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on Risk Management |
| By: | Chunle Huang |
| Abstract: | In this note, we study distortion risk measures of step-weighted distribution. |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2607.09132 |
| By: | Brunella Bruno (Bocconi University); Francesco Corielli (Bocconi University); Imma Marino (University of Naples Federico II and CSEF); Giacomo Nocera (Audencia Business School) |
| Abstract: | We examine when a regulatory measure of bank asset risk, the ratio of risk-weighted assets to total assets (RWATA), aligns with a market-based measure of risk, namely the volatility of bank assets estimated using option-pricing techniques. We argue that the informational content of RWATA is conditional on the framework used to generate risk weights. Using a unique hand-collected dataset on the adoption and scope of internal ratings-based (IRB) models, we show that RWATA is unrelated to market-based asset risk on average, but becomes significantly associated with asset volatility among banks that use internal models. The relationship strengthens with the intensity of IRB adoption, particularly when advanced internal models are applied to corporate exposures, and persists among relatively weakly capitalized banks and during periods of financial stress. |
| Keywords: | Bank risk, Asset volatility, Capital regulation, Internal ratings. |
| JEL: | G20 G21 G28 G32 |
| Date: | 2026–07–25 |
| URL: | https://d.repec.org/n?u=RePEc:sef:csefwp:791 |
| By: | Riccardo Alberti; Sven Karbach |
| Abstract: | We study the variance-optimal hedging of European contingent claims written on forwards. We assume that the dynamics of the underlying forward curves follow a Heath--Jarrow--Morton--Musiela stochastic partial differential equation modulated by an infinite-rank stochastic covariance component. The variance-optimal hedge is then given by the Galtchouk--Kunita--Watanabe projection with respect to some covariance-norm quotient generated by the forward curve martingale. We show density of finite-maturity and delivery-window strategies, convergence of spectral finite-rank hedge projections and an exact decomposition of the quadratic hedging error into bucket, rank and residual risk components. In enlarged filtrations, the residual risk is a stochastic-volatility floor for claims loading on non-traded covariance noise. We illustrate the hedging framework in affine stochastic covariance and multiplicative HJMM models, and give a concrete example of the decomposition in a CIR stochastic covariance model. |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2606.28891 |
| By: | Brunella Bruno, Francesco Corielli, Immacolata Marino, Giacomo Nocera |
| Abstract: | We examine when a regulatory measure of bank asset risk, the ratio of risk-weighted assets to total assets (RWATA), aligns with a market-based measure of risk, namely the volatility of bank assets estimated using option-pricing techniques. We argue that the informational content of RWATA is conditional on the framework used to generate risk weights. Using a unique hand-collected dataset on the adoption and scope of internal ratings-based (IRB) models, we show that RWATA is unrelated to market-based asset risk on average, but becomes significantly associated with asset volatility among banks that use internal models. The relationship strengthens with the intensity of IRB adoption, particularly when advanced internal models are applied to corporate exposures, and persists among relatively weakly capitalized banks and during periods of financial stress. |
| Keywords: | Asset volatility, Capital regulation, Internal ratings. |
| JEL: | G20 G21 G28 G32 |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:baf:cbafwp:cbafwp26281 |
| By: | Repullo, Rafael |
| Abstract: | This paper presents a model of the interaction between a bank and a supervisor. The bank privately chooses the risk of its investment portfolio and the supervisor collects nonverifiable information on the future solvency of the bank and, based on of this information, may decide on its early liquidation. The paper characterizes the liquidation decision of the supervisor and the risk-taking decision of the bank. In line with recent empirical literature, the paper shows that supervision is effective in ameliorating the bank's risk-shifting incentives, and that a tougher supervisor leads to lower risk-taking. It also shows that higher noise in the supervisory information may be conducive to lower risk-taking, but that it always reduces welfare. |
| Keywords: | Bank risk taking; Bank supervision; Bank regulation; Capital requirements; Deposit insurance; Bank resolution; Bank liquidation |
| JEL: | G21 G28 D02 |
| Date: | 2025–03 |
| URL: | https://d.repec.org/n?u=RePEc:cpr:ceprdp:20012 |
| By: | Wing Fung Chong |
| Abstract: | This paper studies how a risk holder should combine self-protection and self-insurance when market insurance is absent. In a Bernoulli loss model, self-protection reduces the residual loss probability, while self-insurance reduces the residual loss severity. The risk holder evaluates residual risk using either Value-at-Risk or Tail Value-at-Risk and incurs a joint risk-reduction cost that allows technological interaction between the two activities. We show that Value-at-Risk leads to a threshold-driven solution that the optimal strategy is either no risk reduction, pure self-protection, or pure self-insurance. By contrast, Tail Value-at-Risk creates a direct interaction between residual frequency and residual severity, making the problem non-convex even in the Bernoulli setting. We solve it using an isoquant geometry method based on the marginal-balance curves for self-protection and self-insurance. The analysis identifies when optimal strategies lie on boundaries, extreme constrained candidates, touching components, or crossing components, and shows how the confidence level and the cost technology determine whether self-protection and self-insurance behave as substitutes or complements. |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2606.30363 |
| By: | Alfaro, Laura; Bahaj, Saleem; Czech, Robert; Hazell, Jonathon; Neamtu, Ioana |
| Abstract: | This paper studies a form of liquidity risk that we call Liquidity After Solvency Hedging or "LASH" risk. Financial institutions take LASH risk when they hedge against solvency risk, using strategies that require liquidity when the solvency of the institution improves. We focus on LASH risk relating to interest rate movements. Our framework implies that institutions with longer-duration liabilities than assets — e.g. pension funds and insurers — take more LASH risk as interest rates fall. Using UK regulatory data from 2019-22 on the universe of sterling repo and swap transactions, we measure, in real time and at the institution level, LASH risk for the non-bank sector. We find that at the peak level of LASH risk, a 100bps increase in interest rates would have led to liquidity needs close to the cash holdings of the pension fund and insurance sector. Using a cross-sectional identification strategy, we find that low interest rates caused increases in LASH risk. We then find that the pre-crisis LASH risk of non-banks predicts their bond sales during the 2022 UK bond market crisis, contributing to the yield spike in the market. |
| Keywords: | Liquidity; Monetary policy; Hedging |
| JEL: | E44 F30 G10 G22 G23 |
| Date: | 2025–04 |
| URL: | https://d.repec.org/n?u=RePEc:cpr:ceprdp:20158 |
| By: | Tae-Hwy Lee (Department of Economics, University of California Riverside); Dingli Wang (University of California, Riverside) |
| Abstract: | Risk managers often work with a fitted forecasting model they cannot replace even when its tail forecasts need adjustment. We propose a median-anchored rule that multiplies the distances from the fitted median to Value-at-Risk (VaR) and Expected Shortfall (ES) by a common positive multiplier. The rule preserves VaR--ES ordering, and minimizing VaR check loss gives a closed-form weighted-quantile estimator. We establish consistency, give an asymptotic distribution under high-level conditions accounting for baseline estimation, and derive a VaR coverage-error bound at the forecast origin. When the same multiplier correctly adjusts both VaR and ES, the adjusted pair has lower conditional zero-homogeneous Fissler--Ziegel (FZ0) risk at that origin. Monte Carlo experiments examine this condition and several forms of misspecification. In rolling S&P~500 forecasts the adjustment lowers FZ0 loss in all four GARCH cells, each pairwise significant, with the largest and most robust gain, 10.4%, for Gaussian GARCH at the 1% tail; the 5% gains do not survive the most conservative family-wise adjustments. A quantile-regression baseline marks the boundary: when the fitted tail is already flexible, one multiplier adds little. Filtered historical simulation quantifies what standardized residuals and conditional scales add when available. |
| Keywords: | Backtesting; Elicitability; Fissler--Ziegel Score; Forecast Evaluation; Model Risk; Quantile Regression |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:ucr:wpaper:202604 |
| By: | Fr\'ed\'eric Godin |
| Abstract: | The deep hedging framework of Buehler et al. (2019) trains a neural network policy, via Monte Carlo simulation of price paths and stochastic gradient descent, to minimize a risk measure applied to the terminal hedging error. In a recent stream of papers, my coauthors and I have referred to this technique as reinforcement learning (RL), a characterization that referees on several submissions have challenged on two grounds, among others: first, that because feedback is generated only at the terminal date, with no intermediate reward signal, the method cannot constitute genuine RL; and second, that the absence of a value function, a Bellman equation, temporal-difference (TD) learning, and an explicit exploration mechanism disqualifies the method from the RL category altogether, so that it should instead be labeled a neural-network method for stochastic optimal control. I argue that both objections rest on an unduly narrow, TD-centric reading of what constitutes RL. Once RL is understood, as it is in the standard references of the field, to include Monte Carlo policy-gradient methods and direct (actor-only) policy search as first-class members, the deep hedging algorithm of Buehler et al. (2019) falls squarely within the RL umbrella. |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2607.13353 |
| By: | Nicola Bartolini; Silvia Romagnoli; Amia Santini |
| Abstract: | Power Purchase Agreements (PPAs) are bilateral over-the-counter contracts central to renewable energy financing. While their capacity to stabilise revenues and hedge price risk is well recognised, their OTC structure exposes both parties to counterparty credit risk. This is a dimension yet to be explored in the literature, particularly given the dual price and volumetric uncertainty inherent in renewable sources. This paper develops a framework for the pricing and valuation of wind power PPAs and for quantifying this risk through Credit Valuation Adjustment (CVA) and Debit Valuation Adjustment (DVA). We model the joint dynamics of electricity spot prices and renewable output, incorporate default probabilities, and compute valuation adjustments that reflect the fair value of bilateral credit risk. The framework provides market participants with a transparent metric for PPA valuation under counterparty risk. While initiatives such as the European Investment Bank's pilot guarantee scheme aim to mitigate credit risk for certain offtakers, such interventions do not cover all PPA transactions. Rigorous internal credit risk assessment therefore remains indispensable for lenders, producers, and offtakers alike. |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2607.04781 |
| By: | Pereira, Ana; Tereanu, Eugen; Minnella, Enrico |
| Abstract: | This paper develops an agent-based framework (DeTail) to assess the state-contingent tail effects of releasable macroprudential capital buffers. The model features heterogeneous firms, households, and banks, and a single central bank, all interacting in a fully integrated, stock-flow consistent framework which generates endogenous credit cycles. Using this approach, we evaluate how time-varying capital requirements affect the time-varying distributions of credit growth, firm and household default rates, and bank losses along the credit cycle. Policy experiments show that releasing capital buffers during economic downturns preserves credit supply by improving risky (lower-tail) credit outcomes, reduces both household and firm defaults, and supports macro-financial resilience by limiting tail bank losses. At the same time, capital buffer accumulation during upturns imposes minimal costs and does not significantly constrain lending. These findings support the active use of releasable buffers to mitigate systemic risk and smooth credit cycles without weakening the banking system. JEL Classification: C63, E44, E58, G28 |
| Keywords: | agent-based modelling, and state-dependent effects, credit cycles, macro-financial linkages, macroprudential policy |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:ecb:ecbwps:20263257 |
| By: | Poghosyan, Armine |
| Keywords: | Agricultural Finance |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:ags:aaea26:404882 |
| By: | Mark Whitmeyer |
| Abstract: | We prove that every mean-zero probability law on the real line is the law of X-Y for some identically distributed real-valued random variables X and Y. |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2607.05460 |
| By: | Gopinath, Gita; Meyer, Josefin; Reinhart, Carmen; Trebesch, Christoph |
| Abstract: | Theory suggests that corporate and sovereign bonds are fundamentally different, also because sovereign debt has no bankruptcy mechanism and is hard to enforce. We show empirically that the two assets are more similar than you think, at least when it comes to high-yield bonds over the past 20 years. We use rich new data to compare high-yield US corporate (“junk†) bonds to high-yield emerging market sovereign bonds 2002-2021. Investor experiences in these two asset classes were surprisingly aligned, with (i) similar average excess returns, (ii) similar average risk-return patterns (Sharpe ratios), (iii) similar default frequency, and (iv) comparable haircuts. A notable difference is that the average default duration is higher for sovereigns. Moreover, the two markets co-move differently with domestic and global factors. US “junk†bond yields are more closely linked to US market conditions such as US stock returns, US stock price volatility (VIX), or US monetary policy. |
| Keywords: | Chapter 11; Crisis resolution |
| JEL: | F3 G1 F4 |
| Date: | 2025–04 |
| URL: | https://d.repec.org/n?u=RePEc:cpr:ceprdp:20100 |
| By: | Daniele Angelini |
| Abstract: | Testing self-similarity in fractional processes from a single observed trajectory is difficult under long-range dependence, because the associated Kolmogorov--Smirnov (KS) statistic undergoes a phase transition when $H>1/2$. In this regime, the classical limit collapses to a non-functional absolute Gaussian law and finite-sample convergence becomes severely distorted. This paper introduces a regime-adaptive KS/GL--KS framework based on the discrete Gr\"{u}nwald--Letnikov (GL) fractional derivative. The GL filter removes the low-frequency long-memory singularity while preserving the finite-dimensional $H$-self-similarity needed for distributional identification. We derive the filtered empirical-process limit, prove consistency and local asymptotic behavior of the resulting Hurst estimator, and validate the method through Monte Carlo simulations. Financial applications to realized volatility and equity index prices show how the procedure detects rough volatility and persistent, anti-persistent, or efficient market states. |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2606.27932 |
| By: | Hochmuth, Brigitte; Merz, Monika; Prettenthaler, Fabian |
| Abstract: | This paper studies how individual risk attitudes shape occupational choice and wealth accumulation. Using self-reported individual risk preferences from the German Socioeconomic Panel (GSOEP), we estimate that an increase in risk tolerance raises the probability of a worker transitioning to self-employment. We also develop a life-cycle model of occupational choice with Epstein-Zin preferences and heterogeneous risk attitudes to study how risk aversion interacts with entrepreneurial ability and wealth in determining entry into self-employment and its aggregate implications. Counterfactual simulations show that increasing business risk reduces entry but improves selection by entrepreneurial skills. In contrast, Germany’s “1-Euro GmbH†reform of 2008 weakened the role of risk tolerance for entry and increased participation by more risk-averse individuals. |
| Keywords: | Recursive utility |
| JEL: | E21 E24 J24 |
| Date: | 2025–05 |
| URL: | https://d.repec.org/n?u=RePEc:cpr:ceprdp:20286 |