foreign financial institutions.

VaR model provides a measure of market risk and credit risk, which is not only beneficial to the risk management of financial institutions, but also to the effective supervision of regulatory authorities.

⒈ 1995 Basel Committee agrees that qualified banks can use internal models as the basis for calculating market risk capital requirements, and stipulates that the capital amount that meets market risk requirements can be obtained by multiplying the VaR value calculated by banks using approved internal models by 3. This is mainly because the standard VaR method is difficult to capture the possibility of risk loss in extreme market movements, and the practice of multiplying by 3 provides the necessary capital buffer.

2. The ⒉Group of 30 1993 suggested that at-risk, that is, the value-at-risk method (VaR), should be taken as an appropriate risk measure, especially to measure the market risk of OTC derivatives.

3. 1995, the SEC also issued a proposal to require American companies to adopt VaR model as one of the three feasible methods to disclose their derivatives trading activities.

The trend of these institutions makes the role of VaR model in risk management and supervision of financial institutions increasingly prominent.

Development of international financial risk management

Judging from the development of international financial risk management, in the past 20 years, it has roughly experienced the following stages:

(A) In the early 1980s, due to the debt crisis. Banks generally began to pay attention to the prevention and management of credit risk, and the result was the birth of the Basel Accord. This agreement quantifies risks by giving different weights to different types of assets, which is a general analysis method of bank risks.

(2) With the rapid growth of derivative financial instruments and transactions since 1990s, market risks have become increasingly prominent. Several major crises that shocked the world bank and financial institutions (such as Bahrain Bank and Daiwa Bank) have aroused people's concern about market risks. Some major international banks began to establish their own internal risk measurement and capital allocation models to make up for the shortcomings of the Basel Accord. The main progress includes: a new market risk measurement method-Value at Risk (VaR). The most important representative of this method is the "risk matrix" system of Morgan Bank. Bank performance measurement and capital allocation method —— Credit Bank's "risk-adjusted return on capital (RAROC)" system.

(3) In recent years, some big banks have realized that credit risk is still the key financial risk, and began to attach importance to the measurement of credit risk, trying to establish internal methods and models for measuring credit risk. Among them, JPMorgan Chase's credit indicators and Credit Risk Plus of Credit Suisse's financial products (CSFP) are the most concerned.

Since the 1997 Asian financial crisis broke out, the risks in the world financial industry (such as the losses of 1998 American Long-term Capital Management Company) have shown new characteristics, that is, the losses are no longer caused by a single risk, but by credit risk and market risk. The financial crisis has prompted people to pay more attention to the comprehensive model of market risk and credit risk and the quantification of operational risk, so the comprehensive risk management model has attracted people's attention.

After years of efforts, risk management technology has reached the level of active risk control. At present, the relevant research mainly focuses on the improvement and supplement of the existing technology, and attempts to extend the risk valuation method to other risk areas besides market risk (including credit risk, settlement risk and operational risk).

From the perspective of quantitative management technology of financial risks, international financial organizations and financial institutions have developed the following new technologies.

(1) New Capital Accord

1On June 3, 1999, the Basel Committee on Banking issued the revised draft of 1988 Basel Accord, which paid full attention to the new methods of bank risk management. Specifically, there are three ways to provide a more realistic choice for banks to manage credit risk: ① Modify the existing method as the standard method for most banks to calculate capital. In this case, ② For banks with high complexity, the Basel Committee on Banking thinks that their internal ratings can be used as the basis for determining capital standards, and for some high-risk assets, the weight higher than 100% is allowed. ③ The new agreement clearly states: "Some banks with high complexity have also established credit risk models based on rating results (and other factors). This model aims to cover the risk of the whole portfolio, which does not exist only in the case of relying on external credit rating or internal credit rating. However, due to a series of difficulties, including the availability of data and the effectiveness of the model, the credit risk model obviously cannot play an obvious role in the formulation of the current minimum capital. " The Committee hopes that the credit risk model can be used after further research and experiment, and will pay attention to the progress in this regard. This shows that the Basel Committee on Banking has affirmed the credit risk measurement model currently used by Morgan and other international banks to a certain extent.

It affirms the progress of market risk management and highlights the management of interest rate risk and operational risk. In addition, some new financial innovation tools have been affirmed. For example, the new agreement puts forward a new risk weight measurement scheme for asset securitization, and adopts 20% credit risk conversion weight for some short-term commitments. And clearly pointed out: "The recent development of credit derivatives and other technologies to reduce credit risk has greatly improved the level of bank risk management."

(2) Value at Risk

Among the various methods of risk management, VaR method is the most noticeable. Especially in the past few years, many banks and regulators have begun to use this method as a standard for measuring risks in the whole industry. VaR is attractive because it sums up all the portfolio risks of banks into a simple number and expresses the core of risk management-potential losses in dollars. In fact, VaR is to answer how much the bank portfolio value may lose at most in the next stage under a given probability.

The characteristics of VaR can be used to express the size of market risk simply and clearly. The unit is USD or other currencies. Investors and managers without any technical color and professional background can judge financial risks through VaR value. ② Risk can be calculated in advance, unlike previous risk management methods, which all measure risk afterwards; ③ Not only can the risk of a single financial instrument be calculated. It can also calculate the portfolio risk composed of various financial instruments, which is impossible for traditional financial risk management.

VaR is mainly used for risk control. At present, more than 1000 banks, insurance companies, investment funds, pension funds and non-financial companies have adopted the VaR method as a risk management tool for financial derivatives. Using VaR method to control risks can make each trader or marketing unit know exactly how big the risk of their ongoing financial transactions is, and set a VaR limit for each trader or marketing unit to prevent excessive speculation. If strict VaR management is implemented, some major losses in financial transactions can be completely avoided. ② Used for performance evaluation. In financial investment, high returns are always accompanied by high risks, and traders may take huge risks to pursue profiteering. In order to operate steadily, the company must limit the possible excessive speculation of traders. Therefore, it is necessary to introduce performance evaluation indicators that consider risk factors.

But the VAR method also has its limitations. VaR method mainly measures market risk. If we only rely on the VaR method, we will ignore other kinds of risks, such as credit risk. In addition, from a technical point of view. The VaR value indicates the maximum loss within a certain confidence level, but the possibility that the loss is higher than the VaR value cannot be absolutely ruled out. For example, if the risk value of a certain day is100000 USD and the confidence is 99%, there is still a possibility that the loss of 1% will exceed100000 USD. Once this happens, the impact on the business department will be disastrous. Therefore, in financial risk management, VaR method cannot cover everything, and other qualitative and quantitative analysis methods still need comprehensive application. The Asian financial crisis also reminded risk managers that the value-at-risk method can't predict the exact loss degree of portfolio, nor can it capture the relationship between market risk and credit risk.

(3) risk adjusted return on capital law

Risk adjusted return on capital is the ratio of income to potential loss or the value at risk. When banks use this method to make decisions on the use of funds, they are not based on the absolute level of profits, but on the discounted profit value of capital investment risks.

Every bank knows the relationship between risk and return. When investing, the greater the risk, the greater the expected gain or loss. If the investment loses money, the bank's capital will be eroded, and in the worst case, the bank may fail. Although banks are very sensitive to capital erosion caused by investment losses, they must realize that these risks are borne for profit. The key point is that banks should find an appropriate balance between risk and return, which is also the purpose of RAROC. The key to determine RAROC is the potential loss, that is, the value at risk. The greater the risk value or potential loss, the greater the discount of investment return.

RAROC can be used for performance evaluation. If a trader is engaged in high-risk investment projects, even if the profit is high, the RAROC value will not be high because of the high VaR value, and its performance evaluation will not be high. In fact, the failures of Bahrain Bank, Daiwa Bank and Baifuqin in recent years are all due to the unreasonable evaluation of a person's performance, that is, only the profit level of a person is considered, but the risks he takes while making profits are not considered, so as to be further reused. The RAROC method used in performance evaluation can truly reflect the operating performance of traders, limit their excessive speculation and help avoid the occurrence of large losses.

(4) Credit indicators

1At the beginning of April, 1997, J.P. Morgan Consortium of the United States, together with several other international banks-Deutsche Morgan Fu Jian, Bank of America, UBS, UBS and BZW***, launched the world's first portfolio model to assess the credit risk of banks. Based on the credit rating, this model calculates the probability that a loan or a group of loans will default, and then calculates the probability that the above loans will become bad debts at the same time. This model attempts to reflect the capital value that banks or the whole credit portfolio should prepare once they face the risk of credit rating change or default through the calculation of VaR value. The model covers almost all credit products, including traditional commercial loans; Letters of credit and commitments; Fixed income securities; Commercial contracts, such as trade credit and accounts receivable; And market-driven credit products, such as swap contracts, futures contracts and other derivatives. The specific calculation steps are as follows: first, determine the exposure distribution of each product in the credit portfolio; Secondly, calculate the value change rate of each product (caused by the rise, decline or default of credit rating); Thirdly, summarize the change rate of a single credit product to get a change rate value of a credit portfolio (the relationship between products should be considered when summarizing). It can be seen that under the assumption that all kinds of assets are independent of each other, the risk value of each kind of asset credit risk portfolio is equal to the exposure distribution of such assets and the rate of change of their credit rating or default. That is, it is equal to the change rate of credit rating or default x loan amount.

(5) Recently, the Institute of International Finance in Washington, USA, analyzed and tested the main credit risk models and portfolio models, aiming at finding the best way to measure credit risk, determining a more standardized model to measure credit risk and determining the allocation of capital, thus creating conditions for the development of international banking and its risk supervision, and planning to cooperate with the Basel Committee on Banking in this regard.

VaR risk control model

The basic idea of 1.VaR model

The literal interpretation of VaR is "value at risk", that is, the biggest loss that a financial instrument or its combination will face under the fluctuation of future asset prices within a certain confidence level and a certain holding period. JP。 Morgan's definition is: VaR is an estimate of the maximum market value loss that may occur before a given position is neutralized or revalued; Jorion defines VaR as "the worst expected loss within the holding period of a given confidence interval".

Two. VaR basic model

According to Jorion( 1996), VaR can be defined as:

VaR=E(ω)-ω* ①

Where E(ω) is the expected value of the portfolio; ω is the final value of the portfolio; ω * is the lowest final value of the portfolio at the confidence level α.

Let ω=ω0( 1+R) ②.

Where ω0 is the value of the portfolio at the beginning of holding, and r is the return rate of the portfolio within the set holding period (usually one year).

ω*=ω0( 1+R*) ③

R* is the lowest rate of return of the portfolio at the confidence level α.

According to the basic properties of mathematical expectation, the formulas ② and ③ are substituted into ①, and there are

VaR = E[ω0( 1+R)]-ω0( 1+R *)

=Eω0+Eω0(R)-ω0-ω0R*

=ω0+ω0E(R)-ω0-ω0R*

=ω0E(R)-ω0R*

=ω0[E(R)-R*]

∴VaR=ω0[E(R)-R*] ④

In the above formula, ④ is the VaR value of the portfolio. According to Formula ④, if R* at the confidence level α can be found, the VaR value of the portfolio can be found.

Three. Assumptions of VaR model

VaR models usually assume the following:

1. Market efficiency hypothesis;

Market fluctuation is random and there is no autocorrelation.

Generally speaking, the quantitative analysis of social and economic phenomena with mathematical models must follow its assumptions, especially for China's financial industry, because the market still needs to be standardized, the government intervention behavior is more serious, which can not fully meet the strong effectiveness and randomness of market fluctuations, and can only be treated approximately normally when using VaR model.

Calculation method of VaR model

As can be seen from the previous formulas ① and ④, calculating VAR is equivalent to calculating the values of E(ω) and ω * or E(R) and R*. At present, there are three main methods to calculate VaR.

1. Historical simulation method.

Variance-covariance method

[13] Monte Carlo simulation method (Monte Carlo simulation)

First, the historical simulation method

The "historical simulation method" is to calculate the VaR value of the portfolio by calculating the frequency distribution of the risks and returns of the portfolio in the past period of time, finding out the average return in a period of time in history and the lowest return at a given confidence level α.

The "historical simulation method" assumes that the income is independent and identically distributed with time, and the histogram of historical data samples of the income is used as an estimate of the true distribution of the income. The distribution form is completely determined by the data, and the information will not be lost or distorted. Then, the P quantile data of the histogram of historical data samples is used as the estimation of the fluctuation of P quantile of income distribution.

Generally speaking, in the frequency distribution chart (figure 1, see example 1), the horizontal axis measures the income of the institution on a certain day, and the vertical axis measures the days when the corresponding income group appears in a year, so as to reflect the frequency distribution of the combined income of the institution in the past year.

First, calculate the average daily income E(ω)

Secondly, the size of ω * is determined, which is equivalent to finding and determining the corresponding minimum daily income value given the confidence level α in the interval where the daily income at the left end of the graph is negative.

Set the confidence level to α, because the observation day is t, which means that the difference is abandoned at the left end of the graph.

T=T×α, the lowest value ω * of α probability level can be obtained. From this, we can get:

VaR=E(ω)-ω*

Two. Variance-covariance method

The "variance-covariance" method also uses historical data to calculate the var value of asset portfolio. The basic idea is:

Firstly, the variance, standard deviation and covariance of portfolio returns are calculated by using historical data;

Secondly, assuming that the return of portfolio is normal distribution, the critical value reflecting the degree of distribution deviation from the mean can be obtained at a certain confidence level;

Thirdly, establish the relationship with risk loss, and deduce the VaR value.

Let the average value of an asset portfolio in unit time be μ, the standard deviation be σ, r * ~ μ (μ, σ), and let α be the critical value under the confidence level α. According to the nature of normal distribution, the maximum distance that may deviate from the average at α probability level is μ-α σ.

That is, R*=μ-ασ.

∫E(R)=μ

According to VaR=ω0[E(R)-R*], there are

VaR=ω0[μ-(μ-ασ)]=ω0ασ

Assuming that the holding period is △t and the mean and standard deviation are μ△t and, respectively, the above formula becomes:

VaR=ω0 α

So as long as the standard deviation σ of a combination can be calculated, the value of its VaR can be obtained. Generally speaking, the standard deviation σ of a combination can be calculated by the following formula.

Where n is the type of financial instruments in the portfolio, Pi is the market value of financial instruments of Class I, the standard deviation of financial instruments of Class I, and σij is the correlation coefficient of financial instruments I and J. ..

In addition to historical simulation method and VaRiance-covariance method, there is a more complex "Monte Carlo simulation method" to calculate the var of portfolio. It is based on historical data and assumed parameter characteristics of established distribution, and simulates a large number of portfolio returns through random generation, and then calculates the VaR value.

According to the research of goodhart et al., the basic steps and characteristics of the three methods for calculating VaR are shown in the following table.

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Comparison of risk assessment techniques

classify

Step-by-step HSM var-CoV Monte Carlo

1. Confirm Positions Find all positions of various financial instruments affected by market risks.

3. Identify risk factors Identify various risk factors that affect financial instruments in the portfolio.

3. Obtain the income distribution of risk factors in the holding period, calculate the historical frequency distribution over the years, calculate the standard deviation and correlation coefficient of risk factors over the years, and assume a specific parameter distribution or randomly generate it from historical data through self-help.

4. Relate the return of risk factors with the position of financial instruments, and express the market value of the position as a function of risk factors. Divide positions according to risk factors (risk mapping), and express the market value of positions as a function of risk factors.

5. Calculate the variability of the portfolio. Simulate the frequency distribution of portfolio income by using the results obtained from steps 3 and 4. Assuming that the risk factors are normally distributed, calculate the standard deviation of the portfolio. Simulate the frequency distribution of portfolio income by using the results obtained from steps 3 and 4.

6. Derive VAR with the given confidence interval.

Arrange the portfolio order, and choose that the loss is just ≥ 1% or 5% probability.

Use 2.33( 1%) or 1.65(5%) times the standard deviation of the portfolio to arrange the order of the portfolio, and choose the loss just ≥ 1 under the probability of 1% or 5%.

Application of VaR model in financial risk management

The application of VaR model in financial risk management is more and more extensive. Especially with the continuous improvement of VaR model, it is not only applied to the quantitative study of market risk and use risk of financial institutions, but also organically combined with the planning model theories such as linear programming model (LPM) and nonlinear programming model (ULPM) to determine the best quantitative analysis method of market risk of financial institutions, thus helping financial institutions to make optimal decisions on potential risk control.

Regarding the application of VaR in foreign countries, as pointed out in the introduction, the Basel Committee requires qualified banks to combine the VaR value with the internal model of the bank to calculate the capital amount that meets the market risk requirements; G20 suggested using VaR to measure the market risk of derivatives, and thought it was the best way to measure and control the market risk. The SEC also requires American companies to adopt the VaR model as one of the three feasible methods to disclose their derivatives trading activities. This shows that not only financial institutions are increasingly using VaR as a method to judge their own financial risks, but also more and more regulators are using VaR as a method to judge the risks of financial institutions.

The introduction of VaR model in China only started in recent years, and there are many research results. However, the application of VaR model is really in the initial stage. Financial institutions have fully realized the advantages of VaR and are studying the VaR model suitable for their own operating characteristics.