scholarly journals Practice Oriented and Monte Carlo Based Estimation of the Value-at-Risk for Operational Risk Measurement

Risks ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 50 ◽  
Author(s):  
Francesca Greselin ◽  
Fabio Piacenza ◽  
Ričardas Zitikis
Keyword(s):  
Monte Carlo ◽  
Value At Risk ◽  
Sampling Error ◽  
Risk Measure ◽  
Simulated Data ◽  
Operational Risk ◽  
Computational Effort ◽  
Risk Measurement ◽  
Sampling Errors ◽  
Eu Regulation

We explore the Monte Carlo steps required to reduce the sampling error of the estimated 99.9% quantile within an acceptable threshold. Our research is of primary interest to practitioners working in the area of operational risk measurement, where the annual loss distribution cannot be analytically determined in advance. Usually, the frequency and the severity distributions should be adequately combined and elaborated with Monte Carlo methods, in order to estimate the loss distributions and risk measures. Naturally, financial analysts and regulators are interested in mitigating sampling errors, as prescribed in EU Regulation 2018/959. In particular, the sampling error of the 99.9% quantile is of paramount importance, along the lines of EU Regulation 575/2013. The Monte Carlo error for the operational risk measure is here assessed on the basis of the binomial distribution. Our approach is then applied to realistic simulated data, yielding a comparable precision of the estimate with a much lower computational effort, when compared to bootstrap, Monte Carlo repetition, and two other methods based on numerical optimization.

scholarly journals An evaluation and comparison of Value at Risk and Expected Shortfall

2018 ◽  
Vol 15 (4) ◽  
pp. 17-34 ◽  
Author(s):  
Tom Burdorf ◽  
Gary van Vuuren
Keyword(s):  
At Risk ◽  
Monte Carlo ◽  
Emerging Economies ◽  
Value At Risk ◽  
Risk Measures ◽  
Risk Measure ◽  
Expected Shortfall ◽  
Significance Level ◽  
Tail Conditional Expectation ◽  
The Uk

As a risk measure, Value at Risk (VaR) is neither sub-additive nor coherent. These drawbacks have coerced regulatory authorities to introduce and mandate Expected Shortfall (ES) as a mainstream regulatory risk management metric. VaR is, however, still needed to estimate the tail conditional expectation (the ES): the average of losses that are greater than the VaR at a significance level These two risk measures behave quite differently during growth and recession periods in developed and emerging economies. Using equity portfolios assembled from securities of the banking and retail sectors in the UK and South Africa, historical, variance-covariance and Monte Carlo approaches are used to determine VaR (and hence ES). The results are back-tested and compared, and normality assumptions are tested. Key findings are that the results of the variance covariance and the Monte Carlo approach are more consistent in all environments in comparison to the historical outcomes regardless of the equity portfolio regarded. The industries and periods analysed influenced the accuracy of the risk measures; the different economies did not.

scholarly journals Risk management with Tail Quasi-Linear Means

2019 ◽  
Vol 14 (1) ◽  
pp. 170-187
Author(s):  
Nicole Bäuerle ◽  
Tomer Shushi
Keyword(s):  
Risk Management ◽  
Value At Risk ◽  
Risk Measure ◽  
Risk Measurement ◽  
Fundamental Properties ◽  
Risk Distribution ◽  
Entropic Risk Measure ◽  
Elliptical Models ◽  
Linear Means ◽  
Conditional Tail Expectation

AbstractWe generalise Quasi-Linear Means by restricting to the tail of the risk distribution and show that this can be a useful quantity in risk management since it comprises in its general form the Value at Risk, the Conditional Tail Expectation and the Entropic Risk Measure in a unified way. We then investigate the fundamental properties of the proposed measure and show its unique features and implications in the risk measurement process. Furthermore, we derive formulas for truncated elliptical models of losses and provide formulas for selected members of such models.

scholarly journals Estimation of the Portfolio Risk from Conditional Value at Risk Using Monte Carlo Simulation

2021 ◽  
Vol 17 (3) ◽  
pp. 370-380
Author(s):  
Ervin Indarwati ◽  
Rosita Kusumawati
Keyword(s):  
At Risk ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Value At Risk ◽  
Risk Measures ◽  
Risk Measure ◽  
Risk Estimation ◽  
Conditional Value At Risk ◽  
Portfolio Risk ◽  
Portfolio Returns

Portfolio risk shows the large deviations in portfolio returns from expected portfolio returns. Value at Risk (VaR) is one method for determining the maximum risk of loss of a portfolio or an asset based on a certain probability and time. There are three methods to estimate VaR, namely variance-covariance, historical, and Monte Carlo simulations. One disadvantage of VaR is that it is incoherent because it does not have sub-additive properties. Conditional Value at Risk (CVaR) is a coherent or related risk measure and has a sub-additive nature which indicates that the loss on the portfolio is smaller or equal to the amount of loss of each asset. CVaR can provide loss information above the maximum loss. Estimating portfolio risk from the CVaR value using Monte Carlo simulation and its application to PT. Bank Negara Indonesia (Persero) Tbk (BBNI.JK) and PT. Bank Tabungan Negara (Persero) Tbk (BBTN.JK) will be discussed in this study.  The  daily  closing  price  of  each  BBNI  and BBTN share from 6 January 2019 to 30 December 2019 is used to measure the CVaR of the two banks' stock portfolios with this Monte Carlo simulation. The steps taken are determining the return value of assets, testing the normality of return of assets, looking for risk measures of returning assets that form a normally distributed portfolio, simulate the return of assets with monte carlo, calculate portfolio weights, looking for returns portfolio, calculate the quartile of portfolio return as a VaR value, and calculate the average loss above the VaR value as a CVaR value. The results of portfolio risk estimation of the value of CVaR using Monte Carlo simulation on PT. Bank Negara Indonesia (Persero) Tbk and PT. Bank Tabungan Negara (Persero) Tbk at a confidence level of 90%, 95%, and 99% is 5.82%, 6.39%, and 7.1% with a standard error of 0.58%, 0.59%, and 0.59%. If the initial funds that will be invested in this portfolio are illustrated at Rp 100,000,000, it can be interpreted that the maximum possible risk that investors will receive in the future will not exceed Rp 5,820,000, Rp 6,390,000 and Rp 7,100,000 at the significant level 90%, 95%, and 99%

scholarly journals MODEL NON LINIER GARCH (NGARCH) UNTUK MENGESTIMASI NILAI VALUE at RISK (VaR) PADA IHSG

2015 ◽  
Vol 4 (2) ◽  
pp. 59
Author(s):  
I KOMANG TRY BAYU MAHENDRA ◽  
KOMANG DHARMAWAN ◽  
NI KETUT TARI TASTRAWATI
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Risk Measure ◽  
Risk Measurement ◽  
Bad News ◽  
Good News ◽  
Investment Risk ◽  
Positive Return ◽  
Is Value

In investment, risk measurement is important. One of risk measure is Value at Risk (VaR). There are many methods that can be used to estimate risk based on VaR framework. One of them Non Linier GARCH (NGARCH) model. In this research, determination of VaR used NGARCH model. NGARCH model allowed for asymetric behaviour in the volatility such that “good news” or positive return and “bad news” or negative return. Based on calculations of VaR, the higher of the confidence level and the longer the investment period, the risk was greater. Determination of VaR using NGARCH model was less than GARCH model.

scholarly journals PERHITUNGAN UKURAN RISIKO UNTUK MODEL KERUGIAN AGREGAT

2020 ◽  
Vol 14 (1) ◽  
pp. 21
Author(s):  
Nadya Pratiwi ◽  
Aprida Siska Lestia ◽  
Nur Salam
Keyword(s):  
Monte Carlo ◽  
Standard Deviation ◽  
Monte Carlo Method ◽  
Value At Risk ◽  
Risk Measure ◽  
Random Variable ◽  
Insurance Companies ◽  
Loss Model ◽  
Aggregate Loss ◽  
Conditional Tail Expectation

In the case of nonlife insurance, insurance companies are very potential to get losses if claims submitted by customers (policyholders) exceeds the reserves of budgeted claims. It is the risk that have to managed properly by insurance companies . One possible disadvantage is the aggregate loss model. The aggregate loss model is a random variable that states the total of all losses incurred in an insurance policy block. This kind of loss can be modeled using a collective risk approach where the number of claims is a discrete random variable and the size of claim is a continuous random variable. The purpose of this study is to determine risk measure of standard deviation premium principle, value at risk (VaR), and conditional tail expectation (CTE) of the aggregate loss model. Standard deviation premium principle risk measure of aggregate loss model is determined analytically by substituted it expected value and varians. Meanwhile, VaR risk measure is determined using numerical method by Monte Carlo method, then the quantile value and it confidence interval for the actual value will estimate. In the CTE calculation, based on the loss data obtained in the Monte Carlo method, the CTE value is estimated by calculating the average loss that exceeds the VaR value. If the data size is large enough, the CTE value estimation will converge to the actual value.Keywords: Aggregate Loss Model, Standard Deviation Premium Principle, Value at Risk (VaR), Conditional Tail Expectation (CTE).

scholarly journals Pomiar ryzyka rynkowego miarą wartoś​ci zagrożonej. Metoda kombinowania prognoz ​

2018 ◽  
pp. 183-198
Author(s):  
Piotr Mazur
Keyword(s):  
At Risk ◽  
Financial Institutions ◽  
Value At Risk ◽  
Risk Measure ◽  
Market Risk ◽  
Risk Measurement ◽  
Conditional Value At Risk ◽  
Parametric Methods ◽  
Combining Forecasts

The article discusses the measurement of market risk by Value at Risk method. Value at Risk measure is an important element of risk measurement mainly for financial institutions but can also be used by other companies. The Value at Risk is presented together with its alternative Conditional Value at Risk. The main methods of VaR estimation were divided into nonparametric, parametric and semi-parametric methods. The next part of the article presents a method of combining forecasts, which can be used in the context of forecasting Value at Risk.

IMPRECISE PREVISIONS FOR RISK MEASUREMENT

2003 ◽  
Vol 11 (04) ◽  
pp. 393-412 ◽  
Author(s):  
RENATO PELESSONI ◽  
PAOLO VICIG
Keyword(s):  
Value At Risk ◽  
Risk Measures ◽  
Risk Measure ◽  
Sufficient Conditions ◽  
Risk Measurement ◽  
Random Numbers ◽  
Coherent Risk Measure ◽  
Coherent Risk ◽  
Consistency Properties ◽  
Special Case

In this paper the theory of coherent imprecise previsions is applied to risk measurement. We introduce the notion of coherent risk measure defined on an arbitrary set of risks, showing that it can be considered a special case of coherent upper prevision. We also prove that our definition generalizes the notion of coherence for risk measures defined on a linear space of random numbers, given in literature. Consistency properties of Value-at-Risk (VaR), currently one of the most used risk measures, are investigated too, showing that it does not necessarily satisfy a weaker notion of consistency called 'avoiding sure loss'. We introduce sufficient conditions for VaR to avoid sure loss and to be coherent. Finally we discuss ways of modifying incoherent risk measures into coherent ones.

scholarly journals PENGUKURAN RISIKO GLUE-VALUE-AT-RISK PADA DATA DISTRIBUSI ELLIPTICAL (Studi Kasus: Data Saham PT Indocement Tunggal Prakarsa Tbk, PT Unilever Indonesia Tbk, PT United Tractors Tbk, Periode 1 Juni 2018 – 29 November 2019)

2020 ◽  
Vol 9 (1) ◽  
pp. 76-86
Author(s):  
Dede Andrianto ◽  
Di Asih I Maruddani ◽  
Tarno Tarno
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Risk Measure ◽  
Risk Measurement ◽  
Risk Level ◽  
Translation Invariance ◽  
Elliptical Distribution ◽  
Confidence Levels ◽  
High Selection ◽  
Selection Of

Risk measurement is carried out to determine the risk. Popular methods that can be used to measure risk at a confidence level are Value-at-Risk (VaR) and Tail-Value-at-Risk (TVaR). A Risk measurement should satisfy: translation invariance, positive homogenicity, monocity and subadditivity. VaR does not satisfy one of coherent axioms, namely subadditivity. TVaR is considered capable of overcoming VaR problems, but it’s too large for a risk measure. Glue-Value-at-Risk (GlueVaR) is a method that can overcome these problems because it can be valued between VaR and TVaR and fulfills four coherent axioms. In this paper GlueVaR used in the elliptical distribution for normal distribution to measure the risk of the stock of PT Indocement Tunggal Prakarsa Tbk (INTP), PT Unilever Indonesia Tbk (UNVR), and PT United Tractors Tbk (UNTR) for the period June 1st 2018 – 29th November 2019. After knowing the stock return is normally distributed and used confidence levels of α = 95% and β = 98%, a high selection of distortion ℎ1=0,3≤1−𝛽1−𝛼 and ℎ2=0,4≥ℎ1. The high distortion selected makes GlueVaR worth between VaR and TVaR. GlueVaR for INTP, UNVR, and UNTR respectively are 4.886%; 2.999%; and 4.083%. Thus the lowest risk level is PT Unilever Indonesia Tbk.Keywords : Value-at-Risk, Tail-Value-at-Risk, Glue-Value-at-Risk

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