Risks, Volume 12, Issue 1 (January 2024) – 16 articles

Carbon risk, a type of climate risk, is expected to have a crucial impact, especially on high-carbon-emitting, “polluting” firms as opposed to less carbon-intensive, “clean” ones. With a rising number of actions and policies being continuously proposed to mitigate these concerns and an increasing number of investors demanding more climate adaptation initiatives, this transition risk will certainly need to be incorporated into a firm’s credit risk assessment. In this paper, we explore the impact of the carbon risk factor, constructed as the daily median difference in default protection between polluting and clean European firms, on firm creditworthiness using quantile regressions on the tail distribution of credit default swap spreads for different maturities between 2020 and 2023. In particular, the recent European interest rate hikes lead to unexpected conclusions about when the carbon risk factor affects firm creditworthiness and how rapidly the net-zero economy transition must occur. Contrary to the previous literature, we find that investors are expecting the transition to occur in the medium-to-long term. Full article

It has been shown that, despite being consistent and in some cases efficient, maximum pseudo-likelihood (MPL) estimation for copula models overestimates the level of dependence, especially for small samples with a low level of dependence. This is especially relevant in finance and insurance applications when data are scarce. We show that the canonical MPL method uses the mean of order statistics, and we propose to use the median or the mode instead. We show that the MPL estimators proposed are consistent and asymptotically normal. In a simulation study, we compare the finite sample performance of the proposed estimators with that of the original MPL and the inversion method estimators based on Kendall’s tau and Spearman’s rho. In our results, the modified MPL estimators, especially the one based on the mode of the order statistics, have a better finite sample performance both in terms of bias and mean square error. An application to general insurance data shows that the level of dependence estimated between different products can vary substantially with the estimation method used. Full article

Possibility and probability are the two aspects of uncertainty, where uncertainty represents the ignorance of a given individual. The notion of alternative (or event) belongs to the domain of possibility. An event is intrinsically subdivisible and a quadratic metric, whose value is intrinsic or invariant, is used to study it. By subdividing the notion of alternative, a joint (bivariate) distribution of mass appears. The mathematical expectation of X is proved to be invariant using joint distributions of mass. The same is true for $X_{12}$ and $X_{12\dots m}$. This paper describes the notion of $\alpha$-product, which refers to joint distributions of mass, as a way to connect the concept of probability with multilinear matters that can be treated through statistical inference. This multilinear approach is a meaningful innovation with regard to the current literature. Linear spaces over $\mathbb{R}$ with a different dimension can be used as elements of probability spaces. In this study, a more general expression for a measure of variability referred to a single random quantity is obtained. This multilinear measure is obtained using different joint distributions of mass, which are all considered together. Full article

Under the revised market risk framework of the Basel Committee on Banking Supervision, the model validation regime for internal models now requires that models capture the tail risk in profit-and-loss (P&L) distributions at the trading desk level. We develop multi-desk backtests, which simultaneously test all trading desk models and which exploit all the information available in the presence of an unknown correlation structure between desks. We propose a multi-desk extension of the spectral test of Gordy and McNeil, which allows the evaluation of a model at more than one confidence level and contains a multi-desk value-at-risk (VaR) backtest as a special case. The spectral tests make use of realised probability integral transform values based on estimated P&L distributions for each desk and are more informative and more powerful than simpler tests based on VaR violation indicators. The new backtests are easy to implement with a reasonable running time; in a series of simulation studies, we show that they have good size and power properties. Full article

In this study, we proposed two types of hybrid models based on the heterogeneous autoregressive (HAR) model and support vector regression (SVR) model to forecast realized volatility (RV). The first model is a residual-type model, where the RV is first predicted using the HAR model, and the residuals are used to train the SVR model. The residual component is then predicted using the SVR model, and the results from both the HAR and SVR models are combined to obtain the final prediction. The second model is a weight-based model, which is a combination of the HAR and SVR models and uses the same independent variables and dependent variables as the HAR model; we adjust the contribution of the two models to the predicted values by giving different weights to each model. In particular, four volatility models are used in RV forecasting as basic models. For empirical analysis, the RV of returns of the Tokyo stock price index and five individual stocks of TOPIX 30 is used as the dataset. The empirical results reveal that according to the model confidence set test, the weight-type model outperforms the HAR model and the residual-type HAR–SVR model. Full article

This study examines the moderating function of corporate governance (CG) to the relationship between leverage and firm value (FV) using Korean market data. The study employs ordinary least-squares panel data regressions and two methods to manage endogeneity problems. The findings show a meaningful negative relationship between leverage and FV. This relationship, however, disappears, when the interaction variable of leverage × CG is included in the econometric model. These results indicate that an effective CG mechanism may lessen the probability of either the entrenched management-decision-making behavior or the agency costs of debt and, therefore, the negative effect of debt to FV diminishes. Moreover, our data show that the relationship between leverage and FV becomes positive, even though insignificant, for firms with a high level of CG, whereas it stays significantly negative for firms with a low level of CG. We also find that leverage for firms with a high level of CG is lower than those firms with a low level of CG. These additional findings support our conclusion of the moderating role of CG, which also influences the firms’ risk, leverage, and FV. The authors recommend the implementation of a robust CG plan to decrease the information asymmetry and the agency leverage problem. Full article

In non-life insurance practice, actuaries are often faced with the challenge of predicting the number of claims and claim amounts to be incurred at any given time, which serve to implement fair pricing and reserves given the nature of the risk. This paper extends Jewell’s credible distribution in terms of forecasting the distribution of individual risk in cases where the observations are weighted or are grouped in intervals. More specifically, we show how empirical distribution functions can be embedded within Bühlmann’s and Straub’s credibility model. The optimal projection theorem is applied for credibility estimation and more insight into the derivation of the credibility distribution estimators is also provided. In addition, distribution credibility estimators are established and numerical illustrations are presented herein. Two examples of distribution credibility estimation are given, one with insurance loss data and the other with industry financial data. Full article

Socially responsible investments, also referred to as ethical or sustainable investments, have experienced rapid global growth in recent years. They represent an investment approach that incorporates social, environmental, and ethical considerations into decision-making processes. Consequently, the significance of socially responsible investments has captured the attention of academics, prompting inquiries into the impact of integrating social criteria on portfolio performance. The primary objective of this work was to conduct a comparative study of the performance between socially responsible and non-socially responsible investment funds, using funds domiciled in Portugal and Spain. Various multi-factor models, including the three-factor model of Fama and French, the four-factor model of Carhart, and the five-factor model of Fama and French, were employed to assess performance. The sample comprised 125 investment funds, with 43 identified as socially responsible and 82 as non-socially responsible. The study’s findings indicate that there are no significant differences between socially responsible funds and their conventional counterparts. The majority of funds experience performance alterations during periods of crisis compared to crisis-free periods. Additionally, when comparing non-conditional models with conditional models, an improvement in the explanatory power of the latter is observed. This suggests that the inclusion of the dummy variable enhances the quality of fit for the models. Full article

This article combines the traditional definition of portfolio risk with minimum-spanning-tree-based “interconnectedness risk” to improve equal risk contribution portfolio performance. We use betweenness centrality to measure an asset’s importance in a market graph (network). After filtering the complete correlation network to a minimum spanning tree, we calculate the centrality score and convert it to a centrality heuristic. We develop an adjusted variance–covariance matrix using the centrality heuristic to bias the model to assign peripheral assets in the minimum spanning tree higher weights. We test this methodology using the constituents of the S&P 100 index. The results show that the centrality equal risk portfolio can improve upon the base equal risk portfolio returns, with a similar level of risk. We observe that during bear markets, the centrality-based portfolio can surpass the base equal risk portfolio risk. Full article

Variable annuities (VAs) and other long-term equity-linked insurance products are typically difficult to hedge in the incomplete markets. A state-dependent fee tied with market volatility for VAs is designed to contribute the risk-sharing mechanism between policyholders and insurers. Different from prior research, we discuss several aspects on a fair valuation, fee-rate determination and hedging with volatility-dependent fees from the perspective of a VA hedger. A method of efficient hedging strategy as a benchmark compared to other strategies is developed in the stochastic volatility setting. We illustrate this method in guaranteed minimum maturity benefits (GMMBs), but it is also applicable to other equity-linked insurance contracts. Full article

This paper studies properties and applications related to the mixture of the class of distributions built by the Lehmann’s alternative (also referred to in the statistical literature as max-stable or exponentiated distribution) of the form ${\left[G(·)\right]}^{\lambda }$, where $\lambda >0$ and $G(·)$ is a continuous cumulative distribution function. This mixture can be useful in economics, financial, and actuarial fields, where extreme and long tails appear in the empirical data. The special case in which $G(·)$ is the Stoppa cumulative distribution function, which is a good description of the random behaviour of large losses, is studied in detail. We provide properties of this mixture, mainly related to the analysis of the tail of the distribution that makes it a candidate for fitting actuarial data with extreme observations. Inference procedures are discussed and applications to three well-known datasets are shown. Full article

We consider a two-dimensional risk model with simultaneous Poisson arrivals of claims. Each claim of the first input process is at least as large as the corresponding claim of the second input process. In addition, the two net cumulative claim processes share a common Brownian motion component. For this model we determine the Gerber–Shiu metrics, covering the probability of ruin of each of the two reserve processes before an exponentially distributed time along with the ruin times and the undershoots and overshoots at ruin. Full article

This paper proposes a generalized deep learning approach for predicting claims developments for non-life insurance reserving. The generalized approach offers more flexibility and accuracy in solving actuarial reserving problems. It predicts claims outstanding weighted by exposure instead of loss ratio to remove subjectivity associated with premium weighting. Chain-ladder predicted outstanding claims are used as part of the multi-task learning to remove the dependence on case estimates. Grid-search is introduced for hyperparameter tuning to improve model performance. Performance-wise, the Generalized DeepTriangle outperforms both traditional chain-ladder methodology, the automated machine learning approaches (AutoML), and the original DeepTriangle model. Full article

In a rapidly evolving and often volatile crypto market, the ability to use historical data for simulations provides a more realistic assessment of how decentralized finance (DeFi) protocols might perform. This insight is crucial for participants, developers, and investors seeking to make informed decisions. This paper presents a comprehensive study evaluating the dynamic performance of a newly developed DeFi protocol—NOLUS. The main objective of this paper is to present and analyze the built realistic model of the platform. This model could be successfully used to analyze the stability of the platform under different environmental influences by performing various simulations and conducting experiments with different parameters that could not be realized with the real platform. In the article, the key components of the platform are presented in detail and the main dependencies between them are clarified, in addition to the ways of forming multiple variables, and the complex relations between them in the real protocol are explained. The main finding from the experimental part of the study is that the performance of the protocol representation accounts for the expected system behavior. Hence the system simulation could be successfully used to reveal essential protocol behaviors resulting from potential shifts in the crypto market environment and to optimize the protocol’s hyper parameters. Full article

How does a board of directors respond to stringent transnational regulations on corporate governance? We explore this question in a case study that includes interviews with key governance actors of a bank dealing with regulatory changes in the European Union (EU) initiated in 2010 in response to the financial crisis of 2007–2008. Our findings suggest that transnational regulations introduced a conflicting prescription to the directors, who were caught between two needs: existing local governance practices and transnational regulatory compliance. Contributing to the international corporate governance research, our findings corroborate the resistance to transnational regulations and the distrust attributable to boards of directors’ role struggles and the invasive accountability mechanisms introduced by such regulations. We, therefore, contribute to the ongoing discussion on how the conflicting layers of corporate governance—local versus global—and how the discontinuities between competing existing practices and the prescriptions of transnational regulations can provoke micro-resistance. Full article

This paper proposes a simple bounded stochastic motion to model equity price dynamics under shocks. The stochastic process has a quasi-bounded boundary which can be breached if the probability leakage condition is met. The quasi-boundedness of the process at the boundary can thus provide an indicator of the possible risk of equities under price shocks or in distress. Empirical calibration of the model parameters of the proposed process for equities can be performed easily due to the availability of an analytically tractable probability density function which generates fat-tailed distributions consistent with empirical observations. The volatility and mean-reversion of the S&P500 dynamics calibrated by the process are positively and negatively co-integrated, respectively, with the VIX index representing the level of market distress. The process captures the high likelihood of Hertz’s default about two months earlier, using only information until that point, and before the firm filed for Chapter 11 bankruptcy in May 2020 as a result of the COVID-19 pandemic. Empirical calibration of the process for GameStop’s stock price shows that the short squeeze in the stock occurred when the condition for breaching the upper boundary was met on 14 January 2021, i.e., about two weeks before major short-sellers closed out their positions with significant losses. The trading volume of the stock was positively co-integrated with the probability leakage ratio. Full article