The price risk of metal mineral resources is the most common and frequent risk in metal futures trading, which exists in every futures product. This is because the trading of each futures product is based on the prediction of the price change of the product; When the change direction or range of the actual price deviates from the trader's forecast, it will cause corresponding losses.
Exchange rate risk, also known as foreign exchange risk, is the possibility that the value of funds raised by enterprises in foreign currency will change due to exchange rate fluctuations. The risk of exchange rate fluctuation refers to the risk that the project company or other stakeholders who hold or use foreign exchange will suffer losses due to exchange rate fluctuation. The cost and profit of project financing are very sensitive to the exchange rate changes in the financial market. First of all, the risk of exchange rate changes between domestic currency and major international currencies will affect its production costs and expenses, and will also intensify competition in the domestic market, because foreign producers of similar products will find this market more attractive; Secondly, the change of cross exchange rate between currencies will indirectly affect the competitive position of the project in the international market; Finally, exchange rate changes will also have an impact on the debt structure of the project.
The analysis of market risk measurement method of metal mineral products mainly relies on the theory of financial market risk management, and selects market risk value (VaR) as the market risk measurement index of metal mineral products. VaR method was first put forward by JPMorgan Chase and widely used in practice. There are many methods to measure market risk, and VaR method is the mainstream method to measure financial market risk at present. The calculation methods of VaR include historical simulation, variance-oblique variance and Monte Carlo simulation. Compared with historical simulation method and Monte Carlo simulation method, variance-oblique variance method has the advantages of less data and easy operation, and is widely used in practice.
The advantage of VaR is to integrate different market factors and risks in different markets into a single number, accurately measure the potential losses caused by different risk sources and their interactions, and adapt to the trend of dynamic, complex and global integration of financial market development.
The basic idea of VaR calculation method is: firstly, according to the market risk factors of metal mineral products, analyze the role of market risk factors; Secondly, establish a volatility model to predict market risk factors and predict the volatility of market risk factors; Finally, according to the fluctuation of market risk factors, the market risk value and distribution are estimated and the VaR value is calculated.
Calculation of (1) VaR based on GARCH family model
1) the basic principle of var calculation.
VaR translated into value at risk refers to the maximum loss of a financial asset or portfolio under normal market fluctuations. More precisely, it refers to the maximum loss of a financial asset or portfolio within a certain probability level and a specific holding period. In mathematical language, we can define VaR as: Let α∈(0, 1) be a given probability level, then at α level, the VaR of portfolio P is defined as follows.
Risk assessment and decision support technology of foreign oil, gas and mineral resources utilization
Where: Function (α) is the inverse of the cumulative distribution function of income Rp. The essence of VaR is the α quantile of Rp. The conditional variance method of VaR estimation belongs to the analysis method of dynamic VaR calculation, and the core of VaR calculation is the estimation of volatility. Different volatility models make the calculation method of VaR different.
This book is a study of the time series of London copper and RMB exchange rate against the US dollar, and selects the calculation formula of VaR:
Risk assessment and decision support technology of foreign oil, gas and mineral resources utilization
Where: t stands for t day; Pt- 1 is the closing price of the previous trading day; Zα is the critical value of standard normal distribution, while the critical values of 1%, 5% and 10% are -2.33,-1.64 and-1.28 respectively. σt is the conditional standard deviation of the rate of return series estimated by GARCH model.
2) The posterior test of 2)VaR model.
In order to test the validity of the market risk measurement model, it is necessary to test the coverage of the calculation results of VaR model to the actual losses. In this book, Kupiec test is used to test the applicability of the model. Let Ⅳ be the number of times the loss in the test samples is higher than VaR, t be the total number of test samples, a be the established significance level, and f be the failure rate. These include:
Risk assessment and decision support technology of foreign oil, gas and mineral resources utilization
The hypothesis of the test is
Risk assessment and decision support technology of foreign oil, gas and mineral resources utilization
Likelihood ratio statistics are
Risk assessment and decision support technology of foreign oil, gas and mineral resources utilization
Under the initial assumption, LR obeys the X2 distribution and has 1 degrees of freedom. In the case of large samples, it can also be approximated by normal distribution, which also has a good test effect. When (1) is rejected by H0, the VaR model fails.
3) Basic principle of GARCH (p, q) family model.
Financial risks are mainly caused by the fluctuation of financial asset prices. A large number of empirical studies have found that the fluctuation distribution of financial assets has the characteristics of peak, thick tail and fluctuation aggregation, that is, the fluctuation of financial markets often shows heteroscedasticity. Based on the autoregressive conditional heteroscedasticity model (ARCH) proposed by Engle( 1982), Bollerslev established GARCH model, which can better capture these characteristics of financial market risks. ARCH and its extended models such as TGARCH and EGARCH are called GARCH model family. At present, the research on the value-at-risk (VaR) of financial markets based on GARCH family model has been very rich. For example, Gong Rui, Chen Zhongchang and others (2005); Chen Shoudian and Yu Shidian (2007); Jin Xiu and Xu Hongyu (2007); Ding (2009) et al.
Generalized autoregressive conditional heteroscedasticity model (GARCH model) analyzes the volatility of each index. The specific modeling steps are as follows: ① Check the stationarity and autocorrelation of the yield series; ② ARMA model identification based on correlation coefficient and Q statistics; ③ Establish the mean equation, determine the fitting effect of the model according to the residual autocorrelation test, and test the ARCH effect of the sequence residual term by LM method; ④ Estimating the parameters of GARCH model by maximum likelihood method; ⑤ Evaluate the model according to goodness of fit statistics.
A.GARCH model
1986 Bollerslev proposed GARCH model. The general formula of GARCH(p, q) model includes two parts: the mean equation form and the variance equation form. Can be written as
Risk assessment and decision support technology of foreign oil, gas and mineral resources utilization
Where: εt is the residual; Rt is the rate of return; αj is the coefficient of GARCH term, which represents the influence of variance lag period of random error term on current variance; βi is the coefficient of AHCH term, which represents the influence of previous random error term on spot residual variance, and depicts the market's response to new information. σt is conditional variance, which describes the volatility of the market; The model parameters satisfy the following constraints: c≥0, ω≥0, α≥0, β≥0.
B.TGARCH model
The general form of TGARCH (threshold TGARCH) model proposed by Zakoian( 1990) and Glosten, Jaganathan and Runkle( 1993) is as follows.
Risk assessment and decision support technology of foreign oil, gas and mineral resources utilization
Compared with GARCH model, TGARCH model sets a threshold dt- 1 to describe the influence of information.
Where dt- 1 is the nominal variable, and 0 or1is taken; The positive or negative impact on the variance of market conditions is different. When rising, εt≥0 means good news, then its influence coefficient is falling, ε t ≥ 0 means bad news, then its influence coefficient is that if γ ≥ 0, then the information function is asymmetric; If y﹥0, it is considered that there is leverage effect.
In addition, in the above model, the GARCH family process is wide and stationary.
4) Empirical analysis.
A. data sources.
The closing price of metal futures in this topic adopts the closing price of copper futures published by London Futures Exchange, which is downloaded by Great Wisdom Software. The data used for the exchange rate is the exchange rate of RMB against the US dollar, which comes from the statistical data provided by the Federal Reserve Bank of the United States, St. Louis Branch. The data selection interval of the two is from July 22, 2005 to September 4, 2009, in which non-business days and some missing transaction data are deducted. The missing data is treated as the average of the day before and the day after the missing data, each with 1063 data.
B. analysis of the basic characteristics of the yield series.
The market rate of return takes the form of a few days' rate of return, which is defined as
Risk assessment and decision support technology of foreign oil, gas and mineral resources utilization
Where: ri and t are the yield of the I-th market on the T-day; Pi, t is the price of I market on T day, when 1 is taken, it means copper futures market, and when 2 is taken, it means foreign exchange market. The main statistical characteristics of yield series are shown in Figure 9. 18. It can be seen that there are both volatility aggregation and explosiveness, and it can be considered that both yield series are random.
Figure 9. Main statistical characteristics of18 yield series
According to the main statistical characteristics of the yield series given in Table 9. 12, it can be seen from the skewness that the yield series of London copper is on the left and the yield series of RMB against the US dollar is on the right. Both are sharp peaks and thick tails, and the exchange rate market is more obvious than the futures market. J-B statistical test shows that both of them refuse to obey the assumption of normal distribution. From the values of Q(20) and Q2(20), we can know that both the return series and the squared return series are at the significance level of 1%, which denies the original assumption that there is no series correlation, that is, there is a significant series correlation, indicating that the volatility is very significant. Suitable for modeling with GARCH model.
Table 9. Main statistical characteristics of12 two yield series
Parameter estimation of GARCH model;
A. The optimal model of London copper is GARCH( 1,1);
Risk assessment and decision support technology of foreign oil, gas and mineral resources utilization
B The best model of RMB against USD is t arch( 1,1);
Risk assessment and decision support technology of foreign oil, gas and mineral resources utilization
Among them, the data in brackets represent the standard deviation of parameter estimation, * * * means significant at 99% confidence level, and * * means significant at 95% confidence level; * means significant at 90% confidence level.
C. calculation and analysis of c.VaR
The conditional VaRiance of logarithmic yield series of London copper and RMB against USD can be calculated by formulas 9. 14 and 9. 15, and the time-varying standard deviation σt can be obtained, and the var can be calculated according to the formulas. Where Pt- 1 is the closing price of the previous trading day; For the convenience of calculation, it is standardized as 1 yuan. Zα is the critical value of standard normal distribution, while the critical values of 1%, 5% and 10% are -2.33,-1.64 and-1.28 respectively. Compare the daily VaR values with confidence levels of 90%, 95% and 99% with the actual rate of return, as shown in Figure 9. 19.
Fig. 9. 19 Comparison between VaR value and actual rate of return under different confidence levels
D, using the failure rate test of Kupiec to make a posterior test on the established model.
Table 9. 13 Analysis of Posterior Test Results
From Table 9. 13, it can be seen that the LR value of likelihood ratio statistics is less than the critical value at a given confidence level, which shows that the established VaR model is reasonable. By comparing α and F, we can see that GARCH( 1, 1) model of copper futures basically covers the actual losses, while t GARCH( 1, 1) model of RMB/USD slightly underestimates the market risks.
(2) VaR calculation method based on historical simulation.
As a commonly used VaR valuation method, historical simulation method (Hs) is mainly characterized by not making too many assumptions about the probability distribution of future changes of market factors, but only using the historical changes of market factors to construct the probability distribution of future portfolio gains and losses. Given the confidence (95%, 99%), the loss critical values of 5% and 1% in the frequency distribution are obtained by using the distribution function as the VaR values. The historical simulation method comprises the following steps.
1) the process of estimating the risk of assets on the second day with historical simulation method.
Step 1, select the price of I assets in the past n+ 1 day as simulation data;
Step 2: subtract the past N+ 1 adjacent price data to get n daily price gains and losses of the asset;
The third step, the second step represents the possible profit and loss of the first asset the next day (* * * there are n possible situations). By converting the variation into the rate of return, n possible rates of return can be calculated.
The fourth step is to arrange the rate of return in the third step from small to large, and find out the critical rate of return of the corresponding quantile according to different trust levels.
The fifth step is to multiply the current asset price by the critical rate of return in the fourth step, and the amount obtained is the value at risk (VaR) estimated by the historical simulation method.
2) Empirical analysis.
Taking aluminum futures in London market as an example, this paper selects 592 data from 2007/7/ 19 to 2009/118 * *, and the data source is Wonder Information Finance Database. The market rate of return takes the form of a few-day rate of return, and the formula is rt=ln(pt)-ln(pt- 1). According to the calculation steps of historical simulation method, the calculation results of market risk value of estimated long-term forecast under different confidence levels are shown in Figure 9.20.
Figure 9.20 Calculation Results
(3) Comparison of two measurement methods
Generally speaking, GARCH model can better describe the change of stock market return from the perspective of failure days and failure rate. Judging from the calculated VaR value, Hs method obviously overestimates the risk compared with GARCH model. VaR method is to estimate the market risk under the assumption of normal market conditions.
As far as the reliability of estimation results is concerned, Hs method relies too directly on historical data. Therefore, when the selected inspection period is not representative, the VaR value estimated by Hs can not reflect the market risk well. Although the latter method also depends on the historical data of the investigation period, the consequences are not as serious as the former one. The Hs method is simple and easy to understand, and it is the easiest to understand and use. The latter method requires some background knowledge of probability statistics and financial derivatives.
In a word, GARCH model is more accurate and flexible in the measurement of VaR, and has been more and more accepted by most people and become the mainstream in the measurement of VaR under the current situation of rapid changes in the stock market.