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on Risk Management |
| By: | Marek Rutkowski; Huansang Xu |
| Abstract: | This paper examines the valuation and hedging of standard equity protection swap (EPS) products proposed by Xu et al.. To account for financial crises and counterparty default risk, we develop pricing frameworks based on Merton's jump-diffusion model and Szimayer's independent random time default model, under which closed-form valuation formulas and put-call parity relations for European options are derived. Hedging strategies for EPS products are analysed under jump and default risks. While static hedging remains effective in the absence of default, counterparty default risk leads to residual losses that cannot be fully hedged. These losses are quantified and used to define default-adjusted initial premiums under both Black-Scholes and jump-diffusion settings. Numerical results illustrate the effects of jump characteristics and default intensity on hedging costs and premiums, highlighting the importance of incorporating crisis and credit risks in EPS pricing and risk management. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.25450 |
| By: | Roberto Baviera; Pietro Manzoni; Michele Domenico Massaria |
| Abstract: | Modeling the dependence between multiple risk types is a central challenge in contemporary insurance risk management. The standard approaches, L\'evy copulas and zero-mixed models, often face practical difficulties in simulation and parameter calibration. In this paper, we introduce the Comb-Bernoulli model, a novel framework for capturing dependence between sparse time series of insurance risks, bridging the benefits of the two standard approaches. The (traditional) copula structure of the proposed model enables tractable: i) simulation, ii) likelihood evaluation, and iii) estimation of dependence parameters. We present the general properties of the model and analyze in detail the Gaussian copula case with lognormal marginals. Moreover, we illustrate an application using the Danish fire insurance dataset, highlighting both the modeling strengths and numerical efficiency of our approach in real-world risk management. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.25559 |
| By: | Denuit, Michel (Université catholique de Louvain, LIDAM/ISBA, Belgium); Flores-Contro, José Miguel (Université catholique de Louvain, LIDAM/ISBA, Belgium); Robert, Christian Y. |
| Abstract: | This paper studies proportional risk sharing at claim occurrence time in community-based insurance. Each participant is modeled by an individual Cram´er–Lundberg surplus process, and, whenever a claim is reported within the pool, its cost is redistributed according to a fixed allocation matrix. We compare the infinite-time ruin probability of each participant under stand-alone operation and under pool participation. Our main result shows that pooling reduces, for every participant, the infinite-time ruin probability when claim severities belong to a common scale family, the allocation rule satisfies full allocation and actuarial fairness, and each transfer remains bounded by an individual capacity condition. The proof relies on a convex-order comparison between the losses borne inside the pool and the corresponding stand-alone losses. We also clarify the role of these assumptions by showing that, outside this framework, pooling need not be beneficial for all participants. Numerical illustrations with Exponential and LogNormal severities support the theoretical findings and highlight how thedesign of proportional sharing rules affects solvency. The paper thus provides simple and interpretable sufficient conditions under which transparent linear risk-sharing arrangements improve individual solvency in community-based insurance. |
| Keywords: | Community-based insurance ; linear risk-sharing ; risk pooling ; risk process ; ruin probability |
| JEL: | G22 G52 O12 |
| Date: | 2026–03–31 |
| URL: | https://d.repec.org/n?u=RePEc:aiz:louvad:2026007 |
| By: | Marcel Muller; Arno Botha; Conrad Beyers |
| Abstract: | An integrated and extendable approach for stress-testing loan portfolios is presented, which includes both a loan production component and a credit risk component. In this approach, we simulate a completed portfolio using realistic loan parameters and distributional assumptions. Thereafter, we generate the uncertain cash flow history of these loans within a multistate probabilistic framework. We illustrate our approach using a simulation-based study, though the approach can be fit to real-world data. Such a simulation-based approach is ideal for stress-testing since it allows for evaluating a range of conditions. From these completed loans, we compute portfolio-level credit risk metrics, e.g., default and loss rates. Stress scenarios are introduced by varying the loan parameters accordingly within a broader Monte Carlo setup, thereby resulting in a range of portfolios. A classical approach to stress-testing does not typically integrate loan production or embed the correlation structure amongst risk metrics. In our approach, we integrate the forecasting of risk metrics with receipt-generation. Given data, the loan parameters within our extendable approach can be dynamically modelled as functions of input variables using any applicable technique. Overall, our approach can render predictions that are more dynamic and flexibly tuned, which can enhance stress-testing practices within any bank. |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2606.19052 |
| By: | Lescart, Mirco (Université catholique de Louvain, LIDAM/ISBA, Belgium); Kiriliouk, Anna (Université catholique de Louvain, LIDAM/ISBA, Belgium); Naveau, Philippe |
| Abstract: | Extreme value theory offers a statistical framework for quantifying the risk of rare events, with the generalized Pareto (GP) distribution providing the canonical limit model for univariate threshold exceedances. In many applications, however, extremes are intrinsically multivariate, requiring models that capture both marginal tail behaviours and joint extremal dependencies. Under asymptotic dependence, the multivariate GP distribution represents a suitablemodellingfamily, butwhenasymptoticindependencearises, sub-asymptoticmodels are needed. In this work, we propose and study a flexible sub-asymptotic parametric class to model bivariate threshold exceedances. Our new model accommodates a broad range of tail dependence behaviours and contains the standardised multivariate GP distribution as a limiting case while retaining margins that converge to univariate GP tails. Our formulation allows extremal dependence to evolve naturally with the marginal parameters on the original data scale, facilitating direct computation and interpretation of failure probabilities. Model inference is done via a likelihood-free neural Bayes estimation approach, with tailored prior specifications. An extensive simulation study and an application to Belgian rainfall extremes illustrate the estimation framework and the flexibility of the model. |
| Keywords: | Bivariate extremes ; peaks-over-thresholds ; multivariate generalized Pareto distribution ; asymptotic independence ; neural Bayes ; rainfall |
| Date: | 2026–04–15 |
| URL: | https://d.repec.org/n?u=RePEc:aiz:louvad:2026011 |
| By: | Pablo Rodriguez Manzi |
| Abstract: | We study the reconstruction of implied volatility surfaces from sparse and noisy option quotes using deep learning models under no-arbitrage constraints. We compare multiple neural architectures, including multilayer perceptrons, convolutional networks, U-Nets, variational autoencoders, and Transformer-based models against classical SVI parameterizations on option market data. Results show that Transformer and U-Net architectures achieve strong reconstruction accuracy, particularly under sparse observation regimes, while soft arbitrage penalties significantly reduce arbitrage violations with moderate impact on reconstruction error. We further analyze the trade-off between accuracy and arbitrage consistency across architectures and regularization strengths. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.24031 |
| By: | Sara A. Safari; Christoph Schmidhuber |
| Abstract: | We forecast future volatilities and correlations of financial markets based on the current trends in these markets. This complements previous work that models future expected returns by a cubic polynomial of the current trend strength. Empirically, we observe that volatilities and correlations tend to increase day after day in times of strong up- or down-trends. This effect is particularly pronounced in down-trends. It can be accurately quantified by quadratic polynomials of today's trend strengths, which refine common mean-reversion models of volatilities and correlations. Our results improve the prediction of market risk by accounting for market trends. They also support a recent proposal to model financial markets by a lattice gas near its critical point. |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2606.20145 |
| By: | Pierre Brugière (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique); Gabriel Turinici (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique) |
| Abstract: | Option pricing theory, in particular the model of Black & Scholes (1973), provides an explicit solution for constructing a perfectly hedged portfolio in continuous time. However, in practice, trading occurs in dis- crete time and is subject to transaction costs, making the direct applica- tion of continuous-time models often suboptimal. Previous studies, such as Buehler et al. (2018), Buehler et al. (2019), and Cao et al. (2019), have shown that deep learning and reinforcement learning can yield superior hedging strategies compared to traditional continuous-time approaches. However, these methods typically rely on a large number of simulated trajectories (on the order of 10^5 to 10^6) for effective training. In this work, we show that it is possible to train a deep hedging neural network using as few as 256 independent trajectories and still outperform both the classical Black & Scholes model and the Leland model in a Ge- ometric Brownian Motion setting. The Leland model is often considered one of the most effective explicit frameworks for incorporating transac- tion costs, yet it is surpassed by our data-efficient neural network when transaction costs are high. Going one step further, we demonstrate that even 256 overlapping sequences can beat the Leland formula when transaction costs are high and that a single trajectory, consisting of 31 or 91 points and augmented with a random drift (our Random Drift Augmentation method) is sufficient to roughly calibrate our neural network. These results highlight the potential for low-data implementations of deep hedging models in practical financial applications |
| Keywords: | Deep hedging, Machine Learning, Leland, Options, Optimal Strategy, Transaction costss |
| Date: | 2026–06–03 |
| URL: | https://d.repec.org/n?u=RePEc:hal:journl:hal-05642615 |
| By: | Hwee Kwan Chow (School of Economics, Singapore Management University); Jordan Lee (Singapore Management University) |
| Abstract: | This study empirically assesses the drivers of risks to the inflation outlook for a small open economy like Singapore. We apply the inflation-at-risk framework of López-Salido and Loria (2020) and incorporate projections from the Survey of Professional Forecasters (SPF) as point forecasts of inflation. Our findings show that macro-financial risk factors—shaped by Singapore’s openness, role as a financial hub, and exchange rate–centered monetary policy framework—enter nonlinearly into inflation risk models and exert differentiated effects. Foreign price pressures heighten upside risks, and exchange rate policy has proven effective at mitigating them. Tighter global financial conditions amplify inflation risks through cost-push channels, whereas demand weakness produces only muted downside effects. We also record sharp gains in log predictive scores for one-quarter ahead conditional distributions relative to unconditional ones during the post-pandemic inflation surge. One-year-ahead predictive distributions become markedly right‑skewed ahead of the surge, effectively signalling a heightened probability of extreme inflation outcomes. Overall, incorporating inflation risk measures improves both the in-sample fit and the forecast accuracy of predictive distributions of inflation one and four quarters ahead, offering insights for central banks navigating uncertain global conditions. |
| Keywords: | Inflation-at-risk; survey of professional forecasters; quantile regressions; forecast accuracy |
| JEL: | C21 C53 E31 |
| Date: | 2026–02–01 |
| URL: | https://d.repec.org/n?u=RePEc:ris:smuesw:022912 |
| By: | Alex Chan |
| Abstract: | Risk adjustment is a payment mechanism, not only a prediction problem. I extend optimal risk adjustment to dynamic insurance markets in which plans capture future residuals from persistent risk. Under an efficiency criterion, payments should reflect expected profits and losses over the enrollee relationship on margins plans control, not only one-year spending predictions. A finite-cell model separates selection, health production, and manipulable measurement. The framework implies that annual recalculation can tax prevention, high-R² prediction can reduce welfare, and lagged claims anchors are useful only with gaming safeguards. |
| JEL: | C61 D47 D80 D82 I1 I11 I13 |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:nbr:nberwo:35325 |
| By: | Bianchi, Michele Leonardo; Ruzzi, Dario; Segura, Anatoli |
| Abstract: | We use granular regulatory data on euro interest rate swap trades over the period 2021-2024 to analyse the dynamics of Italian banks’ hedging of interest rate risk in their securities portfolio. We find that on average and over the full period, banks use swaps as hedging instruments: a third of the value losses on securities following a 100 basis points upward shift of the yield curve are offset by the associated gains on swap positions. The intensity in securities hedging through swaps increases by 6% after policy rates rise in mid-2022. Causality of such increase is assessed with an analysis based on monetary policy surprises. The increase in hedging intensity during the tightening period is more important for banks with initially lower capital and less stable funding. |
| JEL: | G11 G21 E43 E52 |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:cpr:ceprdp:21588 |
| By: | Takaaki Koike; Marius Hofert; Haruki Tsunekawa |
| Abstract: | The classical tail dependence coefficient (TDC) may fail to capture non-exchangeable features of bivariate tail dependence since it evaluates the underlying copula only along the diagonal. To address this limitation, several measures of strongest manifestation of tail dependence have been proposed in the bivariate case, including a measure based on the tail copula of the underlying bivariate copula. This paper introduces and investigates the multivariate maximal tail concordance measure (MTCM) which extends the bivariate measure to the multivariate case. The MTCM quantifies the largest tail mass over lower hyperrectangles of common unit volume, while the associated maximizer identifies the direction of maximal tail probability. We establish fundamental properties of the MTCM in the multivariate case, including existence of an optimal direction. We also derive analytical representations for several important model classes. Closed-form expressions are further obtained for survival Marshall-Olkin copulas, Archimax and nested Archimedean copulas with regularly varying Archimedean generators. An application to trivariate annual sea-level maxima in England shows that the MTCM can reveal off-diagonal stress directions and substantial differences in the underlying extremal dependence not detected by likelihood- or TDC-based comparisons. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.25766 |
| By: | Alessandro Doldi; Marco Frittelli; Marco Maggis |
| Abstract: | This paper complements and extends Doldi, Frittelli and Maggis, Collective completeness and pricing-hedging duality, Math. Finan. Econ. 19, 757-784 (2025), by studying collective pricing and hedging when admissible risk exchanges form a finitely generated convex cone. The collective First Fundamental Theorem of Asset Pricing and the collective pricing-hedging duality are extended to this setting. A key contribution is a closedness result showing that no collective arbitrage implies the closedness of the aggregate feasibility cone combining infinite-dimensional trading opportunities with finite-dimensional exchanges. The paper also proves that no-collective-arbitrage prices for vectors of contingent claims form a relatively open convex set. Finally, strong collective replicability is introduced and shown to be equivalent to price uniqueness. This leads to an enhanced collective Second Fundamental Theorem of Asset Pricing, providing equivalent characterizations of collective completeness and strong collective completeness in terms of the uniqueness of the collective equivalent martingale measure. We highlight that several core aspects of the theory are substantially altered when exchanges belong to a convex cone rather than a vector space. |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2606.19038 |
| By: | Nicole B\"auerle; Anne MacKay |
| Abstract: | We consider a continuous time investment problem in a multi-asset Black-Scholes market with the following features: The assets' drifts are not known and constitute a source of model ambiguity. However, there is a prior distribution (knowledge) on the possible drifts. Our investor is ambiguity averse and wants to maximize a mean-variance criterion for the terminal wealth where ambiguity aversion is incorporated in a smooth way. We consider here the criterion introduced in Maccheroni et al. 2013 where the variance is decomposed and each part is weighted differently to account for different levels of market risk and model ambiguity aversion. We use a novel approach to find the optimal dynamic investment strategy within the class of all adapted strategies which allow for learning. We also present a number of numerical results which help to understand how the model parameters affect the optimal investment strategy. In general it turns out that ambiguity averse investors invest less in the risky assets. |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2606.11318 |
| By: | Weilun Cheng; Zongxia Liang; Sheng Wang; Xiang Yu |
| Abstract: | This paper investigates a mean-field game (MFG) problem for mean-variance (MV) portfolio management, highlighting a new type of relative performance encoded by the peer-based risk aversion. Specifically, the risk aversion is formulated as a piecewise form that depends on whether the individual's wealth is above or below the population average. Due to the inherent time-inconsistency in the MV criterion, together with the piecewise risk aversion, we encounter a class of time-inconsistent MFG, new to the literature. Our goal is to seek a mean-field equilibrium, characterized by a forward-backward stochastic differential equation (FBSDE) system and a mean-field consistency condition. The new challenge stems from the discontinuous coefficients induced by the piecewise risk aversion. In response, we first propose a smooth regularization technique and obtain the existence of the equilibrium in the intra-personal game for the representative agent by establishing the solution to the discontinuous multi-dimensional FBSDE. Next, by invoking fixed-point arguments and convergence analysis as smoothing regularization vanishes, we conclude the existence of the mean-field equilibrium in the time-inconsistent MFG. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.25824 |
| By: | Dong Yan; Wenrui Ye; Zhiyue Zong; Wenting Chen |
| Abstract: | We extend the return extrapolation framework of Atmaz (2022) to incorporate two behaviorally realistic features absent from the linear benchmark: saturation in belief updating and asymmetry between gains and losses. We introduce a smooth, nonlinear, asymmetric extrapolation function and characterize the optimal portfolio of a CRRA investor under Heston (1993) stochastic volatility as the sum of a sentiment-distorted myopic demand, a variance hedging demand, and a sentiment hedging demand. The resulting semilinear Hamilton-Jacobi-Bellman equation is solved by two independent numerical methods, a finite-difference ADI scheme with time-step policy iteration and a deep learning-driven iterative scheme. The model generates four investor-level behavioral anomalies: asymmetric responses to gains and losses, attenuated reactions at extremes, excess trading volume, and welfare loss rising with the strength of extrapolation, each of which maps onto documented empirical patterns. Its central finding is that saturation acts as an endogenous correction mechanism: at the same local slope at the origin, the asymmetric nonlinear extrapolator carries a smaller welfare loss than a linear one. |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2606.10805 |
| By: | Beyer, Marcel |
| Abstract: | This paper investigates the determinants of distress recovery of insurance companies. I develop three complementary distress definitions capturing market-based signals. To address model uncertainty and heterogeneity across firms and states of the world, I apply a mixture-ofexperts framework to these definitions. In the second part, the paper analyzes the determinants of distress recovery. The results show that firm characteristics, capitalization, asset allocation, and macro-economic conditions explain variation in recovery outcomes. Macroeconomic variables matter more for US insurers, whereas European insurers depend more on firm-specific variables. I benchmark competing empirical approaches to assess robustness and predictive performance. The results indicate that generalized linear models provide more accurate rank estimates of the order in which firms recover, while Cox proportional hazard models offer the most precise point estimate of distress duration. |
| Keywords: | Insurance, Financial Stability, Distress Resilience |
| JEL: | G01 G17 G22 G23 |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:zbw:icirwp:341640 |
| By: | Arvai, Kai; Coimbra, Nuno; Pinchetti, Marco |
| Abstract: | This paper investigates the determinants of international investors' portfolio choices between gold and sovereign bonds in an environment shaped by economic and geopolitical shocks. We develop an endogenous portfolio choice model where reserve safety has a political dimension — sovereign bonds issued by the dominant reserve country are more liquid but exposed to the issuer's sanctions authority, while gold offers sanctions protection at the cost of lower liquidity. Our model implies that US convenience yields fall during periods of high sanction risk, as safe-asset demand fragments along geopolitical lines. Empirically, periods of elevated geopolitical risk coincide with higher gold prices and 10-year Treasury yields. In such periods, the average composition of official reserves shifts toward gold, with countries less aligned with the US in UN voting patterns increasing their holdings by a greater extent. |
| Keywords: | Dominant currency; Safe assets; Sanctions; Gold |
| JEL: | E42 F02 F33 N10 |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:cpr:ceprdp:21575 |
| By: | Andrea Bucci; Giulio Palomba; Eduardo Rossi |
| Abstract: | This paper proposes a Structural Matrix Autoregressive (SMAR) model for the joint analysis of asset returns, realized volatility, and trading volume in a large-dimensional setting. This framework simultaneously captures dynamic spillovers across financial variables and cross-sectional dependence across assets while preserving a parsimonious parameterization relative to conventional vector autoregressive models. The model is estimated on daily data for the constituents of the Dow Jones Industrial Average over the period 2021-2025 and is structurally identified through restrictions consistent with the Mixture of Distributions Hypothesis and efficient market theory. The empirical findings indicate that volatility is the primary driver of trading activity, suggesting that informational shocks are predominantly incorporated into markets through price variability. Forecast error variance decompositions further reveal that, although internal shocks dominate short-term volume dynamics, cross-asset spillovers account for more than 50% of trading volume variation at longer horizons. Finally, an event-study analysis around FOMC announcements supports the proposed decomposition by identifying significant increases in the informative component of trading activity on announcement days followed by rapid mean reversion. |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2606.08141 |