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.

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 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.

scholarly journals Dependence Structure between Conventional and Islamic Indexes: A Copula Approach

2020 ◽  
Vol 4 (2) ◽  
pp. 22-30
Author(s):  
Samia Ben Messaoud ◽  
Mondher Kouki
Keyword(s):  
Empirical Analysis ◽  
Tail Dependence ◽  
Dependence Structure ◽  
Lower Tail ◽  
Copula Models ◽  
Conditional Dependence ◽  
Copula Approach ◽  
Upper Tail Dependence ◽  
Stock Indexes

This article examines the conditional dependence structure between Islamic stock indexes and conventional counterparts. Our empirical analysis relies on Islamic and conventional indexes of dependence distribution using copula methods over the period 1999–2014. The results from the copula models denote that the dependence is not formally symmetric in that the lower tail dependence is significantly larger than the upper tail dependence.

scholarly journals Conditional Dependence between Oil Prices and Exchange Rates in BRICS Countries: An Application of the Copula-GARCH Model

2019 ◽  
Vol 12 (2) ◽  
pp. 99
Author(s):  
Yijin He ◽  
Shigeyuki Hamori
Keyword(s):  
Exchange Rates ◽  
Value At Risk ◽  
Tail Dependence ◽  
Oil Prices ◽  
Dependence Structure ◽  
Copula Models ◽  
Conditional Dependence ◽  
Brics Countries ◽  
T Copula ◽  
Student’S T

We studied the dependence structure between West Texas Intermediate (WTI) oil prices and the exchange rates of BRICS1 countries, using copula models. We used the Normal, Plackett, rotated-Gumbel, and Student’s t copulas to measure the constant dependence, and we captured the dynamic dependence using the Generalized Autoregressive Score with the Student’s t copula. We found that negative dependence and significant tail dependence exist in all pairs considered. The Russian Ruble (RUB)–WTI pair has the strongest dependence. Moreover, we treated five exchange rate–oil pairs as portfolios and evaluated the Value at Risk and Expected Shortfall from the time-varying copula models. We found that both reach low values when the oil price falls sharply.

Dependence structure between money and economic activity: A Markov-switching copula VEC approach

2021 ◽  
pp. 1-17
Author(s):  
Apostolos Serletis ◽  
Libo Xu
Keyword(s):  
Error Correction ◽  
Economic Activity ◽  
Regime Switching ◽  
Markov Switching ◽  
Tail Dependence ◽  
Error Correction Model ◽  
Dependence Structure ◽  
Copula Models ◽  
Correction Model ◽  
Dependence Structures

Abstract This paper examines correlation and dependence structures between money and the level of economic activity in the USA in the context of a Markov-switching copula vector error correction model. We use the error correction model to focus on the short-run dynamics between money and output while accounting for their long-run equilibrium relationship. We use the Markov regime-switching model to account for instabilities in the relationship between money and output, and also consider different copula models with different dependence structures to investigate (upper and lower) tail dependence.

scholarly journals A Method for Systemic Risk Estimation Based on CDS Indices

2015 ◽  
Vol 8 (1) ◽  
pp. 103-124
Author(s):  
Gabriel Gaiduchevici
Keyword(s):  
Goodness Of Fit ◽  
Risk Estimation ◽  
Multivariate Time Series ◽  
Tail Dependence ◽  
Dependence Structure ◽  
Parameter Estimates ◽  
Copula Models ◽  
Goodness Of Fit Tests ◽  
Multi Stage ◽  
Stage Estimation

AbstractThe copula-GARCH approach provides a flexible and versatile method for modeling multivariate time series. In this study we focus on describing the credit risk dependence pattern between real and financial sectors as it is described by two representative iTraxx indices. Multi-stage estimation is used for parametric ARMA-GARCH-copula models. We derive critical values for the parameter estimates using asymptotic, bootstrap and copula sampling methods. The results obtained indicate a positive symmetric dependence structure with statistically significant tail dependence coefficients. Goodness-of-Fit tests indicate which model provides the best fit to data.

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.

Dependence Structure Analysis and VaR Estimation Based on China’s and International Gold Price: A Copula Approach

2020 ◽  
Vol 19 (01) ◽  
pp. 169-193
Author(s):  
Zhicheng Liang ◽  
Junwei Wang ◽  
Kin Keung Lai
Keyword(s):  
Tail Dependence ◽  
Gold Price ◽  
Dependence Structure ◽  
Copula Models ◽  
Simulation Based ◽  
Copula Approach ◽  
Weighted Portfolio ◽  
Pricing Power ◽  
Gold Producer ◽  
Research Period

Since 2013, China has become the world’s largest gold producer and consumer. To gain the corresponding global pricing power in gold, many actions have been taken by China in recent years, including the International Board at Shanghai Gold Exchange, Shanghai-Hong Kong Gold Connect and Shanghai Gold Fix. Our work studies the dependence structure between China’s and international gold price and examines whether these moves are changing the dependence structure. We use GARCH-copula models to detect the dynamic dependence and tail dependence. The research period is set to contain the Financial Crisis in 2008, the dramatical plunge of gold price in 2013 and a series of black swan events in 2016. The empirical study shows that some event driven dependence structure breaks are statistically insignificant. And the time-varying Symmetrized Joe-Clayton copula is the best copula to model the dependence structure based on AIC value. Finally, an example of applications of this dependence structure is given by estimating the VaR of an equally weighted portfolio with a simulation-based method.

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.

Simulation for Mixture of Archimedean Copulas

2012 ◽  
Vol 195-196 ◽  
pp. 738-743
Author(s):  
Shi De Ou
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Tail Dependence ◽  
Likelihood Estimation ◽  
Numerical Results ◽  
Dependence Structure ◽  
Archimedean Copulas ◽  
Copula Models ◽  
Random Samples ◽  
Dependence Structures

Many dependence structures can consist of mixed copulas. In order to analyze the dependence of stock, we present the method of estimation for mixed copula models. Via generating random samples and using maximum likelihood estimation, the parameters of mixture of Archimedean copulas are estimated. Numerical results show that this method estimates effectively the parameters and tail dependence coefficients. Therefore we can use the method to analyze dependence structure for stocks.

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