scholarly journals Modeling risk dependence and portfolio VaR forecast through vine copula for cryptocurrencies

PLoS ONE ◽  
2020 ◽  
Vol 15 (12) ◽  
pp. e0242102
Author(s):  
Khreshna Syuhada ◽  
Arief Hakim
Keyword(s):  
Value At Risk ◽  
Risk Model ◽  
Forecast Accuracy ◽  
Dependence Structure ◽  
Financial Risks ◽  
Portfolio Risk ◽  
Dependence Modeling ◽  
Vine Copula ◽  
Dependence Assumption ◽  
Marginal Risk

Risk in finance may come from (negative) asset returns whilst payment loss is a typical risk in insurance. It is often that we encounter several risks, in practice, instead of single risk. In this paper, we construct a dependence modeling for financial risks and form a portfolio risk of cryptocurrencies. The marginal risk model is assumed to follow a heteroscedastic process of GARCH(1,1) model. The dependence structure is presented through vine copula. We carry out numerical analysis of cryptocurrencies returns and compute Value-at-Risk (VaR) forecast along with its accuracy assessed through different backtesting methods. It is found that the VaR forecast of returns, by considering vine copula-based dependence among different returns, has higher forecast accuracy than that of returns under prefect dependence assumption as benchmark. In addition, through vine copula, the aggregate VaR forecast has not only lower value but also higher accuracy than the simple sum of individual VaR forecasts. This shows that vine copula-based forecasting procedure not only performs better but also provides a well-diversified portfolio.

scholarly journals Large portfolio risk management and optimal portfolio allocation with dynamic elliptical copulas

2018 ◽  
Vol 6 (1) ◽  
pp. 19-46 ◽  
Author(s):  
Xisong Jin ◽  
Thorsten Lehnert
Keyword(s):  
Risk Management ◽  
Value At Risk ◽  
Degrees Of Freedom ◽  
Portfolio Allocation ◽  
Optimal Portfolio ◽  
Gaussian Copula ◽  
High Dimensional ◽  
Dependence Structure ◽  
Portfolio Risk ◽  
Portfolio Risk Management

Abstract Previous research has focused on the importance of modeling the multivariate distribution for optimal portfolio allocation and active risk management. However, existing dynamic models are not easily applied to high-dimensional problems due to the curse of dimensionality. In this paper, we extend the framework of the Dynamic Conditional Correlation/Equicorrelation and an extreme value approach into a series of Dynamic Conditional Elliptical Copulas. We investigate risk measures such as Value at Risk (VaR) and Expected Shortfall (ES) for passive portfolios and dynamic optimal portfolios using Mean-Variance and ES criteria for a sample of US stocks over a period of 10 years. Our results suggest that (1) Modeling the marginal distribution is important for dynamic high-dimensional multivariate models. (2) Neglecting the dynamic dependence in the copula causes over-aggressive risk management. (3) The DCC/DECO Gaussian copula and t-copula work very well for both VaR and ES. (4) Grouped t-copulas and t-copulas with dynamic degrees of freedom further match the fat tail. (5) Correctly modeling the dependence structure makes an improvement in portfolio optimization with respect to tail risk. (6) Models driven by multivariate t innovations with exogenously given degrees of freedom provide a flexible and applicable alternative for optimal portfolio risk management.

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.

Review of dependence modeling in hydrology and water resources

2016 ◽  
Vol 40 (4) ◽  
pp. 549-578 ◽  
Author(s):  
Zengchao Hao ◽  
Vijay P. Singh
Keyword(s):  
Water Resources ◽  
Nonlinear Dependence ◽  
Future Research ◽  
Dependence Structure ◽  
Structure Modeling ◽  
Dependence Modeling ◽  
The Past ◽  
Extreme Dependence ◽  
Vine Copula ◽  
Hydrology And Water Resources

Various methods have been developed over the past five decades for dependence modeling of multivariate variables in hydrology and water resources, but there has been no overall review of techniques commonly used in the field. This paper, therefore, introduces several methods focusing on dependence structure modeling, including parametric distribution, entropy, copula, and nonparametric. Recent advances in modeling dependences mainly reside in nonlinear dependence modeling (including extreme dependence) with flexible marginal distributions, and in high-dimension dependence modeling via the vine copula construction with flexible dependence structures. Strengths and limitations of different methods and avenues for future research, such as dependence modeling in a changing climate, are discussed to aid water resource planners and managers in the selection and application of suitable techniques.

EMPIRICAL ANALYSIS OF THE RELATIONSHIP BETWEEN OIL AND PRECIOUS METALS MARKETS

2018 ◽  
Vol 13 (01) ◽  
pp. 1850003 ◽  
Author(s):  
KHALED MOKNI
Keyword(s):  
Crude Oil ◽  
Value At Risk ◽  
Precious Metals ◽  
Market Risk ◽  
Dependence Structure ◽  
Empirical Results ◽  
Dependence Modeling ◽  
Market Risks ◽  
Risk Managers ◽  
The Relationship

The relationship between crude oil and precious metals has been a major issue in economic and financial literature. In this paper, the FIEGARCH-copula framework was used to investigate the co-movements not only between returns, but also between volatilities and market risks among crude oil and precious metals markets. Based on daily crude oil and the major precious metals prices from January 2, 2000 to December 31, 2016, our empirical results are as follows: First, a significant positive and asymmetric relationship between oil and precious metals returns, volatilities and market risk was detected. Second, the dependence structure between oil-silver and oil-gold for returns and volatilities are time varying, while the other pairs are characterized by constant dependence. Third, based on the dependence modeling between daily Value-at-Risk (VaR) for the long and short trading position, empirical results show that the market risk relationship between crude oil and precious metals change over time and increase with VaR’s confidence level. Our findings are of interest for investors and risk managers in portfolio’s design and allow for a reliable framework for returns and risk prediction.

scholarly journals Diversification in heavy-tailed portfolios: properties and pitfalls

2012 ◽  
Vol 7 (1) ◽  
pp. 26-45 ◽  
Author(s):  
Georg Mainik ◽  
Paul Embrechts
Keyword(s):  
Value At Risk ◽  
Sufficient Conditions ◽  
Tail Dependence ◽  
Dependence Structure ◽  
Portfolio Risk ◽  
Explicit Formulas ◽  
Gain Compensation ◽  
Regularly Varying ◽  
Heavy Tailed ◽  
Loss Severity

AbstractWe discuss risk diversification in multivariate regularly varying models and provide explicit formulas for Value-at-Risk asymptotics in this case. These results allow us to study the influence of the portfolio weights, the overall loss severity, and the tail dependence structure on large portfolio losses. We outline sufficient conditions for the sub- and superadditivity of the asymptotic portfolio risk in multivariate regularly varying models and discuss the case when these conditions are not satisfied. We provide several examples to illustrate the resulting variety of diversification effects and the crucial impact of the tail dependence structure in infinite mean models. These examples show that infinite means in multivariate regularly varying models do not necessarily imply negative diversification effects. This implication is true if there is no loss-gain compensation in the tails, but not in general. Depending on the loss-gain compensation, asymptotic portfolio risk can be subadditive, superadditive, or neither.

Risk-Based Loan Pricing: Portfolio Optimization Approach with Marginal Risk Contribution

2020 ◽  
Vol 66 (8) ◽  
pp. 3735-3753 ◽  
Author(s):  
So Yeon Chun ◽  
Miguel A. Lejeune
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Mixed Integer ◽  
Conditional Value At Risk ◽  
Optimization Approach ◽  
Portfolio Risk ◽  
Loan Pricing ◽  
Acceptance Probability ◽  
Risk Contribution ◽  
Marginal Risk

We consider a lender (bank) that determines the optimal loan price (interest rate) to offer to prospective borrowers under uncertain borrower response and default risk. A borrower may or may not accept the loan at the price offered, and both the principal loaned and the interest income become uncertain because of the risk of default. We present a risk-based loan pricing optimization framework that explicitly takes into account the marginal risk contribution, the portfolio risk, and a borrower’s acceptance probability. Marginal risk assesses the incremental risk contribution of a prospective loan to the bank’s overall portfolio risk by capturing the dependencies between the prospective loan and the existing portfolio and is evaluated with respect to the value-at-risk and conditional value-at-risk measures. We examine the properties and computational challenges of the formulations. We design a reformulation method based on the concavifiability concept to transform the nonlinear objective functions and to derive equivalent mixed-integer nonlinear reformulations with convex continuous relaxations. We also extend the approach to multiloan pricing problems, which feature explicit loan selection decisions in addition to pricing decisions. We derive formulations with multiple loans that take the form of mixed-integer nonlinear problems with nonconvex continuous relaxations and develop a computationally efficient algorithmic method. We provide numerical evidence demonstrating the value of the proposed framework, test the computational tractability, and discuss managerial implications. This paper was accepted by Chung Piaw Teo, optimization.

scholarly journals Value At Risk, Minimum Capital Requirement And The Use Of Extreme Value Distributions: An Application To BRICS Markets

2014 ◽  
Vol 14 (1) ◽  
pp. 135
Author(s):  
John Muteba Mwamba ◽  
Donovan Beytell
Keyword(s):  
South Africa ◽  
At Risk ◽  
Financial Markets ◽  
Value At Risk ◽  
Risk Model ◽  
Capital Requirement ◽  
Financial Risks ◽  
Minimum Capital ◽  
Minimum Capital Requirement ◽  
Green Zone

This paper uses closing prices of the BRICS (Brazil, Russia, India, China, and South Africa) financial markets to implement a risk model that generates point estimates of both Value at Risk (VaR); and Expected Shortfall (ES). The risk model is thereafter backtested using three techniques namely the Basel II green zone, the unconditional test, and the conditional test. We first filter the log-return data using an Autoregressive Regression model (AR) of order one for the conditional mean and an Exponential Generalised Autoregressive Conditional Heteroscedasticity of order one (EGARCH 1,1) for the conditional variance. We thereafter fit the filtered returns by using the Generalised Pareto Distribution (GPD) model before we compute both VaR and ES estimates. We find that the use of the GPD is well suited to financial markets that are highly exposed to global financial risks. Our results show that both VaR and ES estimates for South Africa are very low when compared with those of other BRICS financial markets. We argue that South Africas credit and loan regulations, pioneered by the National Credit Regulator (NCR), might have decreased its exposure to global financial risks. The resulting minimum capital requirement values are found to be significantly different depending on whether the Variance-Covariance or the GPD methodology is used. The backtesting methodologies show that the VaR model used in the paper is more robust and practically reliable.

scholarly journals Portfolio Risk and Dependence Modeling: Application of Factor and Copula Models

2012 ◽  
Author(s):  
Arsalan Azamighaimasi
Keyword(s):  
Factor Model ◽  
Risk Measures ◽  
Random Variable ◽  
Copula Function ◽  
Dependence Structure ◽  
Risk Modeling ◽  
Portfolio Risk ◽  
Copula Models ◽  
Dependence Modeling ◽  
T Copula

We consider portfolio credit risk modeling with a focus on two approaches, the factor model, and the copula model. While other models have received greater scrutiny, both factor and cupola models have received little attention although these are appropriate for rating-based portfolio risk analysis. We review the two models with emphasis on the joint default probability. The copula function describes the dependence structure of a multivariate random variable. In this paper, it is used as a practical to simulation of generate portfolio with different copula, we only use Gaussian and t-copula case. And we generate portfolio default distributions and study the sensitivity of commonly used risk measures with respect to the approach in modeling the dependence structure of the portfolio.  

scholarly journals Estimating Risk of Natural Gas Portfolios by Using GARCH-EVT-Copula Model

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Jiechen Tang ◽  
Chao Zhou ◽  
Xinyu Yuan ◽  
Songsak Sriboonchitta
Keyword(s):  
At Risk ◽  
Natural Gas ◽  
Value At Risk ◽  
Extreme Value Distribution ◽  
Gaussian Copula ◽  
Conditional Value At Risk ◽  
Dependence Structure ◽  
Copula Model ◽  
Portfolio Risk ◽  
Multivariate Gaussian

This paper concentrates on estimating the risk of Title Transfer Facility (TTF) Hub natural gas portfolios by using the GARCH-EVT-copula model. We first use the univariate ARMA-GARCH model to model each natural gas return series. Second, the extreme value distribution (EVT) is fitted to the tails of the residuals to model marginal residual distributions. Third, multivariate Gaussian copula and Studentt-copula are employed to describe the natural gas portfolio risk dependence structure. Finally, we simulate N portfolios and estimate value at risk (VaR) and conditional value at risk (CVaR). Our empirical results show that, for an equally weighted portfolio of five natural gases, the VaR and CVaR values obtained from the Studentt-copula are larger than those obtained from the Gaussian copula. Moreover, when minimizing the portfolio risk, the optimal natural gas portfolio weights are found to be similar across the multivariate Gaussian copula and Studentt-copula and different confidence levels.

scholarly journals Assessing Efficiency of D-Vine Copula ARMA-GARCH Method in Value at Risk Forecasting: Evidence from PSE Listed Companies

2015 ◽  
Vol 63 (4) ◽  
pp. 1287-1295 ◽  
Author(s):  
Václav Klepáč ◽  
David Hampel
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Stock Exchange ◽  
Garch Model ◽  
Dependence Structure ◽  
Process Innovations ◽  
Out Of Sample ◽  
Copula Approach ◽  
Multivariate Probability Distribution ◽  
Vine Copula

The article points out the possibilities of using static D-Vine copula ARMA-GARCH model for estimation of 1 day ahead market Value at Risk. For the illustration we use data of the four companies listed on Prague Stock Exchange in range from 2010 to 2014. Vine copula approach allows us to construct high-dimensional copula from both elliptical and Archimedean bivariate copulas, i.e. multivariate probability distribution, created from process innovations. Due to a deeper shortage of existing domestic results or comparison studies with advanced volatility governed VaR forecasts we backtested D-Vine copula ARMA-GARCH model against the VaR rolling out of sample forecast from October 2012 to April 2014 of chosen benchmark models, e.g. multivariate VAR-GO-GARCH, VAR-DCC-GARCH and univariate ARMA-GARCH type models. Common backtesting via Kupiec and Christoffersen procedures offer generalization that technological superiority of model supports accuracy only in case of an univariate modeling – working with non-basic GARCH models and innovations with leptokurtic distributions. Multivariate VAR governed type models and static Copula Vines performed in stated backtesting comparison worse than selected univariate ARMA-GARCH, i.e. it have overestimated the level of actual market risk, probably due to hardly tractable time-varying dependence structure.

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