A new bivariate Archimedean copula with application to the evaluation of VaR

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Cigdem Topcu Guloksuz ◽  
Pranesh Kumar
Keyword(s):  
Monte Carlo ◽  
Value At Risk ◽  
Simulation Method ◽  
Archimedean Copula ◽  
Dependence Structure ◽  
General Motor ◽  
Copula Models ◽  
Bivariate Normal ◽  
Mc Simulation ◽  
Generator Function

AbstractIn this paper, a new generator function is proposed and based on this function a new Archimedean copula is introduced. The new Archimedean copula along with three representatives of Archimedean copula family which are Clayton, Gumbel and Frank copulas are considered as models for the dependence structure between the returns of two stocks. These copula models are used to simulate daily log-returns based on Monte Carlo (MC) method for calculating value at risk (VaR) of the financial portfolio which consists of two market indices, Ford and General Motor Company. The results are compared with the traditional MC simulation method with the bivariate normal assumption as a model of the returns. Based on the backtesting results, describing the dependence structure between the returns by the proposed Archimedean copula provides more reliable results over the considered models in calculating VaR of the studied portfolio.

Forecasting multivariate VaR and ES using MC-GARCH-Copula model

2020 ◽  
Vol 21 (5) ◽  
pp. 493-516 ◽  
Author(s):  
Hemant Kumar Badaye ◽  
Jason Narsoo
Keyword(s):  
Value At Risk ◽  
Garch Model ◽  
Dependence Structure ◽  
Copula Model ◽  
Copula Models ◽  
Content Type ◽  
Significance Level ◽  
Foreign Currencies ◽  
Out Of Sample ◽  
Weighted Portfolio

Purpose This study aims to use a novel methodology to investigate the performance of several multivariate value at risk (VaR) and expected shortfall (ES) models implemented to assess the risk of an equally weighted portfolio consisting of high-frequency (1-min) observations for five foreign currencies, namely, EUR/USD, GBP/USD, EUR/JPY, USD/JPY and GBP/JPY. Design/methodology/approach By applying the multiplicative component generalised autoregressive conditional heteroskedasticity (MC-GARCH) model on each return series and by modelling the dependence structure using copulas, the 95 per cent intraday portfolio VaR and ES are forecasted for an out-of-sample set using Monte Carlo simulation. Findings In terms of VaR forecasting performance, the backtesting results indicated that four out of the five models implemented could not be rejected at 5 per cent level of significance. However, when the models were further evaluated for their ES forecasting power, only the Student’s t and Clayton models could not be rejected. The fact that some ES models were rejected at 5 per cent significance level highlights the importance of selecting an appropriate copula model for the dependence structure. Originality/value To the best of the authors’ knowledge, this is the first study to use the MC-GARCH and copula models to forecast, for the next 1 min, the VaR and ES of an equally weighted portfolio of foreign currencies. It is also the first study to analyse the performance of the MC-GARCH model under seven distributional assumptions for the innovation term.

scholarly journals PERHITUNGAN VALUE AT RISK (VaR) DENGAN METODE HISTORIS DAN MONTE CARLO PADA SAHAM SUB SEKTOR ROKOK

2018 ◽  
Vol 11 (1) ◽  
pp. 1
Author(s):  
Achmad Dimas ◽  
Muhammad Azhari ◽  
Khairunnisa Khairunnisa
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Value At Risk ◽  
Time Series Data ◽  
Random Number Generation ◽  
Simulation Method ◽  
Series Data ◽  
Historical Simulation ◽  
Historical Method ◽  
Sample Data

The government’s policy, the Indonesian Ulema Council’s (MUI) fatwa, the rise of cigarette issues and anti-smoking campaigns have been a major challenge for the tobacco industry in managing risks. Through this research, the issues will be measured by VaR to know the risk of the company’s shares of cigarette sub sector by using time series data and analyzed by using the simulation method of Historis and Monte Carlo. The results showed the VaR value of GGRM and HMSP stock with the historical method is 3.28 and 2.54%. While the value of VaR shares GGRM and HMSP with Monte Carlo method is 3.52% and 3.14%. Monte Carlo simulation gives greater result than Historical Simulation, because Monte Carlo simulation do iteration repeatedly by involving random number generation and many synthesize the data so that sample data becomes more which makes the calculation is bigger.

scholarly journals Dependence Modelling in Insurance via Copulas with Skewed Generalised Hyperbolic Marginals

2019 ◽  
Vol 0 (0) ◽  
Author(s):  
Vitali Alexeev ◽  
Katja Ignatieva ◽  
Thusitha Liyanage
Keyword(s):  
Value At Risk ◽  
Tail Dependence ◽  
Dependence Structure ◽  
Portfolio Risk ◽  
Total Risk ◽  
Copula Models ◽  
Out Of Sample ◽  
Upper Tail Dependence ◽  
Dependence Modelling ◽  
Best Fit

Abstract This paper investigates dependence among insurance claims arising from different lines of business (LoBs). Using bivariate and multivariate portfolios of losses from different LoBs, we analyse the ability of various copulas in conjunction with skewed generalised hyperbolic (GH) marginals to capture the dependence structure between individual insurance risks forming an aggregate risk of the loss portfolio. The general form skewed GH distribution is shown to provide the best fit to univariate loss data. When modelling dependency between LoBs using one-parameter and mixture copula models, we favour models that are capable of generating upper tail dependence, that is, when several LoBs have a strong tendency to exhibit extreme losses simultaneously. We compare the selected models in their ability to quantify risks of multivariate portfolios. By performing an extensive investigation of the in- and out-of-sample Value-at-Risk (VaR) forecasts by analysing VaR exceptions (i.e. observations of realised portfolio value that are greater than the estimated VaR), we demonstrate that the selected models allow to reliably quantify portfolio risk. Our results provide valuable insights with regards to the nature of dependence and fulfils one of the primary objectives of the general insurance providers aiming at assessing total risk of an aggregate portfolio of losses when LoBs are correlated.

scholarly journals A Comprehensive Statistical Analysis of the Six Major Crypto-Currencies from August 2015 through June 2020

2020 ◽  
Vol 13 (9) ◽  
pp. 192
Author(s):  
Beatriz Vaz de Melo Mendes ◽  
André Fluminense Carneiro
Keyword(s):  
Statistical Analysis ◽  
Value At Risk ◽  
Risk Measures ◽  
Value Theory ◽  
Dependence Structure ◽  
Copula Models ◽  
Underlying Distribution ◽  
First Semester ◽  
Long Run ◽  
Daily Data

After more than a decade of existence, crypto-currencies may now be considered an important class of assets presenting some unique appealing characteristics but also sharing some features with real financial assets. This paper provides a comprehensive statistical analysis of the six most important crypto-currencies from the period 2015–2020. Using daily data we (1) showed that the returns present many of the stylized facts often observed for stock assets, (2) modeled the returns underlying distribution using a semi-parametric mixture model based on the extreme value theory, (3) showed that the returns are weakly autocorrelated and confirmed the presence of long memory as well as short memory in the GARCH volatility, (4) used an econometric approach to compute risk measures, such as the value-at-risk, the expected shortfall, and drawups, (5) found that the crypto-coins’ price trajectories do not contain speculative bubbles and that they move together maintaining the long run equilibrium, and (6) using static and dynamic D-vine pair-copula models, assessed the true dependence structure among the crypto-assets, obtaining robust copula based bivariate dynamic measures of association. The analyses indicate that the strength of dependence among the crypto-currencies has increased over the recent years in the cointegrated crypto-market. The conclusions reached will help investors to manage risk while identifying opportunities for alternative diversified and profitable investments. To complete the analysis we provide a brief discussion on the effects of the COVID-19 pandemic on the crypto-market by including the first semester of 2020 data.

scholarly journals Pengukuran Value at Risk pada Aset Perusahaan dengan Metode Simulasi Monte Carlo

Jurnal MIPA ◽  
2013 ◽  
Vol 2 (1) ◽  
pp. 5
Author(s):  
Leony P. Tupan ◽  
Tohap Manurung ◽  
Jantje D. Prang
Keyword(s):  
At Risk ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Value At Risk ◽  
Simulation Method ◽  
Monte Carlo Simulation Method ◽  
Monte Carlo Data ◽  
Closing Price ◽  
The Mean ◽  
Mean Variance

Telah dilakukan penelitian untuk mengukur Value at Risk (VaR) pada aset perusahaan PT. Indo Tambangraya Megah Tbk (ITMG), PT. Bank Mandiri Tbk (BMRI), dan PT. Astra International Tbk (ASII) serta portofolio yang dapat dibentuk oleh ketiga aset tersebut menggunakan metode simulasi Monte Carlo. Data yang digunakan adalah data return harian diperoleh dari harga penutupan (closing price) saham harian ketiga perusahaan tersebut selama periode tahun 2011. Bobot masing-masing portofolio ditentukan dengan metode Mean Variance Efficient Portofolio. Hasil pengukuran menunjukan bahwa jika dana yang diinvestasikan sebesar Rp 100.000.000,00 dengan tingkat kepercayaan 95% dengan periode adalah 1 hari, maka VaR ITMG sebesar Rp 4.103.963,33, VaR BMRI sebesar Rp 4.060.096,67, dan VaR ASII sebesar Rp 3.353.913,33. Sedangkan VaR portofolio1 (terdiri dari aset ITMG dan BMRI) adalah Rp 3.726.543,33. VaR portofolio2 (terdiri dari aset ITMG dan ASII) adalah Rp 3.233.133,33. VaR portofolio3 (terdiri dari aset BMRI dan ASII) adalah Rp 3.278.933,33. VaR portofolio4 (terdiri dari aset ITMG, BMRI, dan ASII) adalah Rp 3.218.906,67. Nilai VaR portofolio yang lebih rendah dari VaR aset tunggal disebabkan karena adanya efek diversifikasi.Research has been conducted to measure the Value at risk (VaR) at assets PT. Indo Tambangraya Megah Tbk (ITMG), PT. Bank Mandiri Tbk (BMRI), and PT. Astra International Tbk (ASII) and portfolios that can be formed by the three assets using Monte Carlo simulation method. The data used daily return data by the three assets obtained from the closing price of daily stock over a period in 2011. The weight of each portfolio is determined by the Mean Variance Efficient Portfolio method. If the funds invested amounting to Rp 100.000.000,00 with 95% confidence level and the period is 1 day, then the results from measurement VaR ITMG is Rp 4.103.963,33, VaR BMRI is Rp 4.060.096,67 and VaR ASII is Rp 3.353.913,33. While VaR portofolio1 (consists of ITMG and BMRI asset) is Rp 3.726.543,33. VaR portofolio2 (consists of ITMG and ASII asset) Rp 3.233.133,33. VaR portofolio3 (consists of BMRI and ASII asset) is Rp 3.278.933,33. VaR portofolio4 (consists of ITMG, BMRI and ASII asset) is Rp 3.218.906,67. VaR portfolios are lower than VaR of each single asset due to diversification effects.

SPATIAL DEPENDENCE AND AGGREGATION IN WEATHER RISK HEDGING: A LÉVY SUBORDINATED HIERARCHICAL ARCHIMEDEAN COPULAS (LSHAC) APPROACH

2018 ◽  
Vol 48 (02) ◽  
pp. 779-815 ◽  
Author(s):  
Wenjun Zhu ◽  
Ken Seng Tan ◽  
Lysa Porth ◽  
Chou-Wen Wang
Keyword(s):  
Spatial Dependence ◽  
Crop Production ◽  
Archimedean Copula ◽  
Dependence Structure ◽  
Copula Model ◽  
Copula Models ◽  
Basis Risk ◽  
Risk Hedging ◽  
Adverse Weather ◽  
Weather Risk

AbstractAdverse weather-related risk is a main source of crop production loss and a big concern for agricultural insurers and reinsurers. In response, weather risk hedging may be valuable, however, due to basis risk it has been largely unsuccessful to date. This research proposes the Lévy subordinated hierarchical Archimedean copula model in modelling the spatial dependence of weather risk to reduce basis risk. The analysis shows that the Lévy subordinated hierarchical Archimedean copula model can improve the hedging performance through more accurate modelling of the dependence structure of weather risks and is more efficient in hedging extreme downside weather risk, compared to the benchmark copula models. Further, the results reveal that more effective hedging may be achieved as the spatial aggregation level increases. This research demonstrates that hedging weather risk is an important risk management method, and the approach outlined in this paper may be useful to insurers and reinsurers in the case of agriculture, as well as for other related risks in the property and casualty sector.

scholarly journals Fitted Copula Statistical Models for Four African and Four Major Stock Markets

2021 ◽  
pp. 195-227
Author(s):  
Ngozi Fidelia Adum ◽  
Happiness Onyebuchi Obiora-Ilouno ◽  
Francis Chukwuemeka Eze
Keyword(s):  
At Risk ◽  
Akaike Information Criterion ◽  
Stock Markets ◽  
Value At Risk ◽  
Information Matrix ◽  
Information Criterion ◽  
Alternative Methods ◽  
Dependence Structure ◽  
P Value ◽  
Copula Models

The application of copula has become popular in recent years. The use of correlation as a dependence measure has several pitfalls and hence the application of regression prediction model using this correlation may not be an appropriate method. In financial markets, there is often a non-linear dependence between returns. Thus, alternative methods for capturing co-dependency should be considered, such as copula based ones. This paper studies the dependence structure between the four largest African stock markets in terms of market capitalization and other developed stock markets over the period 2003 to 2018 using copula models. The value at risk was used to determine the risk associated with the stock. The ten copula models were fitted to the log returns calculated from the data, two countries at a time of the twenty-eight pairs and examined. The Gumbel copula gives the best fit in terms of log-likelihood values, value of the Akaike information criterion, value of the Bayesian information criterion, value of the consistent Akaike information criterion, value of the corrected Akaike information criterion, value of the Hannan Quinn criterion and p-value of the information matrix equality of White. Estimates of value at risk with probability p for daily returns were computed using the best fitted copula model, from these value at risk, it is seen that SA/FTSE100 have the least risk while EGY/KEN has the highest risk. Prediction is given in terms of correlation and value at risk.

scholarly journals Conditional tail independence in Archimedean copula models

2019 ◽  
Vol 56 (3) ◽  
pp. 858-869
Author(s):  
Michael Falk ◽  
Simone A. Padoan ◽  
Florian Wisheckel
Keyword(s):  
Distribution Function ◽  
Random Vector ◽  
Mild Condition ◽  
Conditional Distribution ◽  
Archimedean Copula ◽  
Tail Behavior ◽  
Copula Models ◽  
Generator Function

AbstractConsider a random vector $\textbf{U}$ whose distribution function coincides in its upper tail with that of an Archimedean copula. We report the fact that the conditional distribution of $\textbf{U}$ , conditional on one of its components, has under a mild condition on the generator function independent upper tails, no matter what the unconditional tail behavior is. This finding is extended to Archimax copulas.

scholarly journals APPLICATION OF MONTE CARLO SIMULATION METHODS IN RISK MANAGEMENT

2007 ◽  
Vol 8 (3) ◽  
pp. 165-168 ◽  
Author(s):  
Alexander Suhobokov
Keyword(s):  
At Risk ◽  
Monte Carlo Simulation ◽  
Risk Management ◽  
Monte Carlo ◽  
Value At Risk ◽  
Simulation Method ◽  
Monte Carlo Algorithm ◽  
Simulation Methods ◽  
Monte Carlo Simulation Method

The paper deals with Monte Carlo simulation method and its application in Risk Management. The author with the help of MATLAB 7.0 introduces new modification of Monte Carlo algorithm aimed at fast and effective calculation of financial organization's Value at Risk (VaR) by the example of Parex Bank's FOREX exposure.

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