CC BY
14opinion about the increasing influence of carbon pricing on investment decisions in the coming years. In 2016, 36% expect investment decisions to be strongly or moderately affected, and by 2020 this figure rises to 82%.
Lastly, one of the most critical questions was about the expectations regarding the choice of policies to reduce GHG emissions in China at different points in time. From now until 2025, the majority has answered that the emphasis will clearly shift towards ETS, environmental tax, and environmental information disclosure.
The historical climate agreement recently achieved in Paris has given a great rise of interest in China's national emission trading scheme to be launched in the nearest future. The world leaders have many reasons to pay so much attention: China - the biggest greenhouse gas source and the first "developing country" that makes efforts towards facing climate change challenges by providing market-based solutions through cap-and-trade policies.
On 3 August 2016, Jiang Zhaoli, Deputy Director General of the Department of Climate Change of the National Development Reform Commission (NDRC), proclaimed that China intends to implement a rolling model for allo ion and compliance for national emissions trading system (ETS). In case its acceptance, this would mean that participating companies would be divided into groups, for example, by sector. These groups would then receive their allowances on different dates and be subject to differing compliance deadlines. The initial allowance allo ion will roll out across different regions in China starting from October 2016 and would be finished by the end of March 2017. Trading is expected to begin in the first half of 2017.
Since the implementation of 7 ETS pilots in 2011, remarkable progress has been recorded, with China already becoming the second largest carbon market in 2013. This is certainly excellent result and serves as a strong business case for an early domestic roll out. More significantly, China's experience can be shared with other developing counterparts that wish to pursue both economic and environmental sustainability.
Bibliography
1. IPCC 5th Assessment Report (AR5), Working Group III Technical Support Unit, 2014
2. China to launch world's largest emissions trading system in 2017. https://icapcarbonaction.com/en/news-archive/309-china-to-launch-world-s-largest-emissions-trading-system-in-2017
3. International Carbon Action Partnership (ICAP), 2016. 'Emissions Trading Worldwide International Carbon Action Partnership, Status Report 2016'. https://icapcarbonaction.com/en/status-report-2016.
4. Benefits of Emissions Trading: Taking Stock of the Impacts of ETS Worldwide https://icapcarbonaction.com/index.php?option=com_atta ch&task=download&id=389
5. Environomist China Carbon Market Research Report 2016. http://www.thesouthpolegroup.com
6. Duan, Maosheng 2015. From Carbon Emissions Trading Pilots to National System: The Road Map for China, Carbon & Climate Law Review, 3/2015. http://carbon-pulse.com/24056/
УДК 336.49
ИСПОЛЬЗОВАНИЕ МЕТОДА МОНТЕ КАРЛО В МНОГОМЕРНОЙ МОДЕЛИ ОЦЕНКИ
БАНКОВСКОГО РИСКА
Катаргин Н.В.
Финансовый университет при Правительстве Российской Федерации, г. Москва
Аннотация. Банкам важно оценивать вероятность одновременного отрицательного отклонения в стоимости активов в хвостах их распределений - в зоне высокого риска. Предлагается использовать для этого метод Монте-Карло, что позволяет моделировать модели со сложными взаимными влияниями входных переменных с произвольным распределением. В качестве примера рассмотрим моделирование портфелей акций и кредитов, цены на которые могут иметь как нормальное, так и любое другое распределение. Составлены портфели активов с оптимальным соотношением доход/риск. Расчеты выполнены в MS Excel с помощью Visual Basic.
Ключевые слова, кредиты, акции, риск, оптимизация портфеля, метод Монте Карло.
MONTE CARLO METHOD IN THE MULTIDIMENSIONAL MODEL OF THE BANKING RISK
Nikolai Katargin
Financial University under the Government of Russian Federation, Moscow, Russia
Abstract. Important for banks to assess the probability of simultaneous negative deviation of the values of assets in the tails of their distributions, in the area of high risk. Proposed to use for this purpose a Monte Carlo method that allows to simulate models with complex mutual influence of the input variables with arbitrary distribution. As example, consider simulation of portfolios of shares and loans, the prices of which have as normal as another distribution. Composed portfolios of assets with the optimal ratio of income/risk. The calculations are performed in MS Excel using Visual Basic.
Keywords: loans, stocks, risk, portfolio optimization, Monte Carlo method.
The risk of a commercial Bank is associated with a random character of asset prices and their possible interdependence, which are described by probability distributions and correlation matrix. An important practical task is to assess the probability of simultaneous negative deviation of the values of assets in the tails of the distributions, in the area unlikely large risks beyond the own reserves of the Bank (VaR). This problem is solved by building a multidimensional probability distribution of the values of assets. Normal distribution used long time, but experience has shown that the "normal distribution is not a good model to describe the joint distributions of many economic and financial variables. This leads to the problem of finding a more adequate multivariate models. The theory of copula functions is one of the possible ways of its solution." "Copula function is a function that aggregates all the information regarding the dependence structure between components of random vector. When private distribution functions which do not necessarily belong to the same family of distributions are taken as components of copula functions, we obtain a multivariate distribution function. As a result, this theory allows enough flexibility to model the structure of dependence between different variables, which can have different private distribution." "They allow to model multivariate extreme events, forming a dependence that does not coincide with the dependence of the multivariate normal distribution and use the distribution with more kurtosis than the kurtosis of a normal distribution. In addition, they can be used to simulate the phenomenon of heavy tails, which is often observed for financial data.
"Copula functions provide an opportunity to share a description of the distribution of the random vector into two parts: specific component and dependencies [1]. As a rule, to build joint distributions using various functions of statistical packages such as Matlab, R; the calculation is quite complied and not intuitive. Monte Carlo method allows to avoid complied calculations and to construct visual simulation models in Excel. The essence of the Monte Carlo method is: to create the "perfect" model and add a random disturbance in accordance with distributions and iteratively calculate the resulting variables. When assessing the probability of joint risks in the asset portfolio are set to the expected value of the assets, their interrelationships and probability distribution of the values of assets.
We consider a portfolio of four interrelated assets. The model uses the principles of Arhimed copulas with branching dependencies:
X1 = a1 + q1 *a1
X2 = a2 + q2*a2 + q1 *b1, 2*a1
X3 = a3 + q3*a3 + q1 *b1, 3*a1 + q2*b2, 3* a2
X4 = a4 + q4*a4 + q1*b1, 4*a1 + q2*b2,
4*a2+q3*b3, 4*a3
Xsum =z1 *X1 +z2*X2 +z3*X3 + z4*X4
Here Xi is the random asset prices, ai is the expected value, ai - the standard deviation (StDev), bi, k are the coefficients linking the change of the k-th asset at a unit price change of the i-th asset, qi is a random variable with given distribution laws, zi is the share of investment in the portfolio.
For simplicity, we take the same expected value (ai =100), the share of assets in the portfolio (1/4) and the impact (bi,k=0,7). Consider two types of assets: shares and loans. The stock price can change in both directions, and the loan (with interest) may be refunded, partially refunded not refunded or restructured, that is expected to be only loss. Accordingly, we use different types of models and distributions:
1) Shares a normal distribution (Fig. 1 A).
2) Stocks, normal with exponential tail on the left, in region of losses (Fig. 1A).
3) Loans, the left half of the normal distribution.
4) Loans, the left half of the normal distribution with tail to the left (Fig.1 B).
Setting up these functions on the points proposed by the experts, discussed in [2]. For stocks we take ct/'=20, for loans ai=2.
Our task is to estimate the probability of large losses (>3c) across the portfolio Xsum. The calculations were performed in Excel using Visual Basic for Applions (VBA). Create the tables for the calculations (Tables 1, 2) and a button with the software module that generates random values qi, given arbitrary distribution functions and the corresponding Xi. Module and an auxiliary table to generate random qi values are presented at the end of the article. Computer runs 10,000 simulations.
Table 2 presents the correlation matrix; similar results were obtained for other models. Table 3 - mean values Xi, their standard deviation and the probability of abnormal values: loss > 3 ci sum .
Figure 2 shows an example of frequency distribution of the values of loans. Table 3 presents the results of calculations by the Monte Carlo method. Visible growth of StDev related assets and shift to the left of the maxima of the frequency distributions. Of most interest are the third row, which presents the probability of large losses (in percent). As the threshold accepted value max(Sum) - 3 StDev(Sum).
For stocks it is 97,8 - 3 21.9 = 32; for loans 96.4 - 31.3 = 92. Of course, for loans this is not entirely correct. For calculation of probabilities used an Excel function COUNTIF().
0,45 OAs 0,3/ p - /25 A /°'2 11 / 0,15 / o,i - ^¿r 0,05 - 0,45 / 0,3 / 0,25 B / 02 / 0,15 0,05 D
-6 -4 -2 2 4 -6 -5 -4 -3 -2 -1
Fig.1. Probability density distributions of values of shares (A) and loans (B) in the presence of the exponential tail.
Table 1. Example Excel spreadsheet with the original data, results of calculations by the Monte Carlo method and
portfolio optimization
b3 0,7 Z d Zd
b2 0,7 0,7 0,195 1 0,195
b1 0,7 0,7 0,7 0,212 2 0,424
StDev 20 20 20 20 0,214 3 0,644
a 100 100 100 100 0,377 4 1,510
YZ'd/Risk 9,25 Sums 1 2,774
X1 X2 X3 X4 Sum Weighted sum
Mean 98,776 98,135 97,577 96,692 97,795 97,596
StDev 20,077 24,312 28,084 31,172 21,918 23,099
p> 3 asum, % 0,04 0,28 1,18 1,92 0,18 0,30
№ X1 X2 X3 X4 Sum Weighted sum
1 115 143,5 126,6 137,7 130,7 132,1
111 120,7 113,8 103,7 112,3 110,9
10000 103 85,1 75,2 94,7 89,5 90,1
Table 2. The correlation of the stock price in model 1. (Stocks, normal distribution).
X1 X2 X3 X4
Xi 1
X2 0,568 1
X3 0,696 0,737 1
X4 0,702 0,738 0,805 1
Figure 2. Frequency distributions of the values of the loans on the model 4: Loans, the left half of a normal distribution with a tail to the left Table 3. The results of calculations by the method Monte Carlo
Model 1. Stocks, normal distribution.
X1 X2 X3 X4 CyMMa
Mean 98,776 98,135 97,577 96,692 97,795
StDev 20,077 24,312 28,083 31,172 21,918
p> 3 osum, % 0,04 0,28 1,18 1,92 0,18
Model 2. Stocks, normal with exponential tail on the left.
Mean 96,749 94,203 92,210 89,966 93,282
StDev 23,217 28,029 32,196 35,803 25,189
p> 3 osum, % 1,42 2,65 4,11 6,03 1,66
Model 3. Loans, the left half of a normal distribution
Mean 98,227 96,999 95,764 94,528 96,379
StDev 1,192 1,443 1,676 1,875 1,307
p> 3 osum, % 0,02 0,31 2,55 9,88 0,25
Model 4. Loans, the left half of the normal distribution with exponential tail on the left.
Mean 97,891 96,458 94,998 93,545 95,723
StDev 1,7489 2,100 2,425 2,747 1,900
p> 3 osum, % 1,45 4,44 11,54 24,50 4,80
It is evident that the diversifi ion of capital in different assets to reduce risk of the portfolio, even at a relatively high correlation of assets. In all four models the losses of the total portfolio were considerably less than losses of asset X4. The obtained results allow to evaluate the risks of large losses, and in all the frequency distributions of the values of assets. Risks with different fractions of assets in the portfolio, Zi, were computed using formulas in Excel: column Weighted sum in the table 1. Moreover, this
technology allows to optimize the portfolio according to the criterion of Risk/reward (£Zd/Risk in tables 1 and 4). For this we need to set the values of asset returns di, a random value Zi, multiply them, sum the pieces and divide the sum by the risk. Further, for calculations using the "Solver" from the package "Data". Target cell is XZd/Risk^Max, the constraint is £Z=1. Table 4 presents the results of the calculations for optimizing portfolios of assets. The return on assets d1 =1, d2 =2, d3 =3, d4 =4.
Table 4. Example of portfolio optimization.
Model Z1 Z2 Z3 Z4 YZd Risk YZ •d/Risk
1 0,195 0,212 0,214 0,377 2,774 0,30 9,25
2 0,118 0,145 0,146 0,590 3,208 0,76 4,22
3 0,179 0,183 0,183 0,455 2,915 0,95 3,07
4 0,199 0,199 0,199 0,402 2,804 7,37 0,38
Summary
1. Monte Carlo method allows to simulate the risks of portfolios of assets with arbitrary distributions of income and losses, as well as their relationships estimated on historical data and expert opinion.
2. The diversifi ion of capital in different assets to reduce risk of the portfolio, even at a relatively high correlation of assets. In four models the losses of the total portfolio were considerably less than losses of asset X4.
Referencies
1. D. Fantazzini. Modeling multivariate distributions using copula functions I. Prikladnaya ekonometrika (Applied econometrics), № 2 (22), 2011, pp. 98-134.
2. N.V. Katargin. Risk assessment, for arbitrary probability distribution of income and risk. Вестник научно-технического развития (Bulletin of scientific-technical development) № 4(92), 2015.
УДК: 338.12.017
ИССЛЕДОВАНИЕ СОСТОЯНИЯ И ПРОГНОЗ РАЗВИТИЯ ТРАНСПОРТНОЙ ИНФРАСТРУКТУРЫ РОССИИ (НА ПРИМЕРЕ МОСТОСТРОИТЕЛЬНОЙ
ОТРАСЛИ)
Кныш М.М., Богомолов А.И. , Финансовый университет при Правительстве Российской Федерации, г. Москва
Аннотация. Проводится исследование состояния и основных тенденций развития транспортной инфраструктуры России и мостостроения как её составной части на основе статистических данных. Приведены примеры наиболее крупных проектов строительства мостов. Приводится пример конкретной мостостроительной компании. Используя методы эконометрического моделирования приведен прогноз развития отрасли на ближайшую перспективу. Показаны статистическая достоверность результатов прогнозирования на основе нелинейной эконометрической модели и статистических данных развития отрасли за последние 8 лет.
Ключевые слова: мостостроение, статистические данные, эконометрическая модель, прогноз
A STUDY OF THE STATUS AND FORECAST OF DEVELOPMENT OF TRANSPORT INFRASTRUCTURE OF RUSSIA (ON THE EXAMPLE OF BRIDGE-BUILDING
INDUSTRY
Knysh M.M., Bogomolov A.I.
Financial University under the Government of the Russian Federation, Moscow
Abstract. The investigation of the situation and main trends in development of Russia's transport infrastructure and bridge building as its component parts on the basis of statistical data. Examples of the major projects of the construction of the bridges. An example of concrete bridge construction company. Using the methods of econometric modeling given the forecast of the industry in the near future. Shows the statistical reliability of the results of prediction based on nonlinear econometric models and statistical data of the development of the industry for the last 8 years
Keywords: bridge engineering, statistics, econometric model, forecast
Характеристика текущего положения отрасли, Региональная неравномерность развития
оценка потенциальных изменений транспортной инфраструктуры ограничивает развитие
_ „ . . единого экономического пространства страны и не
Развитие современной и эффективной
, „ _ позволяет в полной мере осваивать ресурсы регионов.
транспортной инфраструктуры в России имеет особое тт,- „„
r r Наиболее существенны различия между европейской
частью Российской Федерации и другими регионами.
Различия в транспортной обеспеченности между
значение как для экономики в целом, так и для обеспечения национальной безопасности.
