Explore the vast range of titles available.

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.

A risk measure commonly used in financial risk management, namely, Value-at-Risk (VaR), is studied. In particular, we find a VaR forecast for heteroscedastic processes such that its (conditional) coverage probability is close to the nominal. To do so, we pay attention to the effect of estimator variability such as asymptotic bias and mean square error. Numerical analysis is carried out to illustrate this calculation for the Autoregressive Conditional Heteroscedastic (ARCH) model, an observable volatility type model. In comparison, we find VaR for the latent volatility model i.e., the Stochastic Volatility Autoregressive (SVAR) model. It is found that the effect of estimator variability is significant to obtain VaR forecast with better coverage. In addition, we may only be able to assess unconditional coverage probability for VaR forecast of the SVAR model. This is due to the fact that the volatility process of the model is unobservable.

The probability density function (PDF) of the product of two normal random variables remains an open discussion. Researchers have proposed many forms of PDFs. Among these, two notable PDFs are an analytical solution with infinite summation and an integral form with transformation. For practical computation, they must be estimated. The form with infinite summation must be truncated to a finite summation, and the form still in integration must be computed numerically. As a result of this estimation, an error occurs in the value of the estimation. This paper derives upper bounds for the estimation error resulting from truncation and numerical approximation in integral calculations. The upper bound error between the exact PDF and the truncated PDF is expressed as a geometric series using Bessel function inequality and Stirling’s approximation. The geometric formula allows the quantification of the total truncation error to be determined. For the PDF, which is still in integration form, the trapezoidal rule is used for numeric calculation. Hence, the error can be determined using the error-bound formula. The two estimated PDFs have their own advantages and disadvantages. The truncated PDF gives a relatively small upper bound value compared to the numerical calculation integral form PDF for a small value domain. However, the truncated PDF fails to perform for a large value domain, and only the integral form PDF can be used. The error for the estimation is applied to the conventional mass measurement. The results demonstrate that the error can be controlled through an analytical approach.

In a financial system, entities (e.g., companies or markets) face systemic risk that could lead to financial instability. To prevent this impact, we require quantitative systemic risk management we can carry out using conditional value-at-risk (CoVaR) and a network model. The former measures any targeted entity's tail risk conditional on another entity being financially distressed; the latter represents the financial system through a set of nodes and a set of edges. In this study, we modify CoVaR along with its multivariate extension (MCoVaR) considering the joint conditioning events of multiple entities. We accomplish this by first employing a multivariate Johnson's SU risk model to capture the asymmetry and leptokurticity of the entities' asset returns. We then adopt the Cornish-Fisher expansion to account for the analytic higher-order conditional moments in modifying (M)CoVaR. In addition, we attempt to construct a conditional tail risk network. We identify its edges using a corresponding Delta (M)CoVaR reflecting the systemic risk contribution and further compute the strength and clustering coefficient of its nodes. When applying the financial system to global foreign exchange (forex) markets before and during COVID-19, we revealed that the resulting expanded (M)CoVaR forecast exhibited a better conditional coverage performance than its unexpanded version. Its superior performance appeared to be more evident over the COVID-19 period. Furthermore, our network analysis shows that advanced and emerging forex markets generally play roles as net transmitters and net receivers of systemic risk, respectively. The former (respectively, the latter) also possessed a high tendency to cluster with their neighbors in the network during (respectively, before) COVID-19. Overall, the interconnectedness and clustering tendency of the examined global forex markets substantially increased as the pandemic progressed.

Evidence that cryptocurrencies exhibit speculative bubble behavior is well documented. This evidence could trigger global financial instability leading to systemic risk. It is therefore crucial to quantify systemic risk and investigate its transmission mechanism across crypto markets and other global financial markets. We can accomplish this using the so-called multivariate conditional value-at-risk (MCoVaR), which measures the tail risk of a targeted asset from each market conditional on a set of multiple assets being jointly in distress and on a set of the remaining assets being jointly in their median states. In this paper, we aimed to find its analytic formulas by considering multivariate copulas, which allow for the separation of margins and dependence structures in modeling the returns of the aforementioned assets. Compared to multivariate normal and Student’s t benchmark models and a multivariate Johnson’s SU model, the copula-based models with non-normal margins produced a MCoVaR forecast with superior conditional coverage and backtesting performances. Using a corresponding Delta MCoVaR, we found the crypto assets to be potential sources of systemic risk jointly transmitted within the crypto markets and towards the S&P 500, oil, and gold, which was more apparent during the COVID-19 period encompassing the recent 2021 crypto bubble event.

In a financial system, entities (e.g., companies or markets) face systemic risk that could lead to financial instability. To prevent this impact, we require quantitative systemic risk management we can carry out using conditional value-at-risk (CoVaR) and a network model. The former measures any targeted entity’s tail risk conditional on another entity being financially distressed; the latter represents the financial system through a set of nodes and a set of edges. In this study, we modify CoVaR along with its multivariate extension (MCoVaR) considering the joint conditioning events of multiple entities. We accomplish this by first employing a multivariate Johnson’s SU risk model to capture the asymmetry and leptokurticity of the entities’ asset returns. We then adopt the Cornish–Fisher expansion to account for the analytic higher-order conditional moments in modifying (M)CoVaR. In addition, we attempt to construct a conditional tail risk network. We identify its edges using a corresponding Delta (M)CoVaR reflecting the systemic risk contribution and further compute the strength and clustering coefficient of its nodes. When applying the financial system to global foreign exchange (forex) markets before and during COVID-19, we revealed that the resulting expanded (M)CoVaR forecast exhibited a better conditional coverage performance than its unexpanded version. Its superior performance appeared to be more evident over the COVID-19 period. Furthermore, our network analysis shows that advanced and emerging forex markets generally play roles as net transmitters and net receivers of systemic risk, respectively. The former (respectively, the latter) also possessed a high tendency to cluster with their neighbors in the network during (respectively, before) COVID-19. Overall, the interconnectedness and clustering tendency of the examined global forex markets substantially increased as the pandemic progressed.

Recent trends in portfolio management emphasize the importance of reducing carbon footprints and aligning investments with sustainable practices. This paper introduces Sensitivity Value-at-Risk (SensitivityVaR), an advanced distortion risk measure that combines Value-at-Risk (VaR) and Expected Shortfall (ES) with the Cornish–Fisher expansion. SensitivityVaR provides a more robust framework for managing risk, particularly under extreme market conditions. By incorporating first- and second-order distorted stochastic dominance criteria, we enhance portfolio decarbonization strategies, aligning financial objectives with environmental targets such as the Paris Agreement’s goal of a 7% annual reduction in carbon intensity from 2019 to 2050. Our empirical analysis evaluates the impact of integrating carbon intensity data—including Scope 1, Scope 2, and Scope 3 emissions—on portfolio optimization, focusing on key sectors like technology, energy, and consumer goods. The results demonstrate the effectiveness of SensitivityVaR in managing both risk and environmental impact. The methodology led to significant reductions in carbon intensity across different portfolio configurations, while preserving competitive risk-adjusted returns. By optimizing tail risks and limiting exposure to carbon-intensive assets, this approach produced more balanced and efficient portfolios that aligned with both financial and sustainability goals. These findings offer valuable insights for institutional investors and asset managers aiming to integrate climate considerations into their investment strategies without compromising financial performance.

Metaverses have been evolving following the popularity of blockchain technology. They build their own cryptocurrencies for transactions inside their platforms. These new cryptocurrencies are, however, still highly speculative, volatile, and risky, motivating us to manage their risk. In this paper, we aimed to forecast the risk of Decentraland’s MANA and Theta Network’s THETA. More specifically, we constructed an aggregate of these metaverse cryptocurrencies as well as their combination with Bitcoin. To measure their risk, we proposed a modified aggregate risk measure (AggM) defined as a convex combination of aggregate value-at-risk (AggVaR) and aggregate expected shortfall (AggES). To capture their dependence, we employed copulas that link their marginal models: heteroskedastic and ensemble learning-based models. Our empirical study showed that the latter outperformed the former when forecasting volatility and aggregate risk measures. In particular, the AggM forecast was more accurate and more valid than the AggVaR and AggES forecasts. These risk measures confirmed that an aggregate of the two metaverse cryptocurrencies exhibited the highest risk with evidence of lower tail dependence. These results are, thus, helpful for cryptocurrency investors, portfolio risk managers, and policy-makers to formulate appropriate cryptocurrency investment strategies, portfolio allocation, and decision-making, particularly during extremely negative shocks.

The incidence of infectious diseases in children may be affected by climate change-related disaster risks that increase as extreme weather events become more frequent. Therefore, this research aims to diagnose the impact of such disaster risks on the disease incidence, focusing on diarrhoea, dengue haemorrhagic fever (DHF), and acute respiratory infection (ARI), commonly experienced by children. To accomplish this task, we construct integer-valued autoregressive (INAR) models for the number of disease cases among children in several age groups, with an overdispersed distributional assumption to account for its variability that exceeds its central tendency. Additionally, we include the numbers of floods, landslides, and extreme weather events at previous times as explanatory variables. In particular, we consider a case study in Indonesia, a tropical country highly vulnerable to the aforementioned climate change-related diseases and disasters. Using monthly data from January 2010 to December 2024, we find that the incidence of diarrhoea in children is positively impacted by landslides (but negatively affected by floods and extreme weather events). Landslides, frequently caused by excessive rainfall, also increase DHF incidence. Furthermore, the increased incidence of ARI is driven by extreme weather conditions, which are more apparent during and after COVID-19. These findings offer insights into how climate scenarios may increase children’s future health risks. This helps shape health strategies and policy responses, highlighting the urgent need for preventive measures to protect future generations.

Dependent Tail Value-at-Risk, abbreviated as DTVaR, is a copula-based extension of Tail Value-at-Risk (TVaR). This risk measure is an expectation of a target loss once the loss and its associated loss are above their respective quantiles but bounded above by their respective larger quantiles. In this paper, we propose nonparametric estimators for DTVaR and establish their property of consistency. Moreover, we also propose the variability measure around this expected value truncated by the quantiles, called the Dependent Conditional Tail Variance (DCTV). We use this measure for constructing confidence intervals of the DTVaR. Both parametric and nonparametric approaches for DTVaR estimations are explored. Furthermore, we assess the performance of DTVaR estimations using a proposed backtest based on the DCTV. As for the numerical study, we take an application in the insurance claim amount.