Dependent conditional value-at-risk for aggregate risk models
Risk measure forecast and model have been developed in order to not only provide better forecast but also preserve its (empirical) property especially coherent property. Whilst the widely used risk measure of Value-at-Risk (VaR) has shown its performance and benefit in many applications, it is in fa...
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doaj-67dff45f339e4316a9f654c2ec65a0d12021-08-02T04:57:32ZengElsevierHeliyon2405-84402021-07-0177e07492Dependent conditional value-at-risk for aggregate risk modelsBony Parulian Josaphat0Khreshna Syuhada1Statistics Research Division, Institut Teknologi Bandung 40132, IndonesiaCorresponding author.; Statistics Research Division, Institut Teknologi Bandung 40132, IndonesiaRisk measure forecast and model have been developed in order to not only provide better forecast but also preserve its (empirical) property especially coherent property. Whilst the widely used risk measure of Value-at-Risk (VaR) has shown its performance and benefit in many applications, it is in fact not a coherent risk measure. Conditional VaR (CoVaR), defined as mean of losses beyond VaR, is one of alternative risk measures that satisfies coherent property. There have been several extensions of CoVaR such as Modified CoVaR (MCoVaR) and Copula CoVaR (CCoVaR). In this paper, we propose another risk measure, called Dependent CoVaR (DCoVaR), for a target loss that depends on another random loss, including model parameter treated as random loss. It is found that our DCoVaR provides better forecast than both MCoVaR and CCoVaR. Numerical simulation is carried out to illustrate the proposed DCoVaR. In addition, we do an empirical study of financial returns data to compute the DCoVaR forecast for heteroscedastic process of GARCH(1,1). The empirical results show that the Gumbel Copula describes the dependence structure of the returns quite nicely and the forecast of DCoVaR using Gumbel Copula is more accurate than that of using Clayton Copula. The DCoVaR is superior than MCoVaR, CCoVaR and CoVaR to comprehend the connection between bivariate losses and to help us exceedingly about how optimum to position our investments and elevate our financial risk protection. In other words, putting on the suggested risk measure will enable us to avoid non-essential extra capital allocation while not neglecting other risks associated with the target risk. Moreover, in actuarial context, DCoVaR can be applied to determine insurance premiums while reducing the risk of insurance company.http://www.sciencedirect.com/science/article/pii/S2405844021015954Archimedean copulaFarlie-Gumbel-Morgenstern familyGARCH modelPareto distributionasset returns |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Bony Parulian Josaphat Khreshna Syuhada |
spellingShingle |
Bony Parulian Josaphat Khreshna Syuhada Dependent conditional value-at-risk for aggregate risk models Heliyon Archimedean copula Farlie-Gumbel-Morgenstern family GARCH model Pareto distribution asset returns |
author_facet |
Bony Parulian Josaphat Khreshna Syuhada |
author_sort |
Bony Parulian Josaphat |
title |
Dependent conditional value-at-risk for aggregate risk models |
title_short |
Dependent conditional value-at-risk for aggregate risk models |
title_full |
Dependent conditional value-at-risk for aggregate risk models |
title_fullStr |
Dependent conditional value-at-risk for aggregate risk models |
title_full_unstemmed |
Dependent conditional value-at-risk for aggregate risk models |
title_sort |
dependent conditional value-at-risk for aggregate risk models |
publisher |
Elsevier |
series |
Heliyon |
issn |
2405-8440 |
publishDate |
2021-07-01 |
description |
Risk measure forecast and model have been developed in order to not only provide better forecast but also preserve its (empirical) property especially coherent property. Whilst the widely used risk measure of Value-at-Risk (VaR) has shown its performance and benefit in many applications, it is in fact not a coherent risk measure. Conditional VaR (CoVaR), defined as mean of losses beyond VaR, is one of alternative risk measures that satisfies coherent property. There have been several extensions of CoVaR such as Modified CoVaR (MCoVaR) and Copula CoVaR (CCoVaR). In this paper, we propose another risk measure, called Dependent CoVaR (DCoVaR), for a target loss that depends on another random loss, including model parameter treated as random loss. It is found that our DCoVaR provides better forecast than both MCoVaR and CCoVaR. Numerical simulation is carried out to illustrate the proposed DCoVaR. In addition, we do an empirical study of financial returns data to compute the DCoVaR forecast for heteroscedastic process of GARCH(1,1). The empirical results show that the Gumbel Copula describes the dependence structure of the returns quite nicely and the forecast of DCoVaR using Gumbel Copula is more accurate than that of using Clayton Copula. The DCoVaR is superior than MCoVaR, CCoVaR and CoVaR to comprehend the connection between bivariate losses and to help us exceedingly about how optimum to position our investments and elevate our financial risk protection. In other words, putting on the suggested risk measure will enable us to avoid non-essential extra capital allocation while not neglecting other risks associated with the target risk. Moreover, in actuarial context, DCoVaR can be applied to determine insurance premiums while reducing the risk of insurance company. |
topic |
Archimedean copula Farlie-Gumbel-Morgenstern family GARCH model Pareto distribution asset returns |
url |
http://www.sciencedirect.com/science/article/pii/S2405844021015954 |
work_keys_str_mv |
AT bonyparulianjosaphat dependentconditionalvalueatriskforaggregateriskmodels AT khreshnasyuhada dependentconditionalvalueatriskforaggregateriskmodels |
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