Estimation of Value-at-Risk using Weibull distribution – portfolio analysis on the precious metals market

2021 ◽  
Vol 68 (2) ◽  
pp. 38-52
Author(s):  
Dominik Krężołek
Keyword(s):  
At Risk ◽  
Weibull Distribution ◽  
Value At Risk ◽  
Heavy Tails ◽  
Precious Metals ◽  
Portfolio Analysis ◽  
Metal Exchange ◽  
Empirical Distributions ◽  
Empirical Estimates ◽  
Gold Silver

In this paper, we present a modification of the Weibull distribution for the Value-at- Risk (VaR) estimation of investment portfolios on the precious metals market. The reason for using the Weibull distribution is the similarity of its shape to that of empirical distributions of metals returns. These distributions are unimodal, leptokurtic and have heavy tails. A portfolio analysis is carried out based on daily log-returns of four precious metals quoted on the London Metal Exchange: gold, silver, platinum and palladium. The estimates of VaR calculated using GARCH-type models with non-classical error distributions are compared with the empirical estimates. The preliminary analysis proves that using conditional models based on the modified Weibull distribution to forecast values of VaR is fully justified.

scholarly journals Estimation of the value-at-risk parameter: Econometric analysis and the extreme value theory approach

2006 ◽  
Vol 51 (171) ◽  
pp. 32-73 ◽  
Author(s):  
Zorica Mladenovic ◽  
Pavle Mladenovic
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Heavy Tails ◽  
Empirical Distribution ◽  
Risk Estimation ◽  
Value Theory ◽  
Theory Approach ◽  
Empirical Distributions ◽  
Econometric Methods ◽  
Risk Parameter

In this paper different aspects of value-at-risk estimation are considered. Daily returns of CISCO, INTEL and NASDAQ stock indices are analyzed for period: September 1996 - September 2006. Methods that incorporate time varying variability and heavy tails of the empirical distributions of returns are implemented. The main finding of the paper is that standard econometric methods underestimate the value-at-risk parameter if heavy tails of the empirical distribution are not explicitly taken into account. .

Empirical study of value‐at‐risk and expected shortfall models with heavy tails

2006 ◽  
Vol 7 (2) ◽  
pp. 117-135 ◽  
Author(s):  
Fotios C. Harmantzis ◽  
Linyan Miao ◽  
Yifan Chien
Keyword(s):  
At Risk ◽  
Empirical Study ◽  
Value At Risk ◽  
Heavy Tails ◽  
Expected Shortfall

scholarly journals The Arcsine Exponentiated-X Family: Validation and Insurance Application

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-18 ◽  
Author(s):  
Wenjing He ◽  
Zubair Ahmad ◽  
Ahmed Z. Afify ◽  
Hafida Goual
Keyword(s):  
At Risk ◽  
Weibull Distribution ◽  
Value At Risk ◽  
Claims Data ◽  
Numerical Study ◽  
Model Parameters ◽  
Insurance Claims ◽  
Goodness Of Fit Test ◽  
Insurance Claims Data ◽  
Heavy Tailed

In this paper, we propose a family of heavy tailed distributions, by incorporating a trigonometric function called the arcsine exponentiated-X family of distributions. Based on the proposed approach, a three-parameter extension of the Weibull distribution called the arcsine exponentiated-Weibull (ASE-W) distribution is studied in detail. Maximum likelihood is used to estimate the model parameters, and its performance is evaluated by two simulation studies. Actuarial measures including Value at Risk and Tail Value at Risk are derived for the ASE-W distribution. Furthermore, a numerical study of these measures is conducted proving that the proposed ASE-W distribution has a heavier tail than the baseline Weibull distribution. These actuarial measures are also estimated from insurance claims real data for the ASE-W and other competing distributions. The usefulness and flexibility of the proposed model is proved by analyzing a real-life heavy tailed insurance claims data. We construct a modified chi-squared goodness-of-fit test based on the Nikulin–Rao–Robson statistic to verify the validity of the proposed ASE-W model. The modified test shows that the ASE-W model can be used as a good candidate for analyzing heavy tailed insurance claims data.

Analysis of Selected Seasonality Effects in the Following Metal Markets: Gold, Silver, Platinum, Palladium and Copper

2019 ◽  
pp. 59-86
Author(s):  
Krzysztof Borowski ◽  
Małgorzata Łukasik
Keyword(s):  
Financial Markets ◽  
Precious Metal ◽  
Precious Metals ◽  
Weekend Effect ◽  
Commodity Market ◽  
Metal Exchange ◽  
London Metal Exchange ◽  
Interesting Phenomenon ◽  
Gold Silver ◽  
Day Of The Week

The commodity market has been becoming one of the most popular segments of the financial markets among individual and institutional investors in recent years. Similarly to the eąuity market, the problem of anomalies in the commodities market is becoming an interesting phenomenon, especially in the segment of the precious metals. This paper tests the hypothesis of monthly, the day-of-the week and weekend effects of the precious metal markets ąuoted on the London Metal Exchange for gold, silver, platinum and copper in the period of 1.01.1995-31.12.2015 considering also palladium in the period 1.01.1998-31.12.2015. Calculations presented in this paper indicate the absence of the monthly effect on gold, silver, platinum, copper markets but proved occurrence of monthly anomaly in the month of September on palladium market. In the analyzed period day- of-the week effect for any of the studied metal markets was not observed but the weekend effect was registered on the gold and copper markets.

Can Lognormal, Weibull or Gamma Distributions Improve the EWS-GARCH Value-at-Risk Forecasts?

2016 ◽  
Vol 63 (3) ◽  
pp. 329-350
Author(s):  
Marcin Chlebus
Keyword(s):  
At Risk ◽  
Loss Function ◽  
Value At Risk ◽  
Empirical Distribution ◽  
Garch Models ◽  
Quadratic Loss ◽  
Empirical Distributions ◽  
Basel Committee ◽  
Gamma Distributions

In the study, two-step EWS-GARCH models to forecast Value-at-Risk are analysed. The following models were considered: the EWS-GARCH models with lognormal, Weibull or Gamma distributions as a distributions in a state of turbulence, and with GARCH(1,1) or GARCH(1,1) with the amendment to empirical distribution of random error models as models used in a state of tranquillity. The evaluation of the quality of the Value-at-Risk forecasts was based on the Value-at-Risk forecasts adequacy (the excess ratio, the Kupiec test, the Christoffersen test, the asymptotic test of unconditional coverage and the backtesting criteria defined by the Basel Committee) and the analysis of loss func-tions (the Lopez quadratic loss function, the Abad & Benito absolute loss function, the 3rd version of Caporin loss function and the function of excessive costs). Obtained results show that the EWS-GARCH models with lognormal, Weibull or Gamma distributions may compete with EWS-GARCH models with exponential and empirical distributions. The EWS-GARCH model with lognormal, Weibull or Gamma distributions are relatively less conservative, but using them is less expensive than using the other EWS-GARCH models.

Examining the evidence of risk spillovers between Shanghai and London non-ferrous futures markets: a dynamic Copula-CoVaR approach

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Hong Shen ◽  
Yue Tang ◽  
Ying Xing ◽  
Pin Ng
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Global Economy ◽  
Futures Markets ◽  
Ferrous Metal ◽  
Conditional Value At Risk ◽  
Metal Exchange ◽  
London Metal Exchange ◽  
Content Type ◽  
Dynamic Copula

PurposeThis paper aims to examine the evidence of risk spillovers between Shanghai and London non-ferrous futures markets using a dynamic Copula-CoVaR approach.Design/methodology/approachWith daily data, the marginal distributions and optimal Copula functions are determined using the kernel estimation method and squared Euclidean distance test. The conditional value-at-risk and the conditional value-at-risk spillover rate are computed from the Copula estimated parameters based on the Copula-CoVaR model. Also, the dynamic correlation coefficient between the two futures markets is investigated.FindingsThe empirical results are as follows: overall, the risk spillover effect exerted by the London Metal Exchange on the Shanghai Futures Exchange is more significant than vice versa. Moreover, the degree of risk spillovers exerted by the London Metal Exchange on the Shanghai Futures Exchange for zinc and copper are more significant when they are depressed in the London Metal Exchange. Moreover, the dynamic of the correlation between the Shanghai and London futures markets is attributed to be largely due to changes in the global economy.Research limitations/implicationsThe Copula-CoVaR model used in this paper is suitable for measuring the risk spillovers between two different markets, while the risk spillovers across multiple markets or the consideration of multiple risk factors cannot be accurately captured using this framework. Multiple state variables to capture time variation in the conditional moments of return series will be a topic in future research.Practical implicationsThe results provide theoretical support for risk management and monitoring of the non-ferrous futures markets.Originality/valueThe ability of the Copula function to accurately describe a nonlinear relationship and tail correlation is harnessed to measure the risk spillovers, explore the degree and direction of risk spillovers and identify the source of risk spillovers. The global economy is incorporated as a macro factor to explore its inner connection with the dynamic of risk spillovers in the non-ferrous metal futures market.

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