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 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 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.

The dependence structure in volatility between Shanghai and Shenzhen stock market in China

2016 ◽  
Vol 6 (3) ◽  
pp. 264-283 ◽  
Author(s):  
Mingyuan Guo ◽  
Xu Wang
Keyword(s):  
Stock Market ◽  
High Frequency ◽  
Estimation Method ◽  
Garch Model ◽  
Price Volatility ◽  
Market Volatility ◽  
High Frequency Data ◽  
Dependence Structure ◽  
Frequency Data ◽  
Content Type

Purpose – The purpose of this paper is to analyse the dependence structure in volatility between Shanghai and Shenzhen stock market in China based on high-frequency data. Design/methodology/approach – Using a multiplicative error model (hereinafter MEM) to describe the margins in volatility of China’s Shanghai and Shenzhen stock market, this study adopts static and time-varying copulas, respectively, estimated by maximum likelihood estimation method to describe the dependence structure in volatility between Shanghai and Shenzhen stock market in China. Findings – This paper has identified the asymmetrical dependence structure in financial market volatility more precisely. Gumbel copula could best fit the empirical distribution as it can capture the relatively high dependence degree in the upper tail part corresponding to the period of volatile price fluctuation in both static and dynamic view. Originality/value – Previous scholars mostly use GARCH model to describe the margins for price volatility. As MEM can efficiently characterize the volatility estimators, this paper uses MEM to model the margins for the market volatility directly based on high-frequency data, and proposes a proper distribution for the innovation in the marginal models. Then we could use copula-MEM other than copula-GARCH model to study on the dependence structure in volatility between Shanghai and Shenzhen stock market in China from a microstructural perspective.

Household margin insurance of agricultural sector in Indonesia using a farmer exchange rate index

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Atina Ahdika ◽  
Dedi Rosadi ◽  
Adhitya Ronnie Effendie ◽  
Gunardi
Keyword(s):  
Exchange Rate ◽  
Value At Risk ◽  
Agricultural Sector ◽  
Time Varying ◽  
Risk Modeling ◽  
Copula Models ◽  
Content Type ◽  
Premium Calculation ◽  
Index Ratio ◽  
Margin Insurance

PurposeFarmer exchange rate (FER) is the ratio between a farmer's income and expenditure and is also an indicator of farmers’ welfare. There is little research regarding its use in risk modeling in crop insurance. This study seeks to propose a design for a household margin insurance scheme of the agricultural sector based on FER.Design/methodology/approachThis research employs various risk modeling concepts, i.e. value at risk, loss models and premium calculation, to construct the proposed model. The standard linear, static and time-varying copula models are used to identify the dependency between variables involved in calculating FER.FindingsFirst, FER can be considered as the primary variable for risk modeling in agricultural household margin insurance because it demonstrates farmers’ financial ability. Second, temporal dependence estimated using the time-varying copula can minimize errors, reduce the premium rate and result in a tighter guarantee's level of security.Originality/valueThis research extends the previous similar studies related to the use of index ratio in margin insurance loss modeling. Its authenticity is in the use of FER, which represents the farmers' trading capability. FER determines farmers’ losses by considering two aspects: the farmers’ income rate and their ability to fulfill their life and farming needs. Also, originality exists in the use of the time-varying copulas in identifying the dependence of the indices involved in calculating FER.

Valuation of initial margin using bootstrap method

2020 ◽  
Vol 21 (5) ◽  
pp. 543-557
Author(s):  
Modisane Bennett Seitshiro ◽  
Hopolang Phillip Mashele
Keyword(s):  
Probability Distribution ◽  
Financial Market ◽  
Value At Risk ◽  
Risk Model ◽  
Risk Measure ◽  
Bootstrap Method ◽  
Parametric Bootstrap ◽  
Spillover Effects ◽  
Content Type ◽  
Significance Level

Purpose The purpose of this paper is to propose the parametric bootstrap method for valuation of over-the-counter derivative (OTCD) initial margin (IM) in the financial market with low outstanding notional amounts. That is, an aggregate outstanding gross notional amount of OTC derivative instruments not exceeding R20bn. Design/methodology/approach The OTCD market is assumed to have a Gaussian probability distribution with the mean and standard deviation parameters. The bootstrap value at risk model is applied as a risk measure that generates bootstrap initial margins (BIM). Findings The proposed parametric bootstrap method is in favour of the BIM amounts for the simulated and real data sets. These BIM amounts are reasonably exceeding the IM amounts whenever the significance level increases. Research limitations/implications This paper only assumed that the OTCD returns only come from a normal probability distribution. Practical implications The OTCD IM requirement in respect to transactions done by counterparties may affect the entire financial market participants under uncleared OTCD, while reducing systemic risk. Thus, reducing spillover effects by ensuring that collateral (IM) is available to offset losses caused by the default of a OTCDs counterparty. Originality/value This paper contributes to the literature by presenting a valuation of IM for the financial market with low outstanding notional amounts by using the parametric bootstrap method.

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.

Has the dependence structure of the BRICS exchange rates changed after the financial crisis? Evidence from R-Vine copula model

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Zhuoqun Zhang ◽  
Tao Zhang
Keyword(s):  
Financial Crisis ◽  
Exchange Rates ◽  
Trade Policy ◽  
Design Methodology ◽  
Policy Design ◽  
Oil Prices ◽  
Dependence Structure ◽  
Copula Model ◽  
Content Type ◽  
Vine Copula

PurposeThe authors examine the dependence structure of the BRICS exchange rates.Design/methodology/approachThe authors construct a regular vine copula model to study the co-movements of exchange rates in BRICS controlling the influences from the SDR currencies and the oil prices.FindingsThe main findings show that, after the financial crisis, RMB pursued a more balanced strategy shifting from USD-centered to USD-EUR dependency and the oil prices become more dependent on RUB than USD, which could weaken the dollar hegemony. From robustness tests, we find that the inclusion of RMB in SDR has certain but limited impacts on the dependence structure and the influence of the GBP weakened as well. The results have important implications for currency trade, policy design and the future of the BRICS.Originality/valueThe contribution of this paper is twofold. First, we examine the interdependence structure of the BRICS exchange rates controlling for the influence of SDR currencies and the oil prices with R-Vine copula model. Second, we compare the pre- and after-crisis structure and see if the financial crisis and the BRICS summits have changed the structure.

Dependency between Risks and the Insurer’s Economic Capital: A Copula-based GARCH Model

2017 ◽  
Vol 11 (1) ◽  
Author(s):  
Jeungbo Shim ◽  
Seung-Hwan Lee
Keyword(s):  
Value At Risk ◽  
Heavy Tails ◽  
Garch Model ◽  
Joint Modeling ◽  
Market Risk ◽  
Capital Requirements ◽  
Economic Capital ◽  
Series Data ◽  
Dependence Structure ◽  
T Distribution

AbstractCopulas can be a useful tool to capture heavy-tailed dependence between risks in estimating economic capital. This paper provides a procedure of combining copula with GARCH model to construct a multivariate distribution. The copula-based GARCH model using a skewed student’s t-distribution controls for the issues of skewness, heavy tails, volatility clustering and conditional dependencies contained in the financial time series data. Using the sample of U.S. property liability insurance industry, we perform Monte Carlo simulation to estimate the insurer’s economic capital measured by Value-at-Risk (VaR) and Expected Shortfall (ES). The result indicates that the choice of dependence structure and business mix between asset classes and liability lines has a significant impact on the resulting capital requirements and diversification benefits. We find the incremental diversification benefit in terms of a reduction in the total capital requirement from the joint modeling of underwriting risk and market risk compared to the modeling of market risk only.

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.

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.

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