Financial Risk Measurement Research Articles

Entropy-Based Volatility Analysis of Financial Log-Returns Using Gaussian Mixture Models

Volatility in financial markets refers to the variation in asset prices over time. High volatility indicates increased risk, making its evaluation essential for effective risk management. Various methods are used to assess volatility, with the standard deviation of log-returns being a common approach. However, this implicitly assumes that log-returns follow a Gaussian distribution, which is not always valid. In this paper, we explore the use of (differential) entropy to evaluate the volatility of financial log-returns. Estimation of entropy is obtained using a Gaussian mixture model to approximate the underlying density of log-returns. Following this modeling approach, popular risk measures such as Value at Risk and Expected Shortfall can also be computed. By integrating Gaussian mixture modeling and entropy into the analysis of log-returns, we aim to provide a more accurate and robust framework for assessing financial volatility and risk measures.

Analysis of Financial Investment Risk and Preventive Measures

With the development of economic cycle, financial investment has become one of the key exploration directions of enterprises. Scientific financial investment can help enterprises increase the value of assets and expand the scale of operation. However, due to the increasingly complex economic market, financial investment risks are more complex. Based on this, this paper takes the risks faced by enterprises in the process of financial investment as the research basis, sorts out the causes of risks, and puts forward targeted preventive measures, aiming at providing support for enterprises to stabilize operation and obtain more investment returns.

Explainable machine learning for financial risk management: two practical use cases

We explore the potential of machine learning (ML) models applied in two financial risk management areas, i.e., credit risk management and financial risk hedging, through two practical use cases. This comparative study starts with the issue of explainability in complex ML models used in peer-to-peer lending for credit risk management. The first use case examines the limitations of using Kernel-SHAP with dependent features and evaluates different methods for estimating these dependencies using the Lending Club dataset. Our results suggest that accounting for feature dependence improves the understanding and robustness of prediction explanations. The second use case investigates a dynamic method for hedging foreign exchange risk in international equity portfolios, emphasizing the importance of accurate forecasts of currency returns. The analysis demonstrates that predictions yielded by ML models can significantly enhance the hedging of portfolios against currency risk. These findings highlight the transformative potential of advanced ML models in financial risk management, showcasing their capability to improve financial risk measurement and management. Further, our study outlines future research directions to advance this field.

Monte Carlo Estimation of CoVaR

CoVaR is an important measure of financial systemic risk due to its ability to capture tail dependence between the losses of different portfolios and its capacity to predict financial crises. Estimating CoVaR is challenging because its definition involves a zero-probability event, which is unobservable in the data. The existing model-based methods address this issue by assuming simplified structural models, which introduce biases that are difficult to eliminate. In “Monte Carlo Estimation of CoVaR,” Huang, Lin, and Hong propose using Monte Carlo methods to estimate CoVaR, leveraging the modeling flexibility of Monte Carlo simulation. Specifically, they introduce a batching estimator applicable to a wide range of financial models and prove that its best rate of convergence is [Formula: see text], where n is the sample size. Under the widely used delta-gamma approximation model, they further introduce an importance sampling–inspired estimator and prove that its best rate of convergence can be improved to [Formula: see text].

Bitcoin versus S&P 500 Index: Return and Risk Analysis

The S&P 500 Index is considered the most popular trading instrument in financial markets. With the rise of cryptocurrencies over the past few years, Bitcoin has grown in popularity and adoption. This study analyzes the daily return distribution of Bitcoin and the S&P 500 Index and assesses their tail probabilities using two financial risk measures. As a methodology, we use Bitcoin and S&P 500 Index daily return data to fit the seven-parameter General Tempered Stable (GTS) distribution using the advanced fast fractional Fourier transform (FRFT) scheme developed by combining the fast fractional Fourier transform algorithm and the 12-point composite Newton–Cotes rule. The findings show that peakedness is the main characteristic of the S&P 500 Index return distribution, whereas heavy-tailedness is the main characteristic of Bitcoin return distribution. The GTS distribution shows that 80.05% of S&P 500 returns are within −1.06% and 1.23% against only 40.32% of Bitcoin returns. At a risk level (α), the severity of the loss (AVaRα(X)) on the left side of the distribution is larger than the severity of the profit (AVaR1−α(X)) on the right side of the distribution. Compared to the S&P 500 Index, Bitcoin has 39.73% more prevalence to produce high daily returns (more than 1.23% or less than −1.06%). The severity analysis shows that, at α risk level, the average value-at-risk (AVaR(X)) of Bitcoin returns at one significant figure is four times larger than that of the S&P 500 Index returns at the same risk.

Measuring ESG risks in multi-asset portfolios: Decomposing VaRESG into CVaRESG

This study investigates the contribution of different asset classes to investment portfolio risk by integrating environmental, social, and governance (ESG) factors into traditional financial risk measures. We propose a new methodology for decomposing VaRESG by measuring the Component VaRESG (CVaRESG) of a multi-asset financial portfolio. A pilot empirical application's results provide evidence of the reliability of CVaRESG to define the maximum contribution of the risk accepted for securities or parts of the financial portfolio. This study contributes to the debate on how ESG factors can have quantifiable long-term financial impacts and clarifies the risk contribution of each security included in a financial portfolio.

Systemic Financial Risk Forecasting: A Novel Approach with IGSA-RBFNN

Accurate measurement of systemic financial risk is crucial for maintaining the stability of financial markets. Taking China as the subject of investigation, the Chinese Financial Stress Index (CFSI) indicator system was constructed by integrating six dimensions and employing Gray Relation Analysis (GRA) to reduce the dimensionality of the indicators. The CFSI was derived using the Attribute Hierarchy Model (AHM) method with the Criteria Importance Through the Intercriteria Correlation (CRITIC) method, and an Improved Gravitational Search Algorithm (IGSA)-optimized Radial Basis Function Neural Network (RBFNN) was proposed for out-of-sample prediction of CFSI trends from 2024 to 2026. By analyzing the trends in financial pressure indicators, the intricate relationship between financial pressure and economic activity can be effectively discerned. The research findings indicate that (1) the CFSI is capable of accurately reflecting the current financial stress situation in China, and (2) the IGSA-RBFNN demonstrates strong robustness and generalization capabilities, predicting that the CFSI index will reach a peak value of 0.543 by the end of 2024, and there exists a regular pattern of stress rebound towards the end of each year. The novel methodology enables policymakers and regulatory authorities to proactively identify potential risks and vulnerabilities, facilitating the formulation of preventive measures.

Transformation of Various Measures of Financial Risks with their Limitation on Outcomes Associated with Losses

In assessing the risk of investing in various financial assets, risk management focuses on the analysis of the worst possible losses (the right tail of the loss distribution). At the same time, most often, when speaking about losses, it is assumed that losses can, in principle, take on negative values (which corresponds to receiving positive profits). However, there are many theoretical studies suggesting that losses take only positive values. Many risk managers use only a portion of the sample of data that corresponds to positive losses when assessing the relevant risk measures using the statistical method or the Monte Carlo method. The purpose of this paper is to study the transformation of risk estimates of various levels of catastrophicity with such a change in the space of elementary events, and hence the law of loss distribution. The paper uses methods of analysis of financial risks of various levels of catastrophicity, including methods developed in the author’s previous papers. As a result of the study, it turned out that with such a transformation of the random value of losses, all the most important estimates are significantly transformed with the help of risk measures of various catastrophicity. The author concludes that the theoretical conclusions of the work will also contribute to a more conscious understanding of the theoretical results and the results of practical risk assessments, depending on the basis on which this assessment was made: allowing losses to accept negative values or focusing only on their positive values.

A comparative study of fuzzy multi-objective investment project portfolio selection and optimization based on financial return and different risk measurements

Competitiveness in the global market is getting more intense. Due to resource and budget constraints, firms need to achieve their expected goals and satisfy all investment constraints under uncertainty. Selecting the set of projects among other candidates to get the most efficient portfolio requires a lot of attention from the Decision Makers (DMs) as this consideration no longer relies purely on the financial term. This problem becomes a multi-objective problem under uncertainty where the financial return and risk from uncertainty are required into the trading off consideration. Due to the financial uncertainty, the chance-constrained programming has been employed in this study for defuzzifying and solving uncertain optimization problems at a specified confidence level that is defined by the DMs. Then, various kinds of investment or financial risk measures, Lower-Semi Variance Index (LSVI), the absolute deviation with the expected FNPV, and the absolute mean-Conditional Value at Risk (CVaR) gap are provided in the selection of such risk measures to show their differences in characteristics and performances in the obtained results. Since, such problems can consist of many project candidates and complex constraints, which may grow beyond the application of the exact optimization approach, a meta-heuristic method, Genetic Algorithm (GA), is introduced to optimize this problem through designing and constructing a decision support tool for the investment portfolio selection and optimization. The applicability of the proposed comparative approach and the constructed tool are illustrated through examples.

Systemic Financial Risk Forecasting with Decomposition–Clustering-Ensemble Learning Approach: Evidence from China

Establishing a scientifically effective systemic financial risk early warning model is of great significance for prudently mitigating systemic financial risks and enhancing the efficiency of financial supervision. Based on the measurement of systemic financial risk and the network sentiment index of 47 financial institutions, this study adopted the “decomposition–reconstruction–integration” approach, utilizing techniques such as extreme-point symmetric empirical mode decomposition (ESMD), empirical mode decomposition (EMD), variational mode decomposition (VMD), hierarchical clustering, fast independent component analysis (FastICA), attention mechanism, bidirectional long short-term memory neural network (BiLSTM), support vector regression (SVR), and their combination, to construct a systemic financial risk prediction model. The empirical results demonstrate that decomposing and reconstructing relevant indicators before predicting systemic financial risks can enhance prediction accuracy. Among the proposed models, the ESMD-HFastICA-BiLSTM-Attention model exhibits superior performance in systemic financial risk early warning.

Fusion of multifactor modeling and supervised learning algorithms in quantitative finance: a comparative analysis of predictive and explanatory power

Abstract Finance serves as the lifeblood of the real economy’s development, fundamentally aimed at bolstering the real economy and mitigating financial risks. This paper investigates the application of machine learning technologies in finance, organizing a detailed classification and analysis of associated risks within the sector. Specifically, the study employs the Conditional Value at Risk (CoVaR) to quantify systemic financial risks. It introduces both the Fama-French three-factor and five-factor models for constructing multifactor financial models. It assesses the significance and regression coefficients of risk factors within these models to provide a comparative analysis. Moreover, this research develops an early warning model for financial risk by incorporating financial risk measurement indices into the XGBoost machine learning framework. It utilizes the SHAP (Shapley Additive exPlanations) explanatory framework to elucidate the key features influencing financial risk. This comprehensive approach not only enhances the understanding of financial risk dynamics but also advances the predictive capabilities of financial risk management. It was found that the modified R² increased from 36.52% to 56.25% after adding the IMU factor to the three-factor model, and the coefficient of SMB decreased from 0.135 to −0.215 the larger the size of the enterprise. The accuracy of the financial risk early warning model was 96.35%, and the probability of being predicted by the model to be a high-risk sample was lower when the value of the characteristic INDI was taken as [0,0.125]. Financial institutions can enhance their risk prevention ability by combining the financial risk factors obtained from the multifactor model with the supervised learning algorithm.

A prelude to statistics in Wasserstein metric spaces

PurposeThis paper aims mainly at introducing applied statisticians and econometricians to the current research methodology with non-Euclidean data sets. Specifically, it provides the basis and rationale for statistics in Wasserstein space, where the metric on probability measures is taken as a Wasserstein metric arising from optimal transport theory.Design/methodology/approachThe authors spell out the basis and rationale for using Wasserstein metrics on the data space of (random) probability measures.FindingsIn elaborating the new statistical analysis of non-Euclidean data sets, the paper illustrates the generalization of traditional aspects of statistical inference following Frechet's program.Originality/valueBesides the elaboration of research methodology for a new data analysis, the paper discusses the applications of Wasserstein metrics to the robustness of financial risk measures.

Lost in noise? Some thoughts on the use of machine learning in financial market risk measurement

Machine learning has permeated almost all areas in which inferences are drawn from financial data. Nevertheless, in financial market risk measurement most machine learning techniques struggle with some inherent difficulties: Financial time series are very noisy, not stationary and mostly considerably short. This paper contains an easy to implement sequential learning algorithm that overcomes some of these disadvantages. It is based on a Kalman filtering mechanism for quite general stochastic processes and provides a first step in the direction of separating parameter dynamics from the ubiquitous noise component. The core idea here is to use some stylised facts inherent to financial markets time series such as time varying measures of volatility. The new approach is tested using real market data in two different settings. First, a hypothetical portfolio containing credit spread and equity risk is analysed over a time frame containing the outbreak of the global pandemic in 2020 and the beginning of the Russian attack on Ukraine in 2022. Another analysis is focused on US$/EUR exchange rate during a time span containing the global financial crisis of 2008 and the subsequent European sovereign crisis. In all test calculations the proposed sequential learning algorithm performs better than the historical simulation approach used by many firms in the banking industry to meet regulatory capital requirements. Due to its simplicity this method has a high degree of explainability and interpretability which will decrease the inherent model risk. The paper concludes with a discussion of model risk for machine learning in financial institutions. Compared to classical model risk frameworks, the emphasis must be put on the more prominent role of data. The simple approach described in this paper shows that machine learning in financial market risk does not have to get lost in noise.

GLAD: Global–Local Approach; Disentanglement Learning for Financial Market Prediction

Accurate prediction of financial market trends can have a great impact on maximizing profits and avoiding risks. Conventional methods, e.g., regression or SVR, or end-to-end training approaches, coined as deep learning algorithms, have restraints as a consequence of capturing noisy and unnecessary data. Financial market’s data are composed of stock’s price time series that are correlated, and each time series has both global and local dynamics. Inspired by recent advancements in disentanglement representation learning, in this paper, we present a promising model for predicting financial markets that learn disentangled representations of features and eliminate those features that cause interference. Our model uses the informer encoder to extract features, capturing global–local patterns by using the time and frequency domains, augmenting the clean features with time and frequency-based features, and using the decoder to predict. To be more specific, we adopt contrastive learning in the time and frequency domains to learn both global and local patterns. We argue that our methodology, disentangling and learning the influential factors, holds the potential for more accurate predictions and a better understanding of how time series move and behave. We conducted our experiments using the S&P 500, CSI 300, Hang Seng, and Nikkei 225 stock market datasets to predict their next-day closing prices. The results showed that our model outperformed existing methods in terms of prediction error (mean squared error and mean absolute error), financial risk measurement (volatility and max drawdown), and prediction net curves, which means that it may enhance traders’ profits.

Financial distress and stock price crash risk in Egyptian firms

Economic policy uncertainty intensified as a result of the global financial crisis. To overcome these obstacles, firms handle issues with financial distress and crash risk more proactively. This paper offers new insights into the relationship between financial distress and crash risk on the Egyptian stock market during the period of 2014–2021 and presents how managers strengthen the bad news hoarding mechanism to their advantage. Data were collected via financial statements and reports obtained from the Thomson Reuters database using 824 annual observations of 103 Egyptian firms via the generalized method of moments and ordinary least squares. Results show a strong positive impact of financial distress on crash risk using OLS and GMM. Results support the role of managerial opportunism to cover up bad news that undermines a firm’s economic fundamentals. The findings support an agency theory of how financial distress affects crash risk. The findings support conducting robust tests for alternative financial distress and crash risk measures.

The Financial Risk Measurement EVaR Based on DTARCH Models.

The value at risk based on expectile (EVaR) is a very useful method to measure financial risk, especially in measuring extreme financial risk. The double-threshold autoregressive conditional heteroscedastic (DTARCH) model is a valuable tool in assessing the volatility of a financial asset's return. A significant characteristic of DTARCH models is that their conditional mean and conditional variance functions are both piecewise linear, involving double thresholds. This paper proposes the weighted composite expectile regression (WCER) estimation of the DTARCH model based on expectile regression theory. Therefore, we can use EVaR to predict extreme financial risk, especially when the conditional mean and the conditional variance of asset returns are nonlinear. Unlike the existing papers on DTARCH models, we do not assume that the threshold and delay parameters are known. Using simulation studies, it has been demonstrated that the proposed WCER estimation exhibits adequate and promising performance in finite samples. Finally, the proposed approach is used to analyze the daily Hang Seng Index (HSI) and the Standard & Poor's 500 Index (SPI).

Upper limits of financial risk measures of various degrees of catastrophicity

The question of assessing the magnitude of risks using certain risk measures presents one of the most important problems of modern finance. However, many modern risk measures require considerable effort at times and, in practice, the investor would have sufficient knowledge of the upper limits of those risks. Comparing them with their risk appetite, an investor, in the case when the upper limits of risk measures would fit into their risk appetite, could assess this risk as acceptable to themselves. Only if the upper limit of the appropriate risk measure exceeded their risk appetite would there be a need for a detailed assessment of the appropriate risk measure. The aim of this paper is to consider upper limits first for known risk measures such as value at risk, VaR, and expected deficit or notional value at risk of ES. Next, upper limits are obtained for the risk measures VaR to the degree of t, VaR(t ) and ES to the degree of t, ES(t ) introduced by the author into scientific use. Also, using the results of V. Hürlimann, representations for maximum values of risk measures VaR(t ) and ES(t ) . The method of obtaining the described results is the application of certain representations of all these risk measures, the application of P. Chebyshev’s inequalities, as well as the results of V. Hürlimann. As a result of the study, descriptions have been proposed for the upper limits, expressing them only after a few first moments of the loss distribution law. The author concludes that the study of the upper limits of important risk measures of scientific interest has practical value for the express assessment of relevant risks.

Cross-jurisdictional financial crime risks: what can we learn from the UK regulatory data?

PurposeFinancial crime presents a serious threat to the stability and integrity of the global financial system. To combat illicit financial activities, regulatory bodies worldwide have implemented various measures, including the requirement for financial institutions to assess the financial crime risks they are exposed to in the jurisdictions they operate in. These risks include inadequate anti-money laundering and countering the financing of terrorism frameworks and other financial crime risks that have significant strategic implications for firms’ geographical footprints and customer risk classifications. This paper aims to make a contribution to the literature by undertaking a cross-country analysis of 158 countries to shed light on what drives perceived jurisdiction risk of the UK financial services firms.Design/methodology/approachCapturing firms’ perceptions of financial crime risk requires significant data collection efforts, including surveys and interviews with key personnel. This can be highly resource-intensive and may require access to sensitive information that firms may be reluctant to share. Furthermore, the dynamic nature of financial crime risks means that perceptions can change rapidly in response to changes in the regulatory and geopolitical landscape. As a result, capturing and monitoring firms’ perceptions of financial crime risks requires ongoing monitoring and analysis. Capturing firms’ perceptions of financial crime risks at a cross-jurisdictional level is a particularly complex and challenging task that requires careful consideration of a range of factors. As a result of data limitations, empirical investigation of the factors underlying the firms’ perceptions of jurisdiction risk is in its infancy. This paper uses regulatory financial crime data from the UK in a multivariate regression analysis, following a general-to-specific approach where any redundant variables were removed from the general model sequentially.FindingsResults suggest that perceived jurisdiction risk is significantly and positively associated with evasion of tax and regulations, while it is significantly and negatively associated with political stability and regulatory stringency. These have important implications for home and host supervisors with respect to the factors that drive perceived jurisdiction risks and the evaluation of the nature of inherent financial crime risks within regulated firms. The findings confirm the critical role of the shadow economy, political stability and regulatory rigor in shaping jurisdiction risk perceptions. From a policy standpoint, the findings support the case for taking prompt policy action to identify, prioritize and implement specific and targeted measures with respect to the shadow economy, political stability and rigor of regulations to improve international firms’ perceptions of jurisdiction risk.Originality/valueWhile there exists different measures of financial crime risk, it is notoriously challenging to capture firms’ perceptions of it, particularly at a cross-jurisdiction level. This is because financial crime risks can vary significantly across different jurisdictions due to differences in legal and regulatory frameworks, cultural norms and levels of economic development. This makes it difficult for firms to compare and evaluate the financial crime risks they face in different jurisdictions. Besides, firms’ perceptions of financial crime risks can be influenced by a range of subjective factors, including personal experiences, media coverage and hearsay. These perceptions may not always align with objective risk assessments, which are based on more systematic and empirical methods of risk measurement. This paper contributes to the existing literature by undertaking a cross-country analysis drawing on a unique set of UK regulatory financial crime data, which is based on a total of 1,900 annual financial crime data regulatory return (REP-CRIM) submissions to the UK’s Financial Conduct Authority.

Volatility connectedness between global COVOL and major international volatility indices

This research explores dynamic connectedness amongst financial markets using the novel financial risk measure, global common volatility (COVOL) (Engle and Campos-Martins, 2023) and four major asset price implied volatility measures using a TVP-VAR framework. Considering several major international crises, results show that COVOL is a shock receiver while also identifying that VIX is a dominant risk driver of the pricing of risk transmission for the global financial system. The fluctuations of connectedness between COVOL and each implied volatility indices are highly dependent on periods of exceptional stress across international financial markets.

Analysing the Behaviour of Financial Risk Management and Its Impact on Success of Project

In this financial oriented business world, the risk and risk measuring activities such as identifying the issues, analysing and modifying of ambiguity in the credit creation and investment behavioural decision making. (Kishk et. al. 2008) Basically, the risk management process comes when a stakeholder of a corporation or the fund allocator decides on the basis of analysis and attempts to evaluate the probable losses in any investment. To avoid this kind of risk or technically termed as the moral hazard problem, the investor has to take certain necessary action for gaining better profitability or minimize the risk of loss. The risk management strategies are termed as behavior of the financial risk (Moles, 2016). The present paper aims to study the various behavioral decision-making process of the manager or the investor of the corporation towards the profitability. It also aims to emphasizes the impact of this strategic behavior of the firm or corporation’s decision on the successful growth and establishment. The study is significant with respect to evaluate the cause and effect through the strategies implemented by the investors. It also attempted to reveal the project success story by implementing the risk averse practices. The project victory criteria are a measurable or quantifiable term of expected outcome of the running project which must be accepted by the stakeholder. Financial risk measurement is always being an implicit proportion of the management in the firm or industry. The present study adopts the descriptive research method and uses the secondary data sources published in the company’s websites and annual statements. The collected data have been analyzed by an appropriate statistical and econometrical tool to evolve the relationship between the behavioural aspects of risk management strategies and its influence on the project success of the firm. The risk management of credit on commercial bank is most essential for the benefit and stop suffering from the losses on the project. Prevention and controlling the risk of loans and advances is a tough and very challenging target for the business project. It is statistically evidence that there is an association between the profit and credit loss expense. On the whole, the present study explores the profitability and the success of the financial organization.