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on Risk Management |
| By: | Maringer, Dietmar; Stähli, Philipp |
| Abstract: | Drawdown is an important risk measure in both theory and practice. Most drawdown measures use the running peak as the reference point from which to calculate the drawdown. Instead, the start-to-low drawdown (SLD), which references the start of the period, is firstly proposed as a relevant measure for levered investors. Secondly, an application to a levered investor who is also subject to regulatory capital requirements, as seen in the banking or insurance industry, is proposed. Such an investor is faced with regulatory sanctions as soon as their own funds no longer cover capital requirements, i.e., even before equity is exhausted. Portfolio optimization objectives are developed that consider return, cost of capital, and cost of drawdown together: the solvency cost-adjusted return (SCAR) including the cost of drawdown (SCARD). This is applied to the European insurance industry, with capital requirement calculations following the Solvency II standard model. For the empirical analysis, models of life and non-life insurance companies are constructed using EIOPA market overview data, and their investments are optimized for SCAR and SCARD as objectives. The investment universe consists of equity, corporate bond, and government bond indices with data ranging from 2005 to 2024. The characteristics and performance of SCARD-optimal portfolios of the modeled companies are compared to those of SCAR-optimal and equally weighted portfolios. Out-of-sample SCAR and SCARD following both objectives are higher than those of the equally weighted reference portfolio. SCARD-optimal portfolios show lower cost of solvency capital and lower drawdown than their SCAR-optimal counterparts, but also lower returns. The differences in return outweigh those of the other components, resulting in the SCAR and SCARD of SCAR-optimal portfolios tending to be higher than those of SCARD-optimal portfolios. |
| Keywords: | Cost of Solvency Capital, Drawdown Risk, Lever- aged Investors, Portfolio Optimization, Solvency I |
| JEL: | C63 G11 G22 G28 G32 |
| Date: | 2025–10–07 |
| URL: | https://d.repec.org/n?u=RePEc:bsl:wpaper:2025/07 |
| By: | Sahab Zandi; Kamesh Korangi; Juan C. Moreno-Paredes; Mar\'ia \'Oskarsd\'ottir; Christophe Mues; Cristi\'an Bravo |
| Abstract: | Small and Medium-sized Enterprises (SMEs) are known to play a vital role in economic growth, employment, and innovation. However, they tend to face significant challenges in accessing credit due to limited financial histories, collateral constraints, and exposure to macroeconomic shocks. These challenges make an accurate credit risk assessment by lenders crucial, particularly since SMEs frequently operate within interconnected firm networks through which default risk can propagate. This paper presents and tests a novel approach for modelling the risk of SME credit, using a unique large data set of SME loans provided by a prominent financial institution. Specifically, our approach employs Graph Neural Networks to predict SME default using multilayer network data derived from common ownership and financial transactions between firms. We show that combining this information with traditional structured data not only improves application scoring performance, but also explicitly models contagion risk between companies. Further analysis shows how the directionality and intensity of these connections influence financial risk contagion, offering a deeper understanding of the underlying processes. Our findings highlight the predictive power of network data, as well as the role of supply chain networks in exposing SMEs to correlated default risk. |
| Date: | 2025–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2510.09407 |
| By: | Emil Bandoni; Carolina Fugazza |
| Abstract: | Medical expenditures increase sharply with age and can impose a significant finan- cial risk on the elderly, even in settings with universal health insurance. In particular, out-of-pocket medical spending remains highly skewed, with a small fraction of indi- viduals facing catastrophic costs. This paper develops a life-cycle model in which rare, idiosyncratic health shocks generate substantial out-of-pocket expenses late in life. The model demonstrates that accounting for these rare health disasters can explain the moderate risk-taking behavior observed among older investors, without invoking be- quest motives. These findings highlight the importance of tail medical risks in shaping late-life financial decisions. |
| Keywords: | life-cycle portfolio choice, disaster risk, beta distribution, out-of-pocket medical spending |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:cca:wpaper:748 |
| By: | Fengnan Deng; Anand N. Vidyashankar; Jeffrey F. Collamore |
| Abstract: | We obtain sharp large deviation estimates for exceedance probabilities in dependent triangular array threshold models with a diverging number of latent factors. The prefactors quantify how latent-factor dependence and tail geometry enter at leading order, yielding three regimes: Gaussian or exponential-power tails produce polylogarithmic refinements of the Bahadur-Rao $n^{-1/2}$ law; regularly varying tails yield index-driven polynomial scaling; and bounded-support (endpoint) cases lead to an $n^{-3/2}$ prefactor. We derive these results through Laplace-Olver asymptotics for exponential integrals and conditional Bahadur-Rao estimates for the triangular arrays. Using these estimates, we establish a Gibbs conditioning principle in total variation: conditioned on a large exceedance event, the default indicators become asymptotically i.i.d., and the loss-given-default distribution is exponentially tilted (with the boundary case handled by an endpoint analysis). As illustrations, we obtain second-order approximations for Value-at-Risk and Expected Shortfall, clarifying when portfolios operate in the genuine large-deviation regime. The results provide a transferable set of techniques-localization, curvature, and tilt identification-for sharp rare-event analysis in dependent threshold systems. |
| Date: | 2025–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2509.19151 |
| By: | Ohood Aldalbahi; Miryana Grigorova |
| Abstract: | We study randomly distorted Choquet integrals with respect to a capacity c on a measurable space ({\Omega}, F), where the capacity c is distorted by a G-measurable random distortion function (with G a sub-{\sigma}-algebra of F). We establish some fundamental properties, including the comonotonic additivity of these integrals under suitable assumptions on the underlying capacity space. We provide a representation result for comonotonic additive conditional risk measures which are monotone with respect to the first-order stochastic dominance relation (with respect to the capacity c) in terms of these randomly distorted Choquet integrals. We also present the case where the random distortion functions are concave. In this case, the G-randomly distorted Choquet integrals are characterised in terms of comonotonic additive conditional risk measures which are monotone with respect to the stop-loss stochastic dominance relation (with respect to the capacity c). We provide examples, extending some well-known risk measures in finance and insurance, such as the Value at Risk and the Average Value at Risk. |
| Date: | 2025–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2509.17555 |
| By: | Samir Saissi-Hassani (HEC Montréal) |
| Abstract: | La Valeur à Risque (VaR) demeure une mesure clé du risque de marché, notamment sous l’exigence Bâle du backtesting sur la VaR à 1%. Le backtesting standard évalue la couverture du modèle. Le backtesting comparatif mesure son économie. Ces deux approches sont essentielles et complémentaires, certes, mais différentes et parfois contradictoires. Effectivement, un modèle peut être désigné le meilleur économiquement, quoique non conforme réglementairement. Nous documenterons ces faits et approfondirons l’analyse des mécanismes reliés. D’autre part, la littérature actuelle du backtesting comparatif utiliserait inadéquatement le test DM. Lors des périodes de fortes violations groupées de la VaR, les fonctions de score produisent des valeurs extrêmes non indépendantes très asymétriques. La conclusion du test pourrait être invalide à cause d’un problème de stationnarité que la théorie suppose. Pour y remédier, le test DM est reconstruit à l’aide de fonctions de transformation appropriées. Il fournit ainsi des conclusions consistantes et statistiquement identiques, avec plusieurs combinaisons de fonctions de transformation et de fonctions de score distinctes.<p> Value at Risk (VaR) remains a key measure of market risk, notably under the Basel requirement for backtesting on VaR at 1%. Standard backtesting evaluates the model’s coverage. Comparative backtesting measures its economic efficiency. These two approaches are essential and complementary, yet different and sometimes contradictory. Indeed, a model may be deemed the best economically, although not regulatory compliant. We will document those facts and conduct a thorough analysis of the underlying mechanisms involved. Moreover, the way the current literature on comparative backtesting uses the DM test might be inadequate. During periods of heavy clustered VaR violations, score functions produce very asymmetric and non-independent extreme values. A problem of stationarity theoretically assumed could render the test’s conclusion erroneous. To address this, the DM test is rebuilt using suitable transformation functions. It thus provides consistent and statistically identical conclusions with several combinations of distinct transformation functions and score functions. |
| Keywords: | Value at Risk; market risk; Basel settlements; standard backtesting; comparative backtesting; score fonctions; identification fonctions; unconditional coverage; conditional coverage; transformation fo |
| JEL: | C22 C44 C46 C52 G21 G24 G28 G32 |
| Date: | 2025–10–07 |
| URL: | https://d.repec.org/n?u=RePEc:ris:crcrmw:021673 |
| By: | Fabio Cortes; Gonzalo Fernandez Dionis; Yiran Li; Ms. Silvia Ramirez; Xiaoxiao Zhang |
| Abstract: | This paper analyzes the rapid growth and evolving landscape of synthetic risk transfers (SRTs), a securitization tool increasingly used by banks to manage credit risk and optimize capital. Since 2016, over $1 trillion in assets have been synthetically securitized, with recent expansion driven by U.S. banks alongside established European issuers. SRTs enable banks to transfer credit risk on diverse loan pools to investors, facilitating capital relief and supporting additional lending. The paper reviews market trends, common SRT structures, and regulatory frameworks across major jurisdictions. We find that SRTs offer benefits such as enhanced risk management and capital efficiency, and that strengthened prudential requirements and a relatively small SRT market have, for now, contained financial stability risks. However, the rapid growth of SRTs and certain transaction complexities can increase vulnerabilities, including higher leverage in the financial system and exposure to rollover risks. The entry of risk-tolerant investors seeking compelling returns may also weaken credit standards or increase leverage. The paper highlights the importance of close supervisory monitoring, robust reporting, and disclosure to ensure risks are effectively transferred, financial system leverage is contained, and market discipline is maintained as the SRT market continues to expand. |
| Keywords: | Risk; securitization; banks; regulation; stability |
| Date: | 2025–10–03 |
| URL: | https://d.repec.org/n?u=RePEc:imf:imfwpa:2025/200 |
| By: | Yuna Heo (University of Basel - Faculty of Business and Economics; Swiss Finance Institute) |
| Abstract: | This study investigates the impact of cybersecurity risk on bank fragility. By utilizing a novel bank-specific indicator of cybersecurity, we find that an increase in cybersecurity risk raises the probability of bank default. The effect is larger for banks facing deposit withdrawal, but less pronounced for banks with ample liquidity buffers. Further we show that data security laws can help reduce the potential fragility in banking; nonetheless, the influence of cybersecurity risk remains significant. Our findings provide suggestive evidence that cybersecurity risk exacerbates financial instability, but implementing adaptation policies can strengthen resilience against possible cyberattacks. |
| Keywords: | cybersecurity, cyber risk, financial stability, distance-to-default, bank default probability, systemic risk, bank fragility, cyberattacks, data breaches |
| JEL: | G15 G32 G38 Q54 |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:chf:rpseri:rp2569 |
| By: | Christian Laudag\'e; Felix-Benedikt Liebrich |
| Abstract: | Motivated by recent work on monotone additive statistics and questions regarding optimal risk sharing for return-based risk measures, we investigate the existence, structure, and applications of Meyer risk measures. Those are monetary risk measures consistent with fractional stochastic orders suggested by Meyer (1977a, b) as refinement of second-order stochastic dominance (SSD). These so-called $v$-SD orders are based on a threshold utility function $v$. The test utilities defining the associated order are those at least as risk averse in absolute terms as $v$. The generality of $v$ allows to subsume SSD and other examples from the literature. The structure of risk measures respecting the $v$-SD order is clarified by two types of representations. The existence of nontrivial examples is more subtle: for many choices of $v$ outside the exponential (CARA) class, they do not exist. Additional properties like convexity or positive homogeneity further restrict admissible examples, even within the CARA class. We present impossibility theorems that demonstrate a deeper link between the axiomatic structure of monetary risk measures and SSD than previously acknowledged. The study concludes with two applications: portfolio optimisation under a Meyer risk measure as objective, and risk assessment of financial time series data. |
| Date: | 2025–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2509.24747 |
| By: | Xinqiao Xie; Jonathan Yu-Meng Li |
| Abstract: | Conditional risk minimization arises in high-stakes decisions where risk must be assessed in light of side information, such as stressed economic conditions, specific customer profiles, or other contextual covariates. Constructing reliable conditional distributions from limited data is notoriously difficult, motivating a series of optimal-transport-based proposals that address this uncertainty in a distributionally robust manner. Yet these approaches remain fragmented, each constrained by its own limitations: some rely on point estimates or restrictive structural assumptions, others apply only to narrow classes of risk measures, and their structural connections are unclear. We introduce a universal framework for distributionally robust conditional risk minimization, built on a novel union-ball formulation in optimal transport. This framework offers three key advantages: interpretability, by subsuming existing methods as special cases and revealing their deep structural links; tractability, by yielding convex reformulations for virtually all major risk functionals studied in the literature; and scalability, by supporting cutting-plane algorithms for large-scale conditional risk problems. Applications to portfolio optimization with rank-dependent expected utility highlight the practical effectiveness of the framework, with conditional models converging to optimal solutions where unconditional ones clearly do not. |
| Date: | 2025–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2509.23128 |
| By: | Sergio Bianchi; Daniele Angelini |
| Abstract: | We introduce a novel distribution-based estimator for the Hurst parameter of log-volatility, leveraging the Kolmogorov-Smirnov statistic to assess the scaling behavior of entire distributions rather than individual moments. To address the temporal dependence of financial volatility, we propose a random permutation procedure that effectively removes serial correlation while preserving marginal distributions, enabling the rigorous application of the KS framework to dependent data. We establish the asymptotic variance of the estimator, useful for inference and confidence interval construction. From a computational standpoint, we show that derivative-free optimization methods, particularly Brent's method and the Nelder-Mead simplex, achieve substantial efficiency gains relative to grid search while maintaining estimation accuracy. Empirical analysis of the CBOE VIX index and the 5-minute realized volatility of the S&P 500 reveals a statistically significant hierarchy of roughness, with implied volatility smoother than realized volatility. Both measures, however, exhibit Hurst exponents well below one-half, reinforcing the rough volatility paradigm and highlighting the open challenge of disentangling local roughness from long-memory effects in fractional modeling. |
| Date: | 2025–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2509.20015 |
| By: | Zofia Bracha; Pawe{\l} Sakowski; Jakub Micha\'nk\'ow |
| Abstract: | This paper explores the application of deep Q-learning to hedging at-the-money options on the S\&P~500 index. We develop an agent based on the Twin Delayed Deep Deterministic Policy Gradient (TD3) algorithm, trained to simulate hedging decisions without making explicit model assumptions on price dynamics. The agent was trained on historical intraday prices of S\&P~500 call options across years 2004--2024, using a single time series of six predictor variables: option price, underlying asset price, moneyness, time to maturity, realized volatility, and current hedge position. A walk-forward procedure was applied for training, which led to nearly 17~years of out-of-sample evaluation. The performance of the deep reinforcement learning (DRL) agent is benchmarked against the Black--Scholes delta-hedging strategy over the same period. We assess both approaches using metrics such as annualized return, volatility, information ratio, and Sharpe ratio. To test the models' adaptability, we performed simulations across varying market conditions and added constraints such as transaction costs and risk-awareness penalties. Our results show that the DRL agent can outperform traditional hedging methods, particularly in volatile or high-cost environments, highlighting its robustness and flexibility in practical trading contexts. While the agent consistently outperforms delta-hedging, its performance deteriorates when the risk-awareness parameter is higher. We also observed that the longer the time interval used for volatility estimation, the more stable the results. |
| Date: | 2025–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2510.09247 |
| By: | Corina Boar; Denis Gorea; Virgiliu Midrigan |
| Abstract: | We use firm-level data to document that private businesses experience large fluctuations in their profit shares. These are due to large, fat-tailed and transitory changes in output that are not fully accompanied by changes in their inputs. We interpret this evidence using a model of entrepreneurial dynamics. Because firms can limit their exposure to risk by operating at a smaller scale, our model predicts large macroeconomic losses from uninsurable business risk, much larger than those stemming from credit constraints. While self-financing allows entrepreneurs to quickly overcome credit constraints, even wealthy entrepreneurs remain considerably exposed to risk. |
| Keywords: | entrepreneurship, risk, credit constraints, misallocation |
| JEL: | E2 E44 G32 |
| Date: | 2025–10 |
| URL: | https://d.repec.org/n?u=RePEc:bis:biswps:1300 |
| By: | Ta-Chung Chi (Kevin); Ting-Han Fan (Kevin); Raffaele M. Ghigliazza (Kevin); Domenico Giannone (Kevin); Zixuan (Kevin); Wang |
| Abstract: | We forecast the full conditional distribution of macroeconomic outcomes by systematically integrating three key principles: using high-dimensional data with appropriate regularization, adopting rigorous out-of-sample validation procedures, and incorporating nonlinearities. By exploiting the rich information embedded in a large set of macroeconomic and financial predictors, we produce accurate predictions of the entire profile of macroeconomic risk in real time. Our findings show that regularization via shrinkage is essential to control model complexity, while introducing nonlinearities yields limited improvements in predictive accuracy. Out-of-sample validation plays a critical role in selecting model architecture and preventing overfitting. |
| Date: | 2025–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2510.11008 |
| By: | Rohan Shenoy; Peter Kempthorne |
| Abstract: | This paper explores the concept of random-time subordination in modelling stock-price dynamics, and We first present results on the Laplace distribution as a Gaussian variance-mixture, in particular a more efficient volatility estimation procedure through the absolute moments. We generalise the Laplace model to characterise the powerful variance gamma model of Madan et al. as a Gamma time-subordinated Brownian motion to price European call options via an Esscher transform method. We find that the Variance Gamma model is able to empirically explain excess kurtosis found in log-returns data, rejecting a Black-Scholes assumption in a hypothesis test. |
| Date: | 2025–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2510.14093 |
| By: | J\'er\^ome Lelong (LJK); V\'eronique Maume-Deschamps; William Thevenot |
| Abstract: | We study a continuous-time portfolio optimization problem under an explicit constraint on the Deviation Conditional Value-at-Risk (DCVaR), defined as the difference between the CVaR and the expected terminal wealth. While the mean-CVaR framework has been widely explored, its time-inconsistency complicates the use of dynamic programming. We follow the martingale approach in a complete market setting, as in Gao et al. [4], and extend it by retaining an explicit DCVaR constraint in the problem formulation. The optimal terminal wealth is obtained by solving a convex constrained minimization problem. This leads to a tractable and interpretable characterization of the optimal strategy. |
| Date: | 2025–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2509.26009 |