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on Risk Management |
| By: | Chari, Anusha; Dilts Stedman, Karlye; Lundblad, Christian |
| Abstract: | This paper defines risk-on risk-off (RORO), an elusive terminology in pervasive use, as the variation in global investor risk aversion. Our high-frequency RORO index captures time-varying investor risk appetite across multiple dimensions: advanced economy credit risk, equity market volatility, funding conditions, and currency dynamics. The index exhibits risk-off skewness and pronounced fat tails, suggesting its amplifying potential for extreme, destabilizing events. Compared with the conventional VIX measure, the RORO index reflects the multifaceted nature of risk, underscoring the diverse provenance of investor risk sentiment. Practical applications of the RORO index highlight its significance for international portfolio reallocation and return predictability. |
| Keywords: | Risk-on Risk-off; Global investor risk aversion; Extreme events; Tail risk; Return predictability |
| JEL: | F21 F36 F65 G11 G12 G15 G23 |
| Date: | 2025–12 |
| URL: | https://d.repec.org/n?u=RePEc:cpr:ceprdp:20932 |
| By: | Ellis, Cameron M.; Ellul, Andrew; Jotikasthira, Chotibhak; Xu, Jianren |
| Abstract: | We study the causal impact of enterprise-wide risk management (ERM) — designed to move firms away from a "siloed" structure — on product decisions and consumer surplus. Exploiting the staggered rollout of an industry-wide ERM mandate in the insurance sector, we analyze life insurers’ offerings of annuities, which now account for nearly 70% of their premium revenues. We find that insurers respond by reducing risky guarantees, raising fees on the riskiest products, and shifting from traditional variable annuities toward index-linked products that provide natural hedges. To examine mechanisms and welfare outcomes, we develop a structural model that links consumer demand with multi-product supply. The ERM mandate imposes regulatory costs and corrects firms’ misperceptions about guarantee risk and cross-product risk interactions. Higher marginal costs for risky guarantees raise equilibrium prices and decrease their offerings, leading to substantial losses in consumer surplus. Overall, ERM reshapes insurers’ product strategies and risk exposures, enhancing financial stability but at a cost to consumers. |
| JEL: | G22 G28 G32 G11 |
| Date: | 2025–12 |
| URL: | https://d.repec.org/n?u=RePEc:cpr:ceprdp:20882 |
| By: | Shujie Li (Paderborn University) |
| Abstract: | This paper aims to compare the performance of traditional GARCH-type models and an LSTM-based approach for forecasting Value at Risk (VaR) and Expected Shortfall (ES) under different symmetric and skewed distributions. To assess model performance, eight stock indices from diverse international markets are analyzed. The models are evaluated using three backtesting approaches and a model selection criterion, the Weighted Absolute Deviation (WAD). The results indicate that the selected indices exhibit heavy tails and asymmetry. In general, the results obtained under skewed distributions generally outperform those obtained under symmetric distributions. In most cases, the LSTM model is selected as the top performing model. However, some models from the EGARCH family remain strong competitors, especially under the asymmetry distributions, and might be preferred for certain indices. |
| Keywords: | GARCH-type models, EGF, LSTM, VaR, ES, Backtesting |
| JEL: | C45 G52 |
| Date: | 2026–03 |
| URL: | https://d.repec.org/n?u=RePEc:pdn:ciepap:173 |
| By: | Matthew Francis Dixon |
| Abstract: | Agentic AI systems create model risk because uncertain beliefs are coupled to autonomous actions. This paper develops a mathematical framework for quantifying agentic AI risk by representing the system as a partially observed Markov decision process with latent states, Bayesian belief updates, control-dependent losses, and tail-risk functionals. The main methodological contribution is to treat a large language model as an uncertain semantic observation model: the LLM maps high-dimensional evidence into a probability vector over latent regimes, while a Bayesian filter imposes temporal coherence and produces auditable posterior beliefs. The resulting framework separates uncertainty quantification from risk measurement. Uncertainty is represented by posterior entropy, belief drift, and calibration error; risk is represented by the distribution of losses induced by decisions taken under those beliefs. The paper connects this construction to model risk management, coherent risk measures, Bayesian filtering, POMDP theory, robust control, and quantitative portfolio risk. An empirical case study using adjusted daily equity returns from Massive.com illustrates how LLM-inferred belief states can be combined with Bayesian filtering to produce regime probabilities, uncertainty diagnostics, calibration statistics, and VaR/CVaR-style risk measures. The framework is intended as a rigorous foundation for validating agentic AI in financial and other regulated decision environments. |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2606.15473 |
| By: | Yuyu Chen; Liyuan Lin; Ruodu Wang |
| Abstract: | Value-at-Risk (VaR) is a standard regulatory risk measure, and its failure of subadditivity is well known. Much less appreciated is that for sufficiently heavy-tailed losses, VaR can be superadditive uniformly across all probability levels, a phenomenon strictly stronger than the asymptotic superadditivity studied in extreme value theory. We call this property universal VaR superadditivity (UVS). We study UVS and its stronger weighted version (WUVS) as properties of random vectors rather than of marginal distributions. This perspective unifies and extends a recent line of work on iid infinite-mean models. UVS, except for trivial cases, imposes an infinite-mean structure. We establish preservation properties of UVS and WUVS under increasing and convex transformations, weak convergence, and certain distributional mixtures, and use these tools to prove UVS and WUVS for non-identically distributed risks in several large families including completely subscalable, super-Cauchy, and inverted subadditive risks, extending results previously available only in the iid case. In many results, we also establish strict versions of UVS and WUVS, which lead to stronger decision-theoretic implications. As a consequence, for any portfolio satisfying WUVS, every distortion risk measure is superadditive, so an optimal allocation concentrates on a single asset, and diversification is never beneficial. |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2606.22884 |
| By: | Miguel Jiménez; David Sarasa Flores; Alfonso Ugarte |
| Abstract: | This paper introduces a novel measure of Structural Geopolitical Risk (SGR), designed to capture the long-run conditions that shape the likelihood of geopolitical tensions, conflicts, and fragmentation. This paper introduces a novel measure of Structural Geopolitical Risk (SGR), designed to capture the long-run conditions that shape the likelihood of geopolitical tensions, conflicts, and fragmentation. |
| Keywords: | Defense expenditure, Defense expenditure, Local projections, Local projections, Geopolitical risk, Geopolitical risk, Global, Global, Macroeconomic Analysis, Macroeconomic Analysis, Geostrategy, Geostrategy, Country Risk, Country Risk, Working Paper, Working Paper |
| JEL: | F51 F52 D74 P16 C33 C43 |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:bbv:wpaper:2608 |
| By: | Jordi Llorens-Terrazas; Mika Meitz |
| Abstract: | We propose a flexible framework for modeling the predictive distributions of nonlinear, possibly multivariate time series. Our approach expresses a general predictive distribution in an appropriate generative representation that is based on a folklore result from measure theoretic probability. This representation provides a direct simulation-based approximation to the predictive distribution, enabling straightforward computation of forecasts for the conditional mean and variance, fan charts, value at risk, expected shortfall, joint tail risks, and other quantities of interest. We estimate this generative representation using a version of conditional generative adversarial networks and provide a formal statistical analysis of estimation under weak temporal dependence. Specifically, estimation is expressed as a particular minimax problem and we establish consistency of its approximate solutions in Hausdorff distance. The empirical relevance of the approach is illustrated using applications to equity returns, realized variance, and realized covariances. The proposed method is also computationally manageable, with estimation in our applications taking approximately one minute on a standard laptop. |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2606.16773 |
| By: | boughabi, houssam |
| Abstract: | This paper develops a volatility-based framework for crude oil pricing by examining the interaction between financial market volatility and commodity-specific risk. The spot price of oil is modeled as a linear combination of stock market and commodity volatilities, allowing the derivation of equilibrium conditions linking financial and commodity markets. Particular attention is given to the dynamics of the functions (A(t, T)) and (B(t, T)), whose evolution reveals a common trajectory consistent with equilibrium behavior between oil price volatility and underlying commodity risk. The analysis highlights the role of volatility transmission mechanisms in shaping commodity prices and provides a novel perspective on the connection between financial market fluctuations and real economic fundamentals. The findings contribute to the literature on commodity pricing by offering a volatility-driven approach that integrates market expectations and risk dynamics into the valuation of crude oil. |
| Keywords: | Volatility Models, Financial Equilibrium, Long Memory, Commodity Risk |
| JEL: | C22 G13 Q41 |
| Date: | 2025–12–30 |
| URL: | https://d.repec.org/n?u=RePEc:pra:mprapa:129471 |
| By: | Busch, Christopher; Madera, Rocio |
| Abstract: | We introduce a tractable method built around an incomplete-markets model to assess the value of public insurance against permanent idiosyncratic income risk. Our approach translates statistical differences between gross and disposable incomes into a welfare-equivalent variance adjustment. Under homoskedastic Gaussian shocks, the variance ratio of permanent shocks to gross and disposable incomes provides a sufficient statistic for the size of insurance. More generally, with cyclical non-Gaussian shocks, public insurance amounts to a variance reduction by 38-49% in Sweden (tax registers) and 24-31% in the United States (PSID), depending on risk attitudes. Consumption-based measures in the PSID confirm our model-based measure. |
| Keywords: | Tax and transfer system; Partial insurance; Incomplete markets |
| JEL: | D31 D52 E21 |
| Date: | 2026–02 |
| URL: | https://d.repec.org/n?u=RePEc:cpr:ceprdp:21129 |
| By: | Rama Siva Sarwari Mallela; Manuele Leonelli |
| Abstract: | Cryptocurrency markets are prone to violent, synchronised drawdowns, challenging the claim that a basket of crypto-assets offers genuine internal diversification. Because standard covariance-based metrics fail to capture asymptotic tail dependence, they systematically understate systemic risk and overstate diversification benefits precisely when markets crash. This study maps the conditional dependence structure of the cryptocurrency market directly in the joint tails, isolating direct extremal linkages from those mediated by the rest of the system. We analyse the daily returns of the thirteen largest cryptocurrencies over a sequence of 89 overlapping windows spanning late 2021 to 2025. We apply dynamic H\"usler-Reiss graphical models of extremes, estimated separately for joint crashes and rallies, and benchmark them against a Gaussian graphical model of ordinary co-movement. The results reveal a near-complete and stable lower-tail graph, an upper tail that thins over time to re-form sectoral structures, and the dissolution of ordinary token categories into a single block anchored by a Bitcoin-Ethereum core. These findings imply that intra-crypto diversification fails on the downside, standard risk models underestimate market-wide crash probabilities by roughly eight-fold, and dynamic extremal graphs offer a superior tool for systemic risk monitoring. |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2606.16840 |
| By: | Fuster, Andreas; Paligorova, Teodora; Vickery, James |
| Abstract: | We use bond-level data to study how US banks managed securities portfolio risk during the 2022–23 interest rate surge. Rising yields lengthened the effective duration of callable bonds (especially agency MBS) and triggered deposit outflows. Exposed banks reduced both the volume and duration of bond purchases, but rarely sold existing bonds and did not expand qualified accounting hedges. Two frictions constrain adjustment: first, banks systematically avoid realizing losses, especially banks that exclude unrealized losses from regulatory capital. Second, hedging capacity is limited by fixed costs and callable bond complexity. Instead, banks reduced measured exposure by classifying high-risk bonds as held-to-maturity. |
| Keywords: | Banks; Securities; Interest rate risk; Trading; Hedging; Capital regulation |
| JEL: | G11 G21 G23 G28 |
| Date: | 2026–01 |
| URL: | https://d.repec.org/n?u=RePEc:cpr:ceprdp:21036 |
| By: | Takayuki Sakuma |
| Abstract: | This paper develops a robust hedging valuation adjustment (HVA) measure for dynamic hedging. Simulated rebalancing and maturity-unwind trades generate a loss distribution for each no-trade-band rule, and we define robust HVA as the worst-case expected loss over a relative-entropy neighborhood of that distribution. Because band width affects turnover, the same relative-entropy radius applied to different bands can imply different levels of demand-liquidity stress. We distinguish a fixed-radius convention from a fixed benchmark-stress convention and show that wider no-trade bands lower rebalancing costs but raise hedge-error risk. |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2606.26731 |
| By: | Jansen, Kristy; Klingler, Sven; Ranaldo, Angelo; Duijm, Patty |
| Abstract: | Pension funds use interest rate swaps to hedge the interest rate risk arising from their liabilities. Analyzing regulatory data on Dutch pension funds, we show that pension funds with worse funding ratios, indicating greater fragility, use swaps more aggressively. These swap positions expose pension funds to the risk of margin calls, which can exceed 6% of their total assets, when interest rates rise. Pension funds respond to realized margin calls by selling safe government bonds with medium-term maturities. This procyclical selling behavior adversely affects the prices of the sold bonds and thereby exposes pension funds to market liquidity risk. |
| Keywords: | Pension funds; Fixed income; interest rate swaps; Liability Hedging; Liquidity risk; Price impact |
| JEL: | E43 G12 G18 |
| Date: | 2026–01 |
| URL: | https://d.repec.org/n?u=RePEc:cpr:ceprdp:21095 |
| By: | Jagdish Gnawali; Abootaleb Shirvani; Dilmi C. W. Hettiachchi-Halpe-Kankanamalage; W. Brent Lindquist; Svetlozar T. Rachev; Frank J. Fabozzi |
| Abstract: | Classical option pricing models, such as Bachelier and Black--Scholes--Merton, postulate symmetric Brownian diffusion, which limits their capacity to reflect empirical phenomena including return skewness, heavy tails, and volatility asymmetry. This paper develops an innovative extension: the Geometric Asymmetric Brownian Motion (GABM), unifying asymmetric Brownian motion and random walk methodologies within the Bachelier--Black--Scholes--Merton framework. The approach harnesses the Cherny--Shiryaev--Yor invariance principle (CSYIP) to define asymmetric random walk integrals, where local time at the origin generates skewness and state-dependent risk. Closed-form option pricing formulas are derived, and a discrete-time binomial tree algorithm is constructed and shown to converge rigorously to the GABM limit. By incorporating a smoothed functional form based on the normal inverse Gaussian distribution, the model allows for flexible, state-dependent volatility calibration. Numerical experiments demonstrate the resulting option price and implied volatility surfaces, highlighting the framework's enhanced ability to capture persistent market asymmetry and complex risk behaviors observed in empirical data. |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2606.22293 |
| By: | Matthew B. Canzoneri; Behzad T. Diba; Luca Guerrieri; Arsenii Mishin |
| Abstract: | In a model with endogenous risk-taking, deposit insurance and limited liability may lead banks to make risky loans that are socially inefficient. Capital requirements can prevent excessive risk-taking at the cost of reducing liquidity-producing bank deposits. A policy that sets capital requirements just high enough to prevent excessive risktaking will move capital requirements pro-, counter-, or a-cyclically depending on the shock source. However, such a policy requires full knowledge of all the shocks hitting the economy and is not implementable. Simple rules that respond to cyclical conditions—in line with Basel III guidance—perform poorly, whereas a small static capital buffer can do much better. |
| Keywords: | banks; capital requirements; endogenous risk-taking; crises |
| JEL: | C54 E13 G21 |
| Date: | 2026–06–22 |
| URL: | https://d.repec.org/n?u=RePEc:fip:fedgfe:103442 |
| By: | Andersen, Torben M; Bhattacharya, Joydeep; Wang, Min |
| Abstract: | This study compares public social insurance and consumer bankruptcy in a life-cycle model. Without moral hazard, public insurance dominates by providing superior consumption smoothing. However, with moral hazard, bankruptcy protection becomes optimal. Its exemption levels, priced into competitive credit contracts, internalize incentive distortions and can Pareto dominate public insurance. The two policies are strategic substitutes, offering little added benefit when combined. The key trade-off is between public insurance's better risk-sharing and bankruptcy's superior management of incentive problems. |
| Keywords: | Endogenous borrowing constraints |
| Date: | 2025–12 |
| URL: | https://d.repec.org/n?u=RePEc:cpr:ceprdp:20893 |
| By: | Christian Laudag\'e |
| Abstract: | Monetary risk measures quantify the risk of uncertain monetary payoffs (or losses), whereas in time series analysis risk is typically assessed using logarithmic returns. Return risk measures (RRMs) provide an axiomatic foundation for this latter approach, which relies crucially on the positive cone of the space of essentially bounded random variables. We extend RRMs to general ordered vector spaces and characterize positive homogeneity via the geometric epigraph. To investigate geometric convexity and establish connections with monetary risk measures, we specialize the domain to AM-algebras, encompassing Euclidean spaces and spaces of multidimensional essentially bounded random variables. The latter is novel in the context of RRMs and leads to the new classes of systemic and vector-valued RRMs. We establish results on finiteness, continuity, separability, as well as dual and aggregation-based representations. |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2606.26031 |
| By: | Menkveld, Albert J. |
| Abstract: | On average, the squared VIX exceeds realized variance. This implies that investors pay a premium to hold variance risk. But, why *pay* for risk? And, why does the premium correlate with volume? In Grossman-Miller type inelastic markets, investors hold variance risk to hedge against liquidity shocks, because these shocks cause price pressures that add to realized variance. Therefore, a positive variance risk premium must emerge in equilibrium. This result is developed formally, and the model is calibrated to match empirical patterns in the variance risk premium and trading volume around eleven crises between 1993 and 2025. |
| Keywords: | Vix; Liquidity; Cboe vix |
| JEL: | G12 G13 |
| Date: | 2025–11 |
| URL: | https://d.repec.org/n?u=RePEc:cpr:ceprdp:20834 |
| By: | Appelbaum, Elie |
| Abstract: | This paper develops a theoretical model of decision-making under risk in which the agent is a union of individuals with heterogeneous attitudes toward risk. The risk attitude governing the joint decision is endogenously determined as a compromise between individuals' innate preferences, with deviations generating costs. The chosen risk attitude affects the optimal portfolio and, therefore, the risk premium associated with exposure to uncertainty. The analysis shows that the optimal compromise equates the marginal increase in the risk premium with the marginal reduction in deviation costs. Because risk attitudes and portfolio choices are jointly determined, parameter changes affect both sides of this condition, generating feedback effects that may lead to ambiguous or non-monotone comparative statics. The framework provides a tractable approach to modelling endogenous risk attitudes in collective decision-making under uncertainty. |
| Keywords: | household portfolio choice; heterogeneous risk preferences; Endogenous risk attitudes; collective decision making; preference aggregation. |
| JEL: | C18 C44 D80 D81 I10 |
| Date: | 2026–04 |
| URL: | https://d.repec.org/n?u=RePEc:pra:mprapa:129608 |
| By: | Yilong Xu; Maarten Boksem; Charles N. Noussair; Stefan T. Trautmann; Gijs van de Kuilen; Alan Sanfey |
| Abstract: | In theory, individuals\' higher order risk attitudes of prudence and temperance influence saving and investment decisions. Prudent individuals save more when their future income becomes more uncertain, and temperate individuals prefer less risky investments in the presence of greater background risks. In a controlled experiment, we measure individuals' higher order risk attitudes directly, using two different elicitation methods. Participants then make saving and investment decisions under varying levels of background risk. We find strong effects of background risk on saving and investment. Moreover, individual prudence measures correlate with the strength of precautionary saving, while individual temperance measures do not do so with investment. The risk attitudes acquired with the two elicitation methods are strongly correlated with each other. The representative individual is risk averse and prudent, and neutral towards temperance. |
| Keywords: | high-order risks, precautionary saving, portfolio choice, risky decision-making |
| JEL: | C91 D15 D81 E21 E22 G51 |
| Date: | 2025–10 |
| URL: | https://d.repec.org/n?u=RePEc:exc:wpaper:2025-04 |
| By: | Boyarchenko, Nina; Elias, Leonardo |
| Abstract: | We estimate the global price of credit risk from a large cross section of global corporate bond returns. We show that a single factor, constructed as a nonlinear function of past credit spreads, equity market volatility, and their interactions, prices bond returns in both the time series and the cross section. The factor significantly outperforms alternative measures of global financial conditions, explaining up to 13% of variation in bond-level three-month-ahead returns. A high global price of credit risk further translates into deteriorations in local credit conditions, outflows from global funds, and higher expected returns to global funds. |
| Keywords: | Global financial cycle; Return predictability |
| JEL: | F30 G15 G12 |
| Date: | 2026–03 |
| URL: | https://d.repec.org/n?u=RePEc:cpr:ceprdp:21268 |
| By: | Shantanu Awasthi; Minglian Lin; Blair Faber; Michael Roberts; Hassan Butt |
| Abstract: | The Black-Scholes model has been extensively used for option pricing, but exhibits limitations in its reliance on geometric Brownian motion and fixed volatility assumptions. This paper proposes an enhanced model incorporating stochastic volatility with jumps modeled by a L\'evy process. Leveraging multidimensional It\^o calculus, we derive a pricing formula for European call options under the new framework. Additionally, Malliavin calculus enables the derivation of an exact expression for at-the-money implied volatility. The proposed model is shown to better capture empirical features like volatility smiles. Analysis of VIX data demonstrates the model's ability to match observed market volatility. The integration of L\'evy processes and Malliavin calculus represents a valuable advancement in addressing deficiencies in the classic Black-Scholes model. Further empirical testing is warranted to validate the approach across varying market conditions and option types. |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2606.22796 |
| By: | Ren\'e A\"id; Nizar Touzi; St\'ephane Villeneuve |
| Abstract: | We study how forward hedging reshapes incentive provision inside the firm. We consider a risk-averse producer facing demand and production risk that can either operate in-house or delegate production to a risk-averse agent under moral hazard, while hedging output in a competitive forward market with a rational market maker. Within a tractable continuous-time CARA framework, we jointly characterize optimal production, compensation, and static hedging in equilibrium. Delegation and external hedging are partial substitutes because both create value through risk sharing. Delegation can increase firm value even when the agent uses the same technology and is more risk averse than the principal, while access to forward hedging reduces the need to provide incentives through risk exposure. This mechanism delivers two main results. First, the principal hedges less under delegation than under in-house production. Second, this lower hedging demand under delegation raises the equilibrium forward price relative to the integrated benchmark. In the constant-demand case, we show that access to hedging lowers the agent's expected compensation under delegation. Numerical results indicate that this mechanism remains robust in the presence of demand uncertainty. More broadly, our results show that external risk transfer through financial markets feeds back into internal organizational design. |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2606.16493 |
| By: | Xuan Mei; Junze Lin |
| Abstract: | Complex model suites composed of multiple interacting component models are widely used in financial forecasting and risk management. In model performance testing, including in-sample backtesting (BT) and out-of-sample ongoing performance monitoring (OPM), a material gap between a model-suite forecast and the realized outcome must often be attributed to individual component models for development, validation, and regulatory review. This paper studies this gap-attribution problem in the expected loss framework, where exposure at default (EAD), prepayment or single monthly mortality (SMM), probability of default (PD), and loss given default (LGD) interact multiplicatively and are aggregated across loans and projection periods. We first formalize standard walk analysis and show why its attribution is generally order dependent. We then adapt two order-independent attribution frameworks: an augmented Logarithmic Mean Divisia Index (LMDI) approach tailored to the expected-loss structure, and a more general Shapley value approach based on averaging marginal contributions over all component orderings. We derive both elementwise and vectorized formulas to support efficient implementation, with the additional computation time for gap attribution typically limited to a few seconds in practical portfolio-scale examples. Finally, we discuss the connections among walk analysis, LMDI, and Shapley attribution, and show how the attribution framework extends to model suites with an additional Monte Carlo simulation layer. |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2606.21539 |
| By: | Miquel Noguer I Alonso; Ali Al Fallouji |
| Abstract: | Tail-risk management is not only an instrument-selection problem. It is an allocation problem across loss mechanisms: abrupt crash states, volatility repricing, and persistent drawdowns require different forms of protection. This paper develops a continuous-time CVaR framework that places two common protection sleeves -- long out-of-the-money put options and systematic trend-following overlays -- inside one coherent tail-risk mandate. The option sleeve is modeled as a marked-to-market traded asset, so premium drag, diffusion exposure, and jump repricing enter through its physical return process rather than through inconsistent terminal-payoff accounting. The resulting Markov state contains wealth, spot, stochastic variance, and an exponentially weighted log-return signal, and we derive the associated Hamilton--Jacobi--Bellman equation in viscosity form. The main analytical separation is temporal: convex insurance reprices immediately on jump impact, whereas trend following is late on the first shock because its signal must cross zero, but becomes increasingly defensive during persistent drawdowns without requiring fresh option premium. We then give sufficient and local conditions for an interior hybrid allocation, derive a CVaR policy-gradient identity, and introduce a four-axis diagnostic layer separating conditional convexity, tail-event reliability, non-stress carry, and drawdown persistence. Stylized Monte Carlo experiments illustrate the mechanism: fixed equal-weight hybrids and grid-optimized hybrids reduce terminal CVaR relative to either pure sleeve in the reported regimes, while the exact weight location remains calibration-dependent. The contribution is a transparent risk-management framework for deciding how much convex crash protection and how much signal-driven drawdown protection a mandate should hold. |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2607.00883 |
| By: | Jian Sun |
| Abstract: | For a fixed maturity, an arbitrage-free option smile induces natural normalized strike coordinates. This paper makes three contributions. First, it gives an elementary discrete no-arbitrage proof of monotonicity for the central Black--Scholes normalized coordinate \(k/v(k)\), using only finite-strike comparisons, convexity, monotonicity, and put--call parity. Thus the argument applies directly to finitely quoted option chains and does not require a continuously quoted smile, differentiability of option prices, differentiability of implied volatility, digital prices, or density extraction. Second, it extends the same monotonicity principle to the normal, or Bachelier, implied volatility formula, proving that the normalized coordinate \((F-K)/\sigma_N(K)\) is decreasing in strike under static no-arbitrage. Third, it proves a model-free normal-variance identity: remaining normal variance can be represented as a normal-density weighted integral of squared Bachelier implied volatility in the normalized coordinate. This third result is the normal/Bachelier analogue of Fukasawa's lognormal variance identity, which expresses variance-type quantities through Black implied variance in normalized coordinates. The paper therefore complements Fukasawa's continuous-strike normalizing transformation theory with a finite-quote no-arbitrage proof and a new normal-variance counterpart, while connecting the results to the volatility-derivatives literature surveyed by Carr and Lee. |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2606.23883 |
| By: | Wayne Yuan Gao; Zhiheng You |
| Abstract: | We study how the choice of default prior for a common Gaussian scale affects high-dimensional shrinkage risk, highlighting the role played by high-dimensional geometry. Formally, we consider a high-dimensional setting in which the near-zero behavior of the common scale prior has first-order consequences for shrinkage risk, and show that priors that are flat on the variance and those flat on the standard deviation allocate markedly different mass near the zero-scale boundary, leading to distinct shrinkage behavior and informing principled default prior selection. Specifically, under a radial-power benchmark, we establish that the SD-flat benchmark has a one-unit asymptotic risk advantage near the origin, crosses over in the critical regime, and is second-order equivalent to the variance-flat benchmark for strong signals. Proper single global-scale hyperpriors and bounded coordinate-multiplier mixtures inherit these limits through the near-zero exponent of their SD-scale density. For heavier-tailed or sparse priors, that exponent still classifies the common global-scale component, while local-scale tails, model-size priors, or allocation priors can also affect risk. |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2606.23509 |
| By: | Majlesi, Kaveh; Molin, Elin; Roth, Paula |
| Abstract: | We study how fatal and nonfatal health shocks affect households’ ability to meet their financial obligations. We find that fatal shocks substantially increase the likelihood of default and that housing wealth plays a key role as a self-insurance mechanism. Surviving spouses who experience the largest income losses are more likely to sell their homes, and those without housing wealth face a sharply higher risk of debt collection. Notably, these shocks generate intergenerational spillovers. In contrast, nonfatal health shocks lead to only modest increases in default risk. Taken together, our findings suggest that strengthening survivors’ benefits for households with limited resources could improve welfare across generations. |
| Keywords: | Health shocks |
| JEL: | D14 G51 G22 I12 |
| Date: | 2026–02 |
| URL: | https://d.repec.org/n?u=RePEc:cpr:ceprdp:21169 |
| By: | Xu, Yongdeng (Cardiff University, Cardiff, UK); Lyu, Juyi (Loughborough University, UK); Lu, Wenna (Cardiff Metropolitan University, Cardiff, UK) |
| Abstract: | This paper evaluates an Adaptive LASSO-MGARCH model for multivariate volatility forecasting, with an application to green and conventional bonds, equities, energy commodities, and EU carbon allowances. By introducing coefficient-specific adaptive penalisation directly into the multivariate GARCH variance equations, the model delivers a sparse and data-driven volatility spillover structure while preserving positive definiteness of the conditional covariance matrix. Using daily data on green and conventional bonds, equities, energy commodities, and carbon allowances, we show that adaptive regularisation substantially reduces model complexity and improves economic interpretability relative to an unpenalised MGARCH benchmark. Out-of-sample forecasting experiments at multiple horizons demonstrate that the Adaptive LASSO-MGARCH model consistently achieves lower covariance forecast losses, and statistical tests based on the White reality check confirm that these improvements are significant across alternative loss functions. |
| Keywords: | Adaptive LASSO; Multivariate GARCH; Volatility Forecasting; High-Dimensional; Green Finance |
| JEL: | C32 C58 G17 |
| Date: | 2026–03 |
| URL: | https://d.repec.org/n?u=RePEc:cdf:wpaper:2026/4 |
| By: | Luttini, Emiliano; Mekonnen, Dawit; Mercer-Blackman, Valerie Anne; Sørensen, Bent E |
| Abstract: | Using world commodity prices as an instrument, this paper proposes a novel method for decomposing channels of international risk sharing for commodity-exporting countries. The method identifies the commodity "sector'' as the projection of gross national product growth on commodity-price growth, and the non-commodity "sector'' as its orthogonal complement. Commodity-price-induced risk is shared significantly more than other risks, in particular via pro-cyclical government savings, but also via counter-cyclical net international factor income. |
| JEL: | F02 F21 F36 Q02 |
| Date: | 2026–01 |
| URL: | https://d.repec.org/n?u=RePEc:cpr:ceprdp:21100 |
| By: | Shen, Leslie Sheng; Xu, Nancy |
| Abstract: | We show that government policies interact in ways that shape how capital markets price risk. We introduce the concept of fiscal insurance: a mechanism through which certain fiscal tools are perceived by investors to mitigate the risks created by other government policies. Exploiting the 2018--19 U.S. tariff shocks and concurrent federal procurement spending, we find that firms facing higher tariff exposure earn higher risk premia, but this effect is substantially attenuated for firms receiving greater procurement. Procurement itself increases more for politically connected and economically vulnerable firms, revealing both political and economic channels of fiscal insurance. Overall, our evidence documents the existence of fiscal insurance, a cross-policy mechanism, with implications for firm valuation and real activity. |
| Keywords: | Fiscal policy; Risk premia; Tariffs; Uncertainty; Procurement |
| JEL: | G12 G38 E62 G14 |
| Date: | 2026–01 |
| URL: | https://d.repec.org/n?u=RePEc:cpr:ceprdp:21101 |
| By: | Austin Pollok; Kevin Robik |
| Abstract: | Timing-based tilts across asset classes can drive much of the risk and return of a diversified cross-asset portfolio. The standard approach forecasts returns and then optimizes weights. We instead study an end-to-end AI-based policy that maps market states directly to portfolio weights, and we then ask when this one-step modeling approach outperforms simple rules-based strategies. We train these policies on the sixteen most liquid CME futures, where an edge is unlikely to be due to illiquidity, using a differentiable Sharpe ratio loss function, and we benchmark them against equal weighting, risk parity, and time-series momentum. The learned policies rank above the rules on the pooled cross-asset portfolio and in several sub-asset classes, but not uniformly. In gross terms, an LSTM and a transformer-based architecture perform comparably out-of-sample, but diverge when we consider transaction costs. The transformer generates the stronger learned policy, trades far less than the LSTM, and matches or exceeds equal weighting through moderate cost. |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2607.00475 |
| By: | Sushant Acharya; Edouard Challe; Louphou Coulibaly |
| Abstract: | We show that incorporating uninsurable countercyclical income risk into a standard international RBC model can qualitatively and quantitatively account for the quantity puzzles in open-economy macro, namely (i) the Backus-Smith puzzle, (ii) the Backus-Kehoe-Kydland puzzle, and (iii) the weak correlation between the trade balance and the exchange rate. We also show that our model can simultaneously account for the Fama puzzle and the evidence that high interest rate countries have stronger currencies—which representative-agents models that rely only on financial or demand shocks cannot jointly account for. Crucially, our model resolves all these puzzles while relying solely on productivity shocks and thus generates the observed domestic and cross-country macroeconomic comovement. |
| Keywords: | incomplete markets; countercyclical risk; exchange rate; open-economy macro puzzles; macroeconomic comovements |
| JEL: | F41 F44 |
| Date: | 2026–07–01 |
| URL: | https://d.repec.org/n?u=RePEc:fip:fednsr:103524 |
| By: | Mark Whitmeyer |
| Abstract: | Suppose we want to assign a certainty equivalent--one number--to a multivariate risk. Which such assignments are law-invariant, monotone with respect to vector stochastic dominance, and invariant to independent background risk? I show that every such certainty equivalent is a positive mixture of scalar entropic certainty equivalents applied to positive projections of the vector risk. The same representation yields a robust-order characterization: unanimity across such certainty equivalents is equivalent, up to closure, to dominance after adding independent multidimensional background risk. In a social-welfare specialization, the corresponding shadow valuations are welfare weights. |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2607.01229 |
| By: | Yuan Christopher Qiang; Fabio Sigrist |
| Abstract: | We introduce the zero-one censored transformed normal (ZOC-TN) model for proportional responses with potential probability mass at the boundaries 0 and 1. The model combines a censored Gaussian variable with a two-parameter affine-logit transformation on the interior (0, 1). We characterize the transformation parameters, establish large-sample properties, and relate the affine-logit specification to broader classes of interior distributions. Theoretical and experimental results demonstrate that the proposed model can capture a wider range of qualitative density shapes than several benchmark models while remaining parsimonious, computationally efficient, and numerically stable. Furthermore, the ZOC-TN model can be extended (i) to account for nonlinearities and interactions in a tree-boosting machine learning framework and (ii) to explicitly model residual spatio-temporal variability. We apply the ZOC-TN model to loss given default (LGD) modeling for a large dataset of U.S. residential mortgages and compare it to multiple benchmark models. We find that a tree-boosted ZOC-TN model with a spatio-temporal frailty Gaussian process delivers the strongest out-of-sample performance, indicating that mortgage losses are shaped by nonlinear covariate effects and by unaccounted-for space-time variation. |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2606.21515 |
| By: | Martin, Ian; Shi, Ran |
| Abstract: | We derive option-implied bounds on the probability of a crash in an individual stock, and argue a priori that the lower bound should be close to the truth. The lower bound successfully forecasts crashes both in and out of sample. Crucially, our theory-based approach avoids the "crying wolf" problem faced by risk-neutral crash probabilities, which severely overstate crash risk during crisis periods. Despite having no free parameters, the lower bound outperforms elastic net, ridge, and Lasso models that flexibly but atheoretically combine stock characteristics, risk-neutral probabilities and the bound itself, because such models overfit during crisis periods. |
| JEL: | G12 G13 G17 G01 |
| Date: | 2026–03 |
| URL: | https://d.repec.org/n?u=RePEc:cpr:ceprdp:21236 |