Variance-covariance Method Research Articles

RADIATION PROTECTION MEASUREMENTS WITH THE VARIANCE-COVARIANCE METHOD IN THE STRAY RADIATION FIELDS FROM PHOTON AND PROTON THERAPY FACILITIES.

The microdosimetric variance-covariance method was used to study the stray radiation fields from the photon therapy facility at the Technical University of Denmark and the scanned proton therapy beam at the Skandion Clinic in Uppsala, Sweden. Two TEPCs were used to determine the absorbed dose, the dose-average lineal energy, the dose-average quality factor and the dose equivalent. The neutron component measured by the detectors at the proton beam was studied through Monte Carlo simulations using the code MCNP6. In the photon beam the stray absorbed dose ranged between 0.3 and 2.4 μGy per monitor unit, and the dose equivalent between 0.4 and 9 μSv per monitor unit, depending on beam energy and measurement position. In the proton beam the stray absorbed dose ranged between 3 and 135 μGy per prescribed Gy, depending on detector position and primary proton energy.

Analysıs of Market Rısk in Stock Investment Usıng Value at Rısk Method (Study on Manufacturıng Companıes in Lq-45 Lısted on Indonesıa Stock Exchange)

Capital flows as one part of this economic growth is sourced from the capital markets namely Indonesia stock exchange. The capital markets have a function of economics because capital markets provide a facility or vehicle which brings together two interests, namely those who have excess funds and those who need funds. Before investing, investors should set a goal of investing and the magnitude of the funds invested. Any investment decisions taken have the risks borne by the investor, either investment in bonds or stocks. Stocks with known characteristics of high risk-high return, which means the stock provides an opportunity to earn high profits but also potentially high loss risk. Value at Risk (VaR) models has been extensively used not only in the banking sector but also in calculating in many sectors. The aim of this paper is to outline Value at Risk methodology by giving more emphasis on variance covariance method, historical simulation, and Monte Carlo model. The model used to investigate the applicability and usefulness of VaR in stock investment in Indonesia Manufacturing companies. Using the methodologies as described, the maximum potential loss on each stock and its portfolio of nine stocks calculated at 95% confidence level. The models were validated using back testing and Kupiec test. The research found that there are different results of VaR calculated using variance covariance, historical simulation, and Monte Carlo models. However, variance covariance model is the valid one to measure the maximum potential loss of stocks.

Value-at-Risk Estimation of Foreign Exchange Rate Risk in India

Banks are required to maintain an appropriate level of capital which must commensurate with the riskiness of their portfolio. Recently, the Reserve Bank of India (RBI) issued a circular on Prudential Guidelines on Capital Adequacy—Implementation of Internal Models Approach (IMA) for Market Risk to select a suitable method for the banks to determine the regulatory capital requirement under the market risk exposure. Banks which adopt this approach are required to quantify market risk through their own Value-at-Risk (VaR) model. Therefore, it is a challenging task for risk managers of the bank to select an appropriate risk model which reasonably covers the risk of the bank’s portfolio. Use of wrongly calibrated risk models may lead to undercapitalised banking system. This article aims at exploring the suitable risk model for measuring foreign exchange risk in banks’ portfolio. The objective of present study is to empirically test the appropriate VaR model for foreign exchange rate risk. Value-at-Risk has been estimated for foreign exchange rate risk by using parametric variance–covariance method and non-parametric historical simulation (HS) method. Under parametric method, VaR is estimated by assuming that returns follow normal and Student’s t-distribution. Backtesting results for various VaR models have been done based on Kupiec’s proportion of failures (KPOF) test and regulatory ‘traffic light’ test. This article concludes that when returns are non-normal, VaR model based on the assumption of normality significantly underestimates the risk. Our empirical results based on backtesting show that most accurate VaR estimates are obtained from Student’s t VaR model.

A dynamic double asymmetric copula generalized autoregressive conditional heteroskedasticity model: application to China's and US stock market

Modeling the relationship between multiple financial markets has had a great deal of attention in both literature and real-life applications. One state-of-the-art technique is that the individual financial market is modeled by generalized autoregressive conditional heteroskedasticity (GARCH) process, while market dependence is modeled by copula, e.g. dynamic asymmetric copula-GARCH. As an extension, we propose a dynamic double asymmetric copula (DDAC)-GARCH model to allow for the joint asymmetry caused by the negative shocks as well as by the copula model. Furthermore, our model adopts a more intuitive way of constructing the sample correlation matrix. Our new model yet satisfies the positive-definite condition as found in dynamic conditional correlation-GARCH and constant conditional correlation-GARCH models. The simulation study shows the performance of the maximum likelihood estimate for DDAC-GARCH model. As a case study, we apply this model to examine the dependence between China and US stock markets since 1990s. We conduct a series of likelihood ratio test tests that demonstrate our extension (dynamic double joint asymmetry) is adequate in dynamic dependence modeling. Also, we propose a simulation method involving the DDAC-GARCH model to estimate value at risk (VaR) of a portfolio. Our study shows that the proposed method depicts VaR much better than well-established variance–covariance method.

Optimal Combined Forecasting Method for Foreign Workers in Chiangmai

This paper is concerned with the performance of combination method for forecasting the foreign workers in Chiang Mai, Thailand. The forecasting performance is compare among six combination method. i.e., Simple Average method (AVG), Variance-Covariance method (VAR), Harmonic Mean method (HARM), Simple Average Control (AVG-C) , Variance-Covariance Control method (VAR-C) and Harmonic Mean Control method (HARM-C). The results suggest that, the mean absolute percentage errors (MAPE) of the Variance-Covariance Control method (VAR-C) are the lowest. The Variance-Covariance Control method was optimal for forecasting the foreign workers in Chiang Mai, Thailand.

Based on Vari Combination Forecasting Model for Power Plant Flue Gas Oxygen Contentance-Covariance Method

Focusing on the problem which power plant flue gas oxygen content is hard to predict efficiently, an intelligent hybrid prediction method is proposed. First, the RBF neural network and principal component analysis method are utilized to reduce the dimension of the input variables. Second, the case-based reasoning method is carried on to predict the flue gas oxygen content based on the above analysis results. Then, in order to reflect the cumulative effect of the flue gas oxygen content with time, the GM (1, 1) grey prediction method is used to predict the current flue gas oxygen content value. Finally, the final flue gas oxygen content is obtained by the variance-covariance method of weight combination forecasting. Simulations and industrial results show that the proposed intelligent hybrid prediction model has high accuracy and robustness, and can solve the problem of predicting the flue gas oxygen content effectively.

A Combination Method for Mid-Long Term Power Load Simulation and Prediction

In view of the singleness of effect evaluation indexes in combination forecasting, this paper considered both benefit factors and cost factors. The entropy method and the variance-covariance method are adopted to determine the relative importance of these indicators and to get the weight of each single model. This improved combination forecasting model took both prediction accuracy and curve similarity into consideration, which is more accurate and reliable.

Value-at-risk based on generalized error distribution using a quantile approach

This study proposes the use of the quantile method under generalized error distribution (GED) value-at-risk (VaR) forecasts assuming non-normality, fitting the returns data with the GED. This application is more efficient and flexible not only because it can accommodate both normality and non-normality within one model but also because it is as easy to use as the variance-covariance method. Based on the failure rates determined and the results of the Kupiec test, it would appear that the proposed method can considerably enhance the accuracy of estimates of VaR.

EXTREME VALUE AT RISK: A SCENARIO FOR RISK MANAGEMENT

This paper uses the generalised extreme value (GEV) distribution to model the extreme losses that are likely to occur during market crashes, in the case of an investor who has long positions in stocks and currencies. The null hypothesis – which tests for normality of asset returns – is rejected due to asymmetry of these returns. We assume that the asymmetric behaviour and volatility of the returns are captured by the shape and scale parameters, respectively, of a GEV distribution. The data set includes stock indices for the United States, Japan, the United Kingdom, Germany, France and South Africa, and the South African rand exchange rates against the US dollar observed from 3 January 2005 to 30 December 2009. In addition, we divide this sample period into two periods: the pre-crisis period, from 3 January 2005 to 31 December 2007 and the crisis period, from 1 January 2008 to 30 December 2009. We compared the estimates of value at risk (VaR) using an extreme value theory (EVT) model, with the estimates derived from the traditional variance–covariance method and found that during the crisis the 99% extreme VaR estimates are more reliable as they lie within the Basel II green zone. These results suggest that, at higher quintiles, the VaR estimates based on EVT are reliable and more accurate than estimates from the traditional method.

Identification of clusters in tissue samples in gene expression data with Principal Component Analysis based on relative variance matrix

Principal Component Analysis (PCA) has been in use as a preprocessing step to clustering for long. We have focused on the clustering of tissue samples in gene expression data. Different clustering techniques and algorithm are available in literature on gene expression data but with the existing ambiguity on the number of clusters, apart from relying on biologically known groups. A consensus is needed to reach on the number of clusters in the wide variety of existing clustering techniques based on different similarity or dissimilarity metrics. The conventional usage of PCA for clustering is either by forcing the unit variance to each variable or the high magnitude of variance of an individual variable is allowed to dominate the entire results of PCA. We propose the use of relative variance covariance method in PCA, so as to give due consideration to the joint and individual variances in the dataset and identify clusters with principal component loadings. We emphasize empirically that the proposed approach of PCA is conclusively more informative than the available approaches to identify cluster structure in tissue samples (sample expression profiles). Clusters formed are valid with the existing results on the data set under study and with valid biological background. Key words: Clustering methods, gene expression analysis, principal component analysis, the relative variance covariance matrix, principal component loadings.

The exchange rate risk of Chinese yuan: Using VaR and ES based on extreme value theory

This paper applies extreme value theory (EVT) to estimate the tails of return series of Chinese yuan (CNY) exchange rates. We find that the degree of fitting Pareto distribution to the data of the tail of return series is extremely high. The empirical results indicate that expected shortfall cannot improve the tail risk problem of value-at-risk (VaR). The evidence of back testing indicates that EVT-based VaR values underestimate the risks of exchange rates such as USD/CNY and HKD/CNY, which may be caused by the continuous appreciation of CNY against USD and HKD. However, compared with VaR values calculated by historical simulation and variance–covariance method, VaR values calculated by EVT can measure the risk more accurately for the exchange rates of JPY/CNY and EUR/CNY.

Fast Lidar and Radar Multiple-Scattering Models. Part I: Small-Angle Scattering Using the Photon Variance–Covariance Method

Abstract A fast, approximate method is described for the calculation of the intensity of multiply scattered lidar returns from clouds. At each range gate it characterizes the outgoing photon distribution by its spatial variance, the variance of photon direction, and the covariance of photon direction and position. The result is that for an N-point profile the calculation is O(N) efficient yet it implicitly includes all orders of scattering, in contrast with the O(Nm/m!) efficiency of models that explicitly consider each scattering order separately for truncation at m-order scattering. It is also shown how the shape of the scattering phase function near 180° may be taken into account for both liquid water droplets and ice particles. The model considers only multiple scattering due to small-angle forward-scattering events, which is suitable for most ground-based and airborne lidars because of their small footprint on the cloud. For spaceborne lidar, it must be used in combination with the wide-angle multiple scattering model described in Part II of this two-part paper.

Application of the Beck model to stock markets: Value-at-Risk and portfolio risk assessment

We apply the Beck model, developed for turbulent systems that exhibit scaling properties, to stock markets. Our study reveals that the Beck model elucidates the properties of stock market returns and is applicable to practical use such as the Value-at-Risk estimation and the portfolio analysis. We perform empirical analysis with daily/intraday data of the S&P500 index return and find that the volatility fluctuation of real markets is well-consistent with the assumptions of the Beck model: The volatility fluctuates at a much larger time scale than the return itself and the inverse of variance, or “inverse temperature”, β obeys Γ -distribution. As predicted by the Beck model, the distribution of returns is well-fitted by q -Gaussian distribution of Tsallis statistics. The evaluation method of Value-at-Risk (VaR), one of the most significant indicators in risk management, is studied for q -Gaussian distribution. Our proposed method enables the VaR evaluation in consideration of tail risk, which is underestimated by the variance–covariance method. A framework of portfolio risk assessment under the existence of tail risk is considered. We propose a multi-asset model with a single volatility fluctuation shared by all assets, named the single β model, and empirically examine the agreement between the model and an imaginary portfolio with Dow Jones indices. It turns out that the single β model gives good approximation to portfolios composed of the assets with non-Gaussian and correlated returns.

Nanodosimetry in a clinical neutron therapy beam using the variance-covariance method and Monte Carlo simulations

Nanodosimetric single-event distributions or their mean values may contribute to a better understanding of how radiation induced biological damages are produced. They may also provide means for radiation quality characterization in therapy beams. Experimental nanodosimetry is however technically challenging and Monte Carlo simulations are valuable as a complementary tool for such investigations. The dose-mean lineal energy was determined in a therapeutic p(65)+Be neutron beam and in a 60Co γ beam using low-pressure gas detectors and the variance-covariance method. The neutron beam was simulated using the condensed history Monte Carlo codes MCNPX and SHIELD-HIT. The dose-mean lineal energy was calculated using the simulated dose and fluence spectra together with published data from track-structure simulations. A comparison between simulated and measured results revealed some systematic differences and different dependencies on the simulated object size. The results show that both experimental and theoretical approaches are needed for an accurate dosimetry in the nanometer region. In line with previously reported results, the dose-mean lineal energy determined at 10 nm was shown to be related to clinical RBE values in the neutron beam and in a simulated 175 MeV proton beam as well.

Nanodosimetric measurements and calculations in a neutron therapy beam

A comparison of calculated and measured values of the dose mean lineal energy (y(D)) for the former neutron therapy beam at Louvain-la-Neuve is reported. The measurements were made with wall-less tissue-equivalent proportional counters using the variance-covariance method and simulating spheres with diameters between 10 nm and 15 microm. The calculated y(D)-values were obtained from simulated energy distributions of neutrons and charged particles inside an A-150 phantom and from published y(D)-values for mono-energetic ions. The energy distributions of charged particles up to oxygen were determined with the SHIELD-HIT code using an MCNPX simulated neutron spectrum as an input. The mono-energetic ion y(D)-values in the range 3-100 nm were taken from track-structure simulations in water vapour done with PITS/KURBUC. The large influence on the dose mean lineal energy from the light ion (A > 4) absorbed dose fraction, may explain an observed difference between experiment and calculation. The latter being larger than earlier reported result. Below 50 nm, the experimental values increase while the calculated decrease.

Determinations of H*(10) and its dose components onboard aircraft

Aircrew is in general receiving a higher average annual dose than other occupationally exposed personnel, and about half of the effective dose is deposited by high-LET neutron secondaries. A recent investigation of the cancer incidence following the atomic bombs at Hiroshima and Nagasaki has put forward the possibility that the relative biological efficiency for neutrons could be underestimated. If so, the effective dose to aircrew from this component would increase and the estimation of this component will become even more important. Different ambient dose equivalent measurement techniques and calculation methods have recently been compared on a dedicated flight. The experimental results are compared with calculations made with the codes EPCARD 3.2 and an updated version of FLUKA and different galactic proton spectra. The aircraft circulated within the target areas at two constant altitudes with a flight route variation of only about 1 degrees in longitude and latitude to reduce the influence from variations in atmospheric and geomagnetic shielding. The instrumentation consisted of tissue-equivalent proportional counters (TEPC) and a silicon diode spectrometer. Measurements were performed for 2 h to reduce the statistical uncertainties in the results. The TEPCs were evaluated either according to single-event analysis techniques or the variance-covariance method. Besides the total ambient dose equivalent, the instruments can be evaluated to reveal the low- and high-LET components. The EPCARD and FLUKA simulations can determine the contribution from each type of particle directly. The ratio between the calculated and the measured average value of the ambient dose equivalent rate was 1.00 +/- 0.08 with all instruments included for EPCARD and 0.97 +/- 0.07 when FLUKA was used. The measured high-LET component and the calculated neutron component are not quite identical, but should be similar. The agreement was always within 20%. The high-LET component contributed with about 57% at N57 E8 and 48% at N42 E12.

Measuring Market Risk for Commercial Banks in the Volatile Environment of an Emerging Market Economy

Measuring Market Risk for Commercial Banks in the Volatile Environment of an Emerging Market EconomySlovenian commercial banks have two possibilities for calculating capital charges for the market risks to which they are exposed. Due to the capital decree legislated by the Bank of Slovenia, they can use standardized methodology or apply an internal model. An internal model can be based on different risk measures, with each risk measure having its strengths and weaknesses. Consequently, the volume of risk calculated using a specific risk measure will vary among risk measures. Basel II regulation assumes VaR methodology for capital requirements calculations for the market risks to which commercial banks are exposed. There are two commonly used methods for VaR calculation - historical simulation and the variance-covariance method. Each has its strengths and weaknesses. The goal of this paper is to present the methodology of volatility and time weighted historical simulation as an internal model for market risk measurement in Slovenian commercial banks. The methodology is based on historical simulation and tries to remove the disadvantages of this method with GJR GARCH volatility modelling and the time weighting of returns.

코퓰러과 극단치이론을 이용한 위험척도의 추정 및 성과분석

금융위험의 측정 및 관리를 위한 도구로서 분포의 꼬리 부분과 관련한 위험척도로 VaR가 현재 널리 활용되고 있다. 특히 VaR의 정확한 추정을 위해 정규분포를 가정한 기존의 방법보다는 극단치이론을 이용한 방법이 최근 관심을 끌고 있다. 지금까지 극단치이론을 이용한VaR의 추정에 관한 연구는 대부분 단변량의 경우에 대해 이루어졌다. 본 논문에서는 코퓰러를 극단치이론에 결부시켜 다변량 극단치분포를 모형화하여 포트폴리오 위험측정을 다루고 있다. 특히 본 연구에서는 포트폴리오 위험 척도로 VaR와 더불어 ES에 대한 추정 방법도 함께 논의하였다. 포트폴리오 위험측정을 위한 방법으로 본 논문에서 논의한 코퓰러-극단치이론에 의한 접근방법이 기존의 분산-공분산 방법보다 상대적으로 우수한지를 실증자료에 대한 사후검증을 통해 살펴보았다. VaR, a tail-related risk measure is now widely used as a tool for a measurement and a management of financial risks. For more accurate measurement of VaR, recently we are particularly concerned about the approach based on extreme value theory rather than the traditional method based on the assumption of normal distribution. However, many studies about the approaches using extreme value theory was done only for the univariate case. In this paper, we discuss portfolio risk measurements with modelling multivariate extreme value distributions by combining copulas and extreme value theory. We also discuss the estimation of ES together with VaR as portfolio risk measures. Finally, we investigate the relative superiority of EVT-copula approach than variance-covariance method through the back-testing of an empirical data.

Porovnanie prístupov na výpočet hodnoty v riziku menových portfólií

In this paper historical performance of eleven approaches for estimation of one-day 95% value-at-risk is evaluated. Random sample of 1000 foreign exchange portfolios consisting of positions in EUR and USD with CZK as a base currency was considered. Since foreign exchange portfolio consists of linear instruments, historical simulation and the variance-covariance method for VaR estimation were investigated. Performance of all approaches was evaluated using seven performance criteria. With minimal degree of simplification we can say that variance-covariance method using exponentially weighted averages with is the best approach. This approach produces risk estimates which are systematically lowest ones and with high time volatility. It also achieves perfect coverage (95 %) and the highest correlation between risk measure and absolute value of the outcome. RiskMetrics variance-covariance approach was dominant in spite of violation of normality assumption.

The Effect of Misestimating Correlation on Value at Risk

Value at risk (VaR) is an estimate of the worst loss over a target horizon with a given level of confidence. Despite its shortcomings, the Basel Committee on Banking Supervision has chosen it as the standard method to measure the market risk of a portfolio of financial assets. This measure of risk is widely used by practitioners and regulators because of its conceptual simplicity and flexibility. This article examines the systematic relationship between correlation misestimation and the corresponding value-at-risk miscalculation. To this end, first a semi-parametric approach, and then a parametric approach is developed. Both approaches are based on a simulation setup. Various linear and non-linear portfolios are considered, as well as variance-covariance and Monte-Carlo simulation methods are employed. Results show that the VaR error increases significantly as the correlation error increases, particularly in the case of well-diversified linear portfolios. In the case of option portfolios, this effect is more pronounced for short-maturity, in-the-money options. The use of MC simulation to calculate VaR magnifies the correlation bias effect. These results have important implications for measuring market risk accurately.