
on Risk Management 
By:  Baishuai Zuo; Chuancun Yin; Jing Yao 
Abstract:  In this paper, we propose the multivariate range ValueatRisk (MRVaR) and the multivariate range covariance (MRCov) as two risk measures and explore their desirable properties in risk management. In particular, we explain that such rangebased risk measures are appropriate for risk management of regulation and investment purposes. The multivariate range correlation matrix (MRCorr) is introduced accordingly. To facilitate analytical analyses, we derive explicit expressions of the MRVaR and the MRCov in the context of the multivariate (log)elliptical distribution family. Frequentlyused cases in industry, such as normal, student$t$, logistic, Laplace, and Pearson type VII distributions, are presented with numerical examples. As an application, we propose a rangebased meanvariance framework of optimal portfolio selection. We calculate the rangebased efficient frontiers of the optimal portfolios based on real data of stocks' returns. Both the numerical examples and the efficient frontiers demonstrate consistences with the desirable properties of the rangebased risk measures. 
Date:  2023–05 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2305.09097&r=rmg 
By:  Pierre Durand (Université Paris Est Créteil, ERUDITE, 94010 Créteil Cedex, France); Gaëtan Le Quang (Univ Lyon, Université Lumière Lyon 2, GATE UMR 5824, F69130 Ecully, France); Arnold Vialfont (Université Paris Est Créteil, ERUDITE, 94010 Créteil Cedex, France) 
Abstract:  Using a database comprising US bank balance sheet variables covering the 20002018 period and the list of failed banks as provided by the FDIC, we run various models to exhibit the main determinants of bank default. Among these models, Logistic Regression, Random Forest, Histogrambased Gradient Boosting Classification and Gradient Boosting Classification perform the best. Relying on various machine learning interpretation tools, we manage to provide evidence that 1) capital is a stronger predictor of default than liquidity, 2) Basel III capital requirements are set at a too low level. More precisely, having a look at the impact of the interaction between capital ratios (the riskweighted ratio and the simple leverage ratio) and the liquidity ratio (liquid assets over total assets) on the probability of default, we show that the influence of capital on this latter completely outweighs that of liquidity, which is in fact very limited. From a prudential perspective, this questions the recent stress put on liquidity regulation. Concerning capital requirements, we provide evidence that setting the riskweighted ratio at 15% and the simple leverage ratio at 10% would significantly decrease the probability of default without hampering banks'activities. Overall, these results therefore call for strengthening capital requirements while at the same time releasing the regulatory pressure put on liquidity. 
Keywords:  Basel III; capital requirements ; liquidity regulation ; bankruptcy prediction models ; statistical learning ; classification 
JEL:  C44 G21 G28 
Date:  2023 
URL:  http://d.repec.org/n?u=RePEc:gat:wpaper:2308&r=rmg 
By:  Aigner, Philipp 
Abstract:  Most insurers in the European Union determine their regulatory capital requirements based on the standard formula of Solvency II. However, there is evidence that the standard formula inaccurately reflects insurers' risk situation and may provide misleading steering incentives. In the second pillar, Solvency II requires insurers to perform a socalled 'Own Risk and Solvency Assessment' (ORSA). In their ORSA, insurers must establish their own risk measurement approaches, including those based on scenarios, in order to derive suitable risk assessments and address shortcomings of the standard formula. The idea of this paper is to identify scenarios in such a way that the standard formula in connection with the ORSA provides a reliable basis for risk management decisions. Using an innovative method for scenario identification, our approach allows for a simple but relatively precise assessment of marginal and even nonmarginal portfolio changes. We numerically evaluate the proposed approach in the context of market risk employing an internal model from the academic literature and the Solvency Capital Requirement (SCR) calculation under Solvency II. 
Keywords:  Risk measurement, Enterprise Risk Management, Own Risk and Solvency Assessment, Solvency II 
JEL:  G22 G28 G32 
Date:  2023 
URL:  http://d.repec.org/n?u=RePEc:zbw:icirwp:4823&r=rmg 
By:  Makoto Okawara (Faculty of Economics, The University of Tokyo); Akihiko Takahashi (Faculty of Economics, The University of Tokyo) 
Abstract:  The environment surrounding banks is becoming increasingly severe. Particularly, to prevent the next financial crisis, Basel III requires financial institutions to prepare higher levels of capitals by January 1st, 2028, and the financial stability board (FSB) suggests the risk appetite framework (RAF) as their internal risk management. Hence, efficient usage of their own capitals for banks is more important than ever to improve profitability. Under such circumstances, this paper is the first to consider an optimization problem for a typical loan portfolio of international banks under comprehensive risk constraints with realistic profit margins and funding costs to achieve an efficient capital allocation. Concretely, after taking concentration risks on large individual obligors into account, we obtain a loan portfolio that attains the maximum profit under Basel regulatory capital and loan market constraints, as well as internal management constraints, namely risk limits on business units and industrial sectors. Moreover, we separately calculate credit risk amounts of the internal constraints in terms of regulatory and economic capitals to compare the optimized profits. In addition, considering sharp increases in default probabilities of all obligors as in the global financial crisis, we perform a stress test on the optimization results to investigate the effects of changes in risk amounts and profits. As a result, we propose to unify risk constraints on the business units and industrial sectors by using credit risk amounts in terms of economic capitals. 
Date:  2023–05 
URL:  http://d.repec.org/n?u=RePEc:tky:fseres:2023cf1214&r=rmg 
By:  Sebastian Jaimungal; Silvana M. Pesenti; Yuri F. Saporito; Rodrigo S. Targino 
Abstract:  We define and develop an approach for risk budgeting allocation  a risk diversification portfolio strategy  where risk is measured using a dynamic timeconsistent risk measure. For this, we introduce a notion of dynamic risk contributions that generalise the classical Euler contributions and which allow us to obtain dynamic risk contributions in a recursive manner. We prove that, for the class of dynamic coherent distortion risk measures, the risk allocation problem may be recast as a sequence of strictly convex optimisation problems. Moreover, we show that any selffinancing dynamic risk budgeting strategy with initial wealth of $1$ is a scaled version of the unique solution of the sequence of convex optimisation problems. Furthermore, we develop an actorcritic approach, leveraging the elicitability of dynamic risk measures, to solve for risk budgeting strategy using deep learning. 
Date:  2023–05 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2305.11319&r=rmg 
By:  Julien Hambuckers (HEC École de Gestion de l'Université de Liège); Marie Kratz (ESSEC Business School  Essec Business School, CREAR  Center of Research in Econofinance and Actuarial sciences on Risk / Centre de Recherche Econofinancière et Actuarielle sur le Risque  Essec Business School); Antoine UsseglioCarleve (AU  Avignon Université) 
Abstract:  We introduce a method to estimate simultaneously the tail and the threshold parameters of an extreme value regression model. This standard model finds its use in finance to assess the effect of market variables on extreme loss distributions of investment vehicles such as hedge funds. However, a major limitation is the need to select ex ante a threshold below which data are discarded, leading to estimation inefficiencies. To solve these issues, we extend the tail regression model to nontail observations with an auxiliary splicing density, enabling the threshold to be selected automatically. We then apply an artificial censoring mechanism of the likelihood contributions in the bulk of the data to decrease specification issues at the estimation stage. We illustrate the superiority of our approach for inference over classical peaksoverthreshold methods in a simulation study. Empirically, we investigate the determinants of hedge fund tail risks over time, using pooled returns of 1, 484 hedge funds. We find a significant link between tail risks and factors such as equity momentum, financial stability index, and credit spreads. Moreover, sorting funds along exposure to our tail risk measure discriminates between high and low alpha funds, supporting the existence of a fear premium. 
Keywords:  Extreme value theory generalized Pareto regression censored maximum likelihood, Extreme value theory, generalized Pareto regression, censored maximum likelihood 
Date:  2023–04–07 
URL:  http://d.repec.org/n?u=RePEc:hal:wpaper:hal04090916&r=rmg 
By:  Leccadito, Arturo (Université catholique de Louvain, LIDAM/LFIN, Belgium); Staino, Alessandro; Toscano, Pietro 
Abstract:  In this paper we introduce the dynamic Gerber model (DGC) and compare its performance in the prediction of VaR and ES compared to alternative parametric, nonparametric and semiparametric methods to estimate the variancecovariance matrix of returns. Based on ES backtests, the DGC method produces, overall, accurate ES forecasts. Furthermore, we use the Model Confidence Set (MCS) procedure to identify the superior set of models (SSM). For all the portfolios and VaR/ES confidence levels we consider, the DGC is found to belong to the SSM. 
Keywords:  VaR ; ES ; Gerber statistic ; parametric methods ; nonparametric methods ; semiparametric methods 
Date:  2022–11–29 
URL:  http://d.repec.org/n?u=RePEc:ajf:louvlf:2022011&r=rmg 
By:  Dejian Tian; Xunlian Wang 
Abstract:  Motivated by the results of static monetary or starshaped risk measures, the paper investigates the representation theorems in the dynamic framework. We show that dynamic monetary risk measures can be represented as the lower envelope of a family of dynamic convex risk measures, and normalized dynamic starshaped risk measures can be represented as the lower envelope of a family of normalized dynamic convex risk measures. The link between dynamic monetary risk measures and dynamic starshaped risk measures are established. Besides, the sensitivity and time consistency problems are also studied. A specific normalized time consistent dynamic starshaped risk measures induced by $ g $expectations are illustrated and discussed in detail. 
Date:  2023–05 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2305.02481&r=rmg 
By:  Denuit, Michel (Université catholique de Louvain, LIDAM/ISBA, Belgium); Robert, Christian Y. 
Abstract:  This paper considers a risk sharing scheme of independent discrete losses that combines risk retention at individual level, risk transfer for too expensive losses and risk pooling for the middle layer. This ensures that pooled losses can be considered as being uniformly bounded. We study the nosabotage requirement and diversification effects when the conditional mean risksharing rule is applied to allocate pooled losses. The nosabotage requirement is equivalent to Efron’s monotonicity property for conditional expectations, which is known to hold under logconcavity. Elementary proofs of this result for discrete losses are provided for finite population pools. The nosabotage requirement and diversification effects are then examined within large pools. It is shown that Efron’s monotonicity property holds asymptotically and that risk can be eliminated under fairly general conditions which are fulfilled in applications. 
Keywords:  Risk pooling ; PeertoPeer (P2P) insurance ; Conditional mean risksharing ; Likelihood ratio order ; Logconcavity 
Date:  2023–03–10 
URL:  http://d.repec.org/n?u=RePEc:aiz:louvad:2023010&r=rmg 
By:  Duden, Christoph; Offermann, Frank; Mußhoff, Oliver 
Abstract:  Extreme weather events pose an economic threat to farms. The risk management behaviour against such events is often studied using prospect theory as a framework, but empirically deriving corresponding parameters in the field involving farmers is challenging. To address this issue, we compare three methods of eliciting prospect theory parameters using a multiple price list design in Germany: a framed field experiment, a framed student experiment and an artefactual field experiment. The results show that these experiments generate different prospect theory parameters. The lower the probability the higher the differences, which is particularly important for managing risk from lowprobability shocks. Despite these differences, the mean coefficients of the three experiments reveal a low willingness to pay for crop insurance. We find evidence that individual responses to the artefactual and student experiments correlate with the risk attitude selfassessment, whereas responses to the framed field experiment correlate with the purchase of crop insurance. 
Keywords:  prospect theory, risk management, catastrophic risk, behavioural economics, decision analysis 
Date:  2023 
URL:  http://d.repec.org/n?u=RePEc:zbw:daredp:2301&r=rmg 
By:  Aigner, Philipp; Schlütter, Sebastian 
Abstract:  Gradient capital allocation, also known as Euler allocation, is a technique used to redistribute diversified capital requirements among different segments of a portfolio. The method is commonly employed to identify dominant risks, assessing the riskadjusted profitability of segments, and installing limit systems. However, capital allocation can be misleading in all these applications because it only accounts for the current portfolio composition and ignores how diversification effects may change with a portfolio restructuring. This paper proposes enhancing the gradient capital allocation by adding "orthogonal convexity scenarios" (OCS). OCS identify risk concentrations that potentially drive portfolio risk and become relevant after restructuring. OCS have strong ties with principal component analysis (PCA), but they are a more general concept and compatible with common empirical patterns of risk drivers being fattailed and increasingly dependent in market downturns. We illustrate possible applications of OCS in terms of risk communication and risk limits. 
Keywords:  Risk capital allocation, Scenario analysis, Risk communication, Risklimiting, Principal Component Analysis 
JEL:  G28 G32 D62 H23 
Date:  2023 
URL:  http://d.repec.org/n?u=RePEc:zbw:icirwp:4723&r=rmg 
By:  Ulrich Hege (TSER  Toulouse School of Economics  UT Capitole  Université Toulouse Capitole  UT  Université de Toulouse  EHESS  École des hautes études en sciences sociales  CNRS  Centre National de la Recherche Scientifique  INRAE  Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); Elaine Hutson; Elaine Laing 
Abstract:  Using the SarbanesOxley Act of 2002 as a quasinatural experiment to identify the impact of corporate governance reform on foreign exchange risk hedging, we find that the substantial improvements in governance standards increased derivatives hedging and reduced foreign exchange exposure. The results are robust whether we consider initial reform gap or actual implementation, focus on legally required governance measures or include voluntary concomitant reforms. The economic magnitude of the effect is large. Our findings are corroborated by crosssectional evidence, showing that firms with larger foreign markets exposure and a larger distortion in CEO incentives react more strongly to the reform. Financial hedges are implemented rapidly whereas exposure measures that encompass operational hedges take more time to adjust. 
Keywords:  Risk management, Financial hedging, Operational hedging, Foreign exchange risk, SarbanesOxley Act, Corporate governance reform, Board monitoring, Risktaking incentives 
Date:  2021–06 
URL:  http://d.repec.org/n?u=RePEc:hal:journl:hal03353022&r=rmg 
By:  Christis Katsouris 
Abstract:  This paper considers the specification of covariance structures with tail estimates. We focus on two aspects: (i) the estimation of the VaRCoVaR risk matrix in the case of larger number of time series observations than assets in a portfolio using quantile predictive regression models without assuming the presence of nonstationary regressors and; (ii) the construction of a novel variable selection algorithm, socalled, Feature Ordering by Centrality Exclusion (FOCE), which is based on an assumptionlean regression framework, has no tuning parameters and is proved to be consistent under general sparsity assumptions. We illustrate the usefulness of our proposed methodology with numerical studies of real and simulated datasets when modelling systemic risk in a network. 
Date:  2023–05 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2305.11282&r=rmg 
By:  Maxime Markov; Vladimir Markov 
Abstract:  In this paper, we revisit the relationship between investors' utility functions and portfolio allocation rules. We derive portfolio allocation rules for asymmetric Laplace distributed $ALD(\mu, \sigma, \kappa)$ returns and compare them with the meanvariance approach, which is based on Gaussian returns. We reveal that in the limit of small $\frac{\mu}{\sigma}$, the Markowitz contribution is accompanied by a skewness term. We also obtain the allocation rules when the expected return is a random normal variable in an average and worstcase scenarios, which allows us to take into account uncertainty of the predicted returns. An optimal worstcase scenario solution smoothly approximates between equal weights and minimum variance portfolio, presenting an attractive convex alternative to the risk parity portfolio. Utilizing a microscopic portfolio model with random drift and analytical expression for the expected utility function with lognormal distributed crosssectional returns, we demonstrate the influence of model parameters on portfolio construction. Finally, we address the issue of handling singular covariance matrices by imposing block structure constraints on the precision matrix directly. This comprehensive approach enhances allocation weight stability, mitigates instabilities associated with the meanvariance approach, and can prove valuable for both shortterm traders and longterm investors. 
Date:  2023–05 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2305.08530&r=rmg 
By:  Dionne, Georges (HEC Montreal, Canada Research Chair in Risk Management); El Hraiki, Rayane (HEC Montreal, Canada Research Chair in Risk Management); Mnasri, Mohamed (HEC Montreal, Canada Research Chair in Risk Management) 
Abstract:  We study the intensity of joint hedging of oil and gas prices by US petroleum firms. We aim to explain the rationale for and find the determinants of joint hedging, as well as its impact on firm market value, performance, and riskiness. Joint hedging that takes into account the interdependence between risks should have a positive impact on firm value in the presence of multiple risks. We verify this theory in an innovative way, by testing the effects of hedging oil and gas prices simultaneously and by using an instrumental variable framework to attenuate the problem of endogeneity between firm value and risk management. We find evidence of higher market value, higher accounting performance, and lower riskiness for firms with a high propensity to jointly hedge their oil and gas production to a greater extent. We show that joint hedging dominates singlecommodity hedging. 
Keywords:  Joint hedging; enterprise risk management; oil price; gas price; hedging intensity; bivariate probit; causality; firm value. 
JEL:  C13 C23 C25 D81 G23 G32 
Date:  2023–05–25 
URL:  http://d.repec.org/n?u=RePEc:ris:crcrmw:2023_003&r=rmg 
By:  Sumanjay Dutta; Shashi Jain 
Abstract:  In this paper, we perform a comprehensive study of different covariance and precision matrix estimation methods in the context of minimum variance portfolio allocation. The set of models studied by us can be broadly categorized as: Gaussian Graphical Model (GGM) based methods, Shrinkage Methods, Thresholding and Random Matrix Theory (RMT) based methods. Among these, GGM methods estimate the precision matrix directly while the other approaches estimate the covariance matrix. We perform a synthetic experiment to study the network learning and sample complexity performance of GGM methods. Thereafter, we compare all the covariance and precision matrix estimation methods in terms of their predictive ability for daily, weekly and monthly horizons. We consider portfolio risk as an indicator of estimation error and employ it as a loss function for comparison of the methods under consideration. We find that GGM methods outperform shrinkage and other approaches. Our observations for the performance of GGM methods are consistent with the synthetic experiment. We also propose a new criterion for the hyperparameter tuning of GGM methods. Our tuning approach outperforms the existing methodology in the synthetic setup. We further perform an empirical experiment where we study the properties of the estimated precision matrix. The properties of the estimated precision matrices calculated using our tuning approach are in agreement with the algorithm performances observed in the synthetic experiment and the empirical experiment for predictive ability performance comparison. Apart from this, we perform another synthetic experiment which demonstrates the direct relation between estimation error of the precision matrix and portfolio risk. 
Date:  2023–05 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2305.11298&r=rmg 
By:  René M. Stulz 
Abstract:  This paper assesses the current state of knowledge about crisis risk and its implications for risk management. Better data that became available since the Global Financial Crisis (GFC) has improved our understanding of crisis risk. These data have been used to show that some types of crises become predictable when one accounts for interactions between risks. Specifically, a financial crisis is much more likely in the years following both high credit growth and high asset valuations. However, some other types of crises do not seem predictable. There is no evidence that the frequency of economic and financial crises is increasing. The existing data show that political crises make economic crises more likely, so that, as suggested by the concept of polycrisis, feedback between noneconomic crises and economic crises can be important, but there is no comparable evidence for climate events. Strategies that increase firm operational and financial flexibility appear successful at reducing the adverse impact of crises on firms. 
JEL:  G01 G21 G32 
Date:  2023–05 
URL:  http://d.repec.org/n?u=RePEc:nbr:nberwo:31252&r=rmg 
By:  Felix Fie{\ss}inger; Mitja Stadje 
Abstract:  Focusing on gains instead of terminal wealth, we consider an asset allocation problem to maximize timeconsistently a meanrisk reward function with a general risk measure which is i) lawinvariant, ii) cash or shiftinvariant, and iii) positively homogeneous, and possibly plugged into a general function. We model the market via a generalized version of the multidimensional BlackScholes model using $\alpha$stable L\'evy processes and give supplementary results for the classical BlackScholes model. The optimal solution to this problem is a Nash subgame equilibrium given by the solution of an extended HamiltonJacobiBellman equation. Moreover, we show that the optimal solution is deterministic and unique under appropriate assumptions. 
Date:  2023–05 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2305.09471&r=rmg 
By:  Julio Gálvez (Banco de España) 
Abstract:  This paper assesses the estimation of the socalled equity risk premium, i.e. the expected return on equities in excess of the riskfree rate, using the dividend discount model as the organizing framework. I compare the equity risk premium estimates from different dividend discount models in terms of the insample and outofsample forecasting ability across different time horizons. Using data from the Eurostoxx 50 from 20012021, I find that equity risk premium estimates exhibit similar dynamics, and are elevated during periods of high uncertainty, such as the onset of the COVID19 pandemic. Moreover, I find that the threestage dividend discount model, which divides earnings growth into an extraordinary, transitional and steadystate phase, performs the best in terms of forecasting ability. 
Keywords:  expected returns, equity risk premium, dividend discount model, return predictability 
JEL:  G10 G12 G15 
Date:  2022–05 
URL:  http://d.repec.org/n?u=RePEc:bde:opaper:2207&r=rmg 
By:  Dimitris Korobilis; Maximilian Schr\"oder 
Abstract:  We propose a multicountry quantile factor augmeneted vector autoregression (QFAVAR) to model heterogeneities both across countries and across characteristics of the distributions of macroeconomic time series. The presence of quantile factors allows for summarizing these two heterogeneities in a parsimonious way. We develop two algorithms for posterior inference that feature varying level of tradeoff between estimation precision and computational speed. Using monthly data for the euro area, we establish the good empirical properties of the QFAVAR as a tool for assessing the effects of global shocks on countrylevel macroeconomic risks. In particular, QFAVAR shortrun tail forecasts are more accurate compared to a FAVAR with symmetric Gaussian errors, as well as univariate quantile autoregressions that ignore comovements among quantiles of macroeconomic variables. We also illustrate how quantile impulse response functions and quantile connectedness measures, resulting from the new model, can be used to implement joint risk scenario analysis. 
Date:  2023–05 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2305.09563&r=rmg 
By:  Chase P. Ross; Landon J. Ross 
Abstract:  Corporate cash piles vary across companies and over time. A firm's cash holding is an implicit position in a lowreturn asset that is correlated across firms. Cash generates variation in beta estimates. We show how investors can hedge out the cash on firms' balance sheets when making portfolio choices. We decompose stock betas into components that depend on the firm's cash holding, return on cash, and cashhedged return. Common asset pricing premia — size, value, and momentum — have large implicit cash positions. Portfolios of cashhedged premia often have higher Sharpe ratios because firms' cash returns are correlated. 
Keywords:  value; crosssection of expected returns; cash; size; risk factor; momentum 
JEL:  G12 
Date:  2022–08 
URL:  http://d.repec.org/n?u=RePEc:fip:fedgfe:202255&r=rmg 
By:  Riza Demirer (Department of Economics & Finance, Southern Illinois University Edwardsville, Alumni Hall 3145, Edwardsville IL, 620261102, USA); David Gabauer (Data Analysis Systems, Software Competence Center Hagenberg, Hagenberg, Austria); Rangan Gupta (Department of Economics, University of Pretoria, Private Bag X20, Hatfield 0028, South Africa); Joshua Nielsen (Boulder Investment Technologies, LLC, 1942 Broadway Suite 314C, Boulder, CO, 80302, USA) 
Abstract:  This paper examines the predictability of bubbles across global stock markets and whether or not synchronicity in bubble formation across markets can be predicted via metrics of market risk that are readily available. Utilizing the gold to platinum price ratio (LGP) as an easy to implement risk metric and the LogPeriodic Power Law Singularity (LPPLS) model to detect positive and negative bubble formation at different time scales, we document evidence of synchronized boom and bust cycles of the seven developed equity markets in the G7 bloc. More importantly, our analysis shows that bubbles and their comovements are predictable by the gold to platinum price ratio although the predictive relationship is only detectible via models that account for nonlinearities in the data. We find that predictability is generally stronger for negative bubbles than their positive counterparts and the predictive impact of LGP is strongest for the longterm for negative bubbles, while it is strongest in the shortrun for positive bubbles, meaning that the gold to platinum price ratio serves as a more robust predictor of deeper downward accelerating price formations followed by a rally. The predictability results for the U.S. also carries over to bubble formation in the remaining stock markets of the G7 bloc, to the extent that the gold to platinum price ratio also helps to explain the synchronicity of bubbles across the G7. Our findings provide a valuable opening for market regulators as the results show that readily available metrics of market risk can be used to model and monitor the occurrence of bubbles in financial markets as well as the connectedness of bubbles across the global markets. 
Keywords:  MultiScale Positive and Negative Bubbles, GoldtoPlatinum PriceRatio, Nonparametric CausalityinQuantiles Test, G7 
JEL:  C22 G15 Q02 
Date:  2023–05 
URL:  http://d.repec.org/n?u=RePEc:pre:wpaper:202317&r=rmg 