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In this chapter, we estimate the Expected Shortfall (ES) in conditional autoregressive expectile models by using a nonparametric multiple expectile regression via gradient tree boosting. This approach has the advantages generated by the flexibility of not having to rely on data assumptions and avoids the drawbacks and fragilities of a restrictive estimator such as Historical Simulation. We consider distinct specifications for the information sets that produce the ES estimates. The results obtained with simulated and real market data indicate that the proposed approach has good performance, with some distinctions between the specifications.

The purpose of this paper is to present the method for efficient computation of risk measures using Fourier transform technique. Another objective is to demonstrate that this technique enables an efficient computation of risk measures beyond value-at-risk and expected shortfall. Finally, this paper highlights the importance of validating assumptions behind the risk model and describes its application in the affine model framework.

The method proposed is based on Fourier transform methods for computing risk measures. The authors obtain the loss distribution by fitting a cubic spline through the points where Fourier inversion of the characteristic function is applied. From the loss distribution, the authors calculate value-at-risk and expected shortfall. As for the calculation of the entropic value-at-risk, it involves the moment generating function which is closely related to the characteristic function. The expectile risk measure is calculated based on call and put option prices which are available in a semi-closed form by Fourier inversion of the characteristic function. We also consider mean loss, standard deviation and semivariance which are calculated in a similar manner.

The study offers practical insights into the efficient computation of risk measures as well as validation of the risk models. It also provides a detailed description of algorithms to compute each of the risk measures considered. While the main focus of the paper is on portfolio-level risk metrics, all algorithms are also applicable to single instruments.

The algorithms presented in this paper require little computational effort which makes them very suitable for real-world applications. In addition, the mathematical setup adopted in this paper provides a natural framework for risk model validation which makes the approach presented in this paper particularly appealing in practice.

This is the first study to consider the computation of entropic value-at-risk, semivariance as well as expectile risk measure using Fourier transform method.

Financial markets have experienced considerable turbulence over the past two decades. The recent subprime and sovereign debt crises in the United States and Europe, respectively, have resulted in significant new regulatory responses. They also prompted the re-evaluation of how best to manage and measure financial risk. The 20 chapters in this volume provide a number of different perspectives on financial risk in the post-crisis period where monetary easing has become a predominant monetary policy. While asset price volatility has now returned to levels experienced in the mid-2000s many lessons remain. Among the most important is the need to accurately measure and manage the complex risks that exist in financial markets. Our hope is that the chapters presented here provide a better understanding of how best to do this, while also giving insights for next suitable steps and further developments.

A systemic risk measure is proposed accounting for links and mutual dependencies between financial institutions utilizing tail event information. Financial Risk Meter (FRM) is based on least absolute shrinkage and selection operator quantile regression designed to capture tail event co-movements. The FRM focus lies on understanding active set data characteristics and the presentation of interdependencies in a network topology. Two FRM indices are presented, namely, FRM@Americas and FRM@Europe. The FRM indices detect systemic risk at selected areas and identify risk factors. In practice, FRM is applied to the return time series of selected financial institutions and macroeconomic risk factors. The authors identify companies exhibiting extreme “co-stress” as well as “activators” of stress. With the SRM@EuroArea, the authors extend to the government bond asset class, and to credit default swaps with FRM@iTraxx. FRM is a good predictor for recession probabilities, constituting the FRM-implied recession probabilities. Thereby, FRM indicates tail event behavior in a network of financial risk factors.

Interdependency among industries is vital for understanding economic structures and managing industrial portfolios. However, it is hard to precisely model the interconnecting structure among industries. One of the reasons is that the interdependencies show a different pattern in tail events. This paper aims to investigate industry interdependency with the tail events.

General predictive model of Rapach et al. (2016) is extended to an interdependency model via least absolute shrinkage and selection operator quantile regression and network analysis. A dynamic network approach was applied on the Fama–French industry portfolios to study the time-varying interdependencies.

A denser network with heterogeneous central industries is found in tail cases. Significant interdependency varieties across time are shown under dynamic network analysis. Market volatility is identified as an influential factor of industry connectedness as well as clustering tendency under both normal and tail cases. Moreover, combining dynamic network with prediction direction information into out-of-sample industry return forecasting, a lower tail case is obtained, which gives the most accurate prediction of one-month forward returns. Finally, the Sharpe ratio criterion prefers high-centrality portfolios when tail risks are considered.

This study examines the industry portfolio interactions under the framework of network analysis and also takes into consideration tail risks. The combination of economic interpretation and statistical methodology helps in having a clear investigation of industry interdependency. Moreover, a new trading strategy based on network centrality seems profitable in our data sample.

The purpose of the paper is to better measure the risks and volatility of the Bitcoin market by using the proposed novel risk measurement model.

The joint regression analysis of value at risk (VaR) and expected shortfall (ES) can effectively overcome the non-elicitability problem of ES to better measure the risks and volatility of financial markets. And because of the incomparable advantages of the long- and short-term memory (LSTM) model in processing non-linear time series, the paper embeds LSTM into the joint regression combined forecasting framework of VaR and ES, constructs a joint regression combined forecasting model based on LSTM for jointly measuring VaR and ES, i.e. the LSTM-joint-combined (LSTM-J-C) model, and uses it to investigate the risks of the Bitcoin market.

Empirical results show that the proposed LSTM-J-C model can improve forecasting performance of VaR and ES in the Bitcoin market more effectively compared with the historical simulation, the GARCH model and the joint regression combined forecasting model.

The proposed LSTM-J-C model can provide theoretical support and practical guidance to cryptocurrency market investors, policy makers and regulatory agencies for measuring and controlling cryptocurrency market risks.

A novel risk measurement model, namely LSTM-J-C model, is proposed to jointly estimate VaR and ES of Bitcoin. On the other hand, the proposed LSTM-J-C model provides risk managers more accurate forecasts of volatility in the Bitcoin market.

This study aims to examine whether the methodology proposed by the European Supervisory Authorities (ESAs) within Delegated Regulation (European Union) 2017/653 for the calculation of market risk of certain packaged retail and insurance-based investment products (PRIIPs) is the most appropriate.

Risk models are put into effect to validate the appropriateness of the methodology announced by ESAs. ESAs have announced that the unit-linked (UL) products, labeled as Category II PRIIPs, will be subject to the Cornish–Fisher value-at-risk (CFVaR) methodology for their market risk assessment. We test CFVaR at 97.5% confidence level on 70 UL products, and we test Cornish–Fisher expected shortfall (CFES) at the same confidence level, which acts as a counter methodology for CFVaR.

The paper provides empirical insights about the Cornish-Fisher (CF) expansion being a method that incorporates the possibility of financial instability. When CFVaR by ESAs is calculated, it is shown that CF is in general a more robust risk model than the simpler historical ones. However, when CFES is applied, important points are derived. First, only in half of the occasions the CF expansion can be considered as a reliable method. Second, the CFES is a more coherent risk measure than CFVaR. We conclude that the CF expansion is unable to accurately estimate the market risk of UL products when excessive fat-tailed or non-symmetrical distributions are present. Hence, we suggest that a different methodology could also be considered by the regulatory bodies which will capture the excessive values of products in financial distress.

Literature, both theoretical and applied, regarding PRIIPs, is not extended. Although business and regulators research has begun to intensify in the last two years, to our knowledge this is one of the first studies that uses the CFES methodology for market risk assessment of Category II PRIIPs. In addition, we use a unique data set from a country in the headwinds of the recent financial crisis. This research contributes both to the academic and business community by enriching the existing literature and aiding risk managers in assessing the market risk of certain Category II PRIIPs. Considering the recent efforts of the regulatory authorities at the beginning of 2020 to implement certain amendments to the PRIIPs, we indicate relative risks related with the calculation of the market risk of the aforementioned products. Our findings could contribute to regulatory authorities’ persistent efforts in wrapping up this ongoing project.

This study examines the inter-linkages between Bitcoin prices and CEE stock markets (Hungary, the Czech Republic, Poland, Romania and Croatia).

The dynamic contemporaneous nexus has been analyzed using both the multivariate DECO-GARCH model proposed by Engle and Kelly (2012) and quantile on quantile (QQ) methodology proposed by Sim and Zhou (2015). Our study is implemented using the daily data spanning from 6 September 2012 to 12 August 2019.

First, the findings show that the average return equicorrelation across Bitcoin prices and CEE stock indices are positive, even though it is found to be time-varying over the research period shown. Second, the Bitcoin-CEE stock market association has positive signs for most pairs of quantiles of both variables and represents a rather similar pattern for the cases of Poland, the Czech Republic and Croatia. However, a weaker and primarily negative connectedness is found for Hungary and Romania, respectively. Furthermore, the interconnectedness between the co-movements in the Bitcoin market and stock returns changes significantly across quantiles of both variables within each nation, indicating that the Bitcoin-stock market relationship is dependent on both the cycle of the stock market and the nature of Bitcoin price shocks.

The evidence documented in this study has significant implications for divergent economic agents, including global investors, risk managers and policymakers, who would benefit from a comprehensive knowledge of the Bitcoin-stock market relationship to build efficient risk-hedging models and to conduct appropriate policy reactions to information spillover effects in different time horizons.

This paper is the first study employing both the multivariate DECO-GARCH model and QQ methodology to shed light on the nexus between Bitcoin prices and the stock markets in CEE countries. The DECO model uses more information to compute dynamic correlations between each pair of returns than standard dynamic conditional correlation (DCC) models, declining the estimation noise of the correlations. Besides, QQ approach allows us to capture some nuanced features of the Bitcoin-stock market relationship and explore the interdependence in its entirely. Therefore, the main contribution of this article to the related literature in this field is significant.

本研究旨在探討比特幣的價格與中東歐股市(匈牙利、捷克共和國、波蘭、羅馬尼亞和克羅地亞) 之相互聯繫.

研究使用恩格爾與凱利(2012)(Engle and Kelly (2012)) 提出的多變量DECO-GARCH模型及Sim 與Zhou(2015)(Sim and Zhou ( 2015)) 研製的分位數-分位數方法來分析動態同期的聯繫。我們的研究使用由2012年9月6日至2019年8月12日期間取得的每日數據來進行.

首先、研究結果顯示、跨比特幣價格與中東歐股價指數的平均回報當量關聯是正相關的，即使在研究期間被發現是隨時間而變化的。第二、比特幣與中東歐股市之聯繫在大多數兩變數分位數對而言出現正相關跡象，而且，這聯繫在波蘭、捷克共和國及克羅地亞而言表現一個頗相似的模式。唯就匈牙利而言、這聯繫則較弱、而羅馬尼亞則主要是負聯繫。研究結果亦顯示: 比特幣市場內的聯動與股票回報間之內在關聯會在每個國家內跨兩個變數的分位數而顯著地改變，這顯示比特幣-股市關係是取決於股市的週期和比特幣價格衝擊的本質.

本研究所記載的證據、對不同的經濟行為者而言極具意義 (這包括國際投資者、風險管理經理和政策制定者)，因他們會受惠於對比特幣-股市關係的全面認識，他們可建立有效的風險對沖模型、及在不同時間範圍對資訊溢出效應進行適當的政策反應.

本文為首個研究使用多變量DECO-GARCH模型和分位數-分位數(QQ)方法、來解釋比特幣價格與中東歐國家之股市的關係。這DECO模型使用比標準動態條件關係模型更多資訊，來計算每對回報間之動態關係，這能減少估測雜訊，而且，QQ方法讓我們可以取得比特幣-股市關係的一些細微特徵及全面地探索其相互依賴性。因此，本文的主要貢獻是在這學術領域內有關的文獻上.

The purpose of this study is to investigate the performance of Value-at-Risk (VaR) models for nine Middle East and North Africa Islamic indices using RiskMetrics and VaR parametric models.

The authors test the performance of several VaR models using Kupiec and Engle and Manganelli tests at 95 and 99 per cent levels for long and short trading positions, respectively, for the period from August 10, 2006 to December 14, 2014.

The authors’ findings show that the VaR under Student and skewed Student distribution are preferred at a 99 per cent level VaR. However, at 95 per cent level, the VaR forecasts obtained under normal distribution are more accurate than those generated using models with fat-tailed distributions. These results suggest that VaR is a good tool for measuring market risk. The authors support the use of RiskMetrics during calm periods and the asymmetric models (Generalized Autoregressive Conditional Heteroskedastic and the Asymmetric Power ARCH model) during stressed periods.

These results will be useful to investors and risk managers operating in Islamic markets, because their success depends on the ability to forecast stock price movements. Therefore, because a few Islamic financial institutions use internal models for their capital calculations, the regulatory committee should enhance market risk disclosure.

This study contributes to the knowledge in this area by improving our understanding of market risk management for Islamic assets during the stress periods. Then, it highlights important implications regarding financial risk management. Finally, this study fills a gap in the literature, as most empirical studies dealing with evaluating VaR prediction models have focused on quantifying the model risk in the conventional market.

Motivated by the growing importance of the expected shortfall in banking and finance, this study aims to compare the performance of popular non-parametric estimators of the expected shortfall (i.e. different variants of historical, outlier-adjusted and kernel methods) to each other, selected parametric benchmarks and estimates based on the idea of forecast combination.

Within a multidimensional simulation setup (spanned by different distributional settings, sample sizes and confidence levels), the authors rank the estimators based on classic error measures, as well as an innovative performance profile technique, which the authors adapt from the mathematical programming literature.

The rich set of results supports academics and practitioners in the search for an answer to the question of which estimators are preferable under which circumstances. This is because no estimator or combination of estimators ranks first in all considered settings.

To the best of their knowledge, the authors are the first to provide a structured simulation-based comparison of non-parametric expected shortfall estimators, study the effects of estimator averaging and apply the mentioned profiling technique in risk management.