|
on Risk Management |
| By: | Osadchiy, Maksim |
| Abstract: | This paper extends the classical Vasicek credit risk model by introducing a comprehensive multi-factor framework that simultaneously incorporates key sources of portfolio heterogeneity – namely, variations in asset weights, recovery rates, default probabilities, and asset correlations. By modeling the complex interactions among these factors, our approach provides a more realistic and nuanced assessment of loss distributions and risk measures. Monte Carlo simulations demonstrate that the extended Vasicek-style model yields accurate approximations of portfolio Value at Risk (VaR) across portfolios with diverse recovery profiles and moderate concentration levels. This advancement improves the precision of credit risk measurement, addresses current regulatory gaps, and offers a solid foundation for more sophisticated risk management of heterogeneous credit portfolios. |
| Keywords: | Heterogeneous Credit Portfolios; Granularity Adjustment; Vasicek Model; Value at Risk; Monte Carlo Simulation |
| JEL: | C63 G17 G21 G28 G32 G33 |
| Date: | 2025–11–27 |
| URL: | https://d.repec.org/n?u=RePEc:pra:mprapa:127032 |
| By: | Fabio Bellini; Muqiao Huang; Qiuqi Wang; Ruodu Wang |
| Abstract: | The Lambda Value-at-Risk (Lambda$-VaR) is a generalization of the Value-at-Risk (VaR), which has been actively studied in quantitative finance. Over the past two decades, the Expected Shortfall (ES) has become one of the most important risk measures alongside VaR because of its various desirable properties in the practice of optimization, risk management, and financial regulation. Analogously to the intimate relation between ES and VaR, we introduce the Lambda Expected Shortfall (Lambda-ES), as a generalization of ES and a counterpart to Lambda-VaR. Our definition of Lambda-ES has an explicit formula and many convenient properties, and we show that it is the smallest quasi-convex and law-invariant risk measure dominating Lambda-VaR under mild assumptions. We examine further properties of Lambda-ES, its dual representation, and related optimization problems. |
| Date: | 2025–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2512.23139 |
| By: | Enrique Calder\'in-Ojeda; Yuyu Chen; Soon Wei Tan |
| Abstract: | Capital allocation is a procedure used to assess the risk contributions of individual risk components to the total risk of a portfolio. While the conditional tail expectation (CTE)-based capital allocation is arguably the most popular capital allocation method, its inability to reflect important tail behaviour of losses necessitates a more accurate approach. In this paper, we introduce a new capital allocation method based on the tail central moments (TCM), generalising the tail covariance allocation informed by the tail variance. We develop analytical expressions of the TCM as well as the TCM-based capital allocation for the class of normal mean-variance mixture distributions, which is widely used to model asymmetric and heavy-tailed data in finance and insurance. As demonstrated by a numerical analysis, the TCM-based capital allocation captures several significant patterns in the tail region of equity losses that remain undetected by the CTE, enhancing the understanding of the tail risk contributions of risk components. |
| Date: | 2026–01 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2601.00568 |
| By: | Ambrocio, Gene; Fungáčová, Zuzana; Heikkinen, Joni; Kerola, Eeva; Korhonen, Iikka; Norring, Anni |
| Abstract: | We construct a geopolitical risk indicator for Finland using local, Finnish language news media - FinnGPR. We compare FinnGPR to global and country-specific measures of geopolitical risk derived from Anglo-Saxon media. We show that in the case of Finland, local geopolitical risk perceptions based on local news media differ from global attention on geopolitical risk in Finland as reflected in the global media. We study the effects of FinnGPR on the Finnish economy and find that the Finnish economy tends to be resilient to geopolitical risk shocks. Nevertheless, we find that geopolitical risks can represent a threat to Finnish financial market stability. |
| Keywords: | geopolitical risk, local perceptions, geopolitical attention, news-based index, macroeconomic stability, financial stability |
| JEL: | D80 E44 F50 G0 |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:zbw:bofrdp:334518 |
| By: | Siddhartha Srinivas Rentala |
| Abstract: | This study investigates the efficacy of Conditional Restricted Boltzmann Machines (CRBMs) for modeling high-dimensional financial time series and detecting systemic risk regimes. We extend the classical application of static Restricted Boltzmann Machines (RBMs) by incorporating autoregressive conditioning and utilizing Persistent Contrastive Divergence (PCD) to incorporate complex temporal dependency structures. Comparing a discrete Bernoulli-Bernoulli architecture against a continuous Gaussian-Bernoulli variant across a multi-asset dataset spanning 2013-2025, we observe a dichotomy between generative fidelity and regime detection. While the Gaussian CRBM successfully preserves static asset correlations, it exhibits limitations in generating long-range volatility clustering. Thus, we analyze the free energy as a relative negative log-likelihood (surprisal) under a fixed, trained model. We demonstrate that the model's free energy serves as a robust, regime stability metric. By decomposing the free energy into quadratic (magnitude) and structural (correlation) components, we show that the model can distinguish between pure magnitude shocks and market regimes. Our findings suggest that the CRBM offers a valuable, interpretable diagnostic tool for monitoring systemic risk, providing a supplemental metric to implied volatility metrics like the VIX. |
| Date: | 2025–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2512.21823 |
| By: | Benjamin Avanzi; Debbie Kusch Falden; Mogens Steffensen |
| Abstract: | In high-risk environments, traditional indemnity insurance is often unaffordable or ineffective, despite its well-known optimality under expected utility. This paper compares excess-of-loss indemnity insurance with parametric insurance within a common mean-variance framework, allowing for fixed costs, heterogeneous premium loadings, and binding budget constraints. We show that, once these realistic frictions are introduced, parametric insurance can yield higher welfare for risk-averse individuals, even under the same utility objective. The welfare advantage arises precisely when indemnity insurance becomes impractical, and disappears once both contracts are unconstrained. Our results help reconcile classical insurance theory with the growing use of parametric risk transfer in high-risk settings. |
| Date: | 2025–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2512.21973 |
| By: | Shanyu Han; Yangbo He; Yang Liu |
| Abstract: | We propose a novel framework for risk-sensitive reinforcement learning (RSRL) that incorporates robustness against transition uncertainty. We define two distinct yet coupled risk measures: an inner risk measure addressing state and cost randomness and an outer risk measure capturing transition dynamics uncertainty. Our framework unifies and generalizes most existing RL frameworks by permitting general coherent risk measures for both inner and outer risk measures. Within this framework, we construct a risk-sensitive robust Markov decision process (RSRMDP), derive its Bellman equation, and provide error analysis under a given posterior distribution. We further develop a Bayesian Dynamic Programming (Bayesian DP) algorithm that alternates between posterior updates and value iteration. The approach employs an estimator for the risk-based Bellman operator that combines Monte Carlo sampling with convex optimization, for which we prove strong consistency guarantees. Furthermore, we demonstrate that the algorithm converges to a near-optimal policy in the training environment and analyze both the sample complexity and the computational complexity under the Dirichlet posterior and CVaR. Finally, we validate our approach through two numerical experiments. The results exhibit excellent convergence properties while providing intuitive demonstrations of its advantages in both risk-sensitivity and robustness. Empirically, we further demonstrate the advantages of the proposed algorithm through an application on option hedging. |
| Date: | 2025–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2512.24580 |
| By: | Walter Distaso; Wolfgang Lefever; Angelo Luisi; Francesco Roccazzella (-) |
| Abstract: | Research on natural disasters and credit risk mainly focuses on default probabilities. However, post-default outcomes remain largely unexplored, making the overall impact on credit losses unclear. We address this gap by providing novel empirical evidence on the impact of wildfires on credit losses through the loss given default channel. Exploiting the richness of a proprietary database on defaulted consumer credits in Italy, we determine granular wildfires exposures using satellite-based geospatial data on burned areas. We document a robust negative relationship between wildfire exposure during the post-default recovery period and realized recovery rates. This identifies a loss given default mechanism that complements existing evidence on default risk. The effect is heterogeneous: it is stronger when a larger share of agricultural land is burned and, consistent with evidence that natural disasters affect financially fragile households more severely, further amplified by local socioeconomic vulnerability. These findings call for integrating climate considerations into credit risk management beyond default risk. |
| Keywords: | Natural disasters; Wildfires; Consumer credit; Credit risk; Loss given default |
| JEL: | G21 G51 Q54 |
| Date: | 2025–12 |
| URL: | https://d.repec.org/n?u=RePEc:rug:rugwps:25/1129 |
| By: | Yifan Liu; Shi-Dong Liang |
| Abstract: | The deviation of the efficient market hypothesis (EMH) for the practical economic system allows us gain the arbitrary or risk premium in finance markets. We propose the triplet $(R, H, \sigma)$ theory to give the local and global optimal portfolio, which eneralize from the $(R, \sigma)$ model. We present the formulation of the triplet $(R, H, \sigma)$ model and give the Pareto optimal solution as well as comparing it with the numerical investigations for the Chinese stock market. We define the local optimal weights of the triplet $(\mathbf{w}_{R}, \mathbf{w}_{H}, \mathbf{w}_{\sigma})$, which constructs the triangle of the quasi-optimal investing subspace such that we further define the centroid of the triangle or the incenter of the triangle as the optimal investing weights, which optimizes the mean return, the arbitrary or risk premium and the volatility risk. By investigating numerically the Chinese stock market as an example we demonstrate the validity of the formulation and obtain the global optimal strategy and quasi-optimal investing subspace. The theory provides an efficient way to design the portfolio for different style investors, conservative or aggressive investors, in finance market to maximize the mean return and arbitrary or risk premium with a small volatility risk. |
| Date: | 2026–01 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2601.00281 |
| By: | Fiechter, Chad; Kunwar, Binayak; Mallory, Mindy; Faller, Eugene |
| Abstract: | Grain producers face significant price uncertainty, and while exchange-traded derivatives like futures and options have been extensively studied, little is known about how farmers use structured over-the-counter (OTC) derivatives. This study investigates how U.S. corn producers select among three structured OTC derivative products: Participation, Price Improvement, and Protection contracts, to hedge price risk. Using proprietary data on individual OTC corn derivative contracts provided by Marex Solutions, covering trades executed by U.S. farmers between 2022 and 2024, we adopt a two-stage analytical framework, employing XGBoost machine learning for variable selection and a multinomial logit model for economic interpretation. Our findings reveal distinct behavioral patterns: producers strongly prefer Price Improvement contracts during periods of low prices, Participation contracts at price extremes under moderate volatility, and underutilize Protection structures even when downside risks are pronounced. Counterfactual analysis demonstrates that Price Improvement strategies consistently yield the highest returns, outperforming other structures by 40 to 60 cents per bushel on average, suggesting potential suboptimal decision-making by farmers. This study offers new empirical insights into how producers engage with complex OTC instruments and contribute to the broader literature on commodity market behavior and agricultural finance. |
| Keywords: | Marketing |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:ags:aaea25:360826 |
| By: | Ali Zeytoon-Nejad; Barry Goodwin |
| Abstract: | The conventional functional form of the Constant-Elasticity-of-Substitution (CES) production function is a general production function nesting a number of other forms of production functions. Examples of such functions include Leontief, Cobb-Douglas, and linear production functions. Nevertheless, the conventional form of the CES production specification is still restrictive in multiple aspects. One example is the fact that the marginal effect of increasing input use always has to be to increase the variability of output quantity by the conventional construction of this function. This paper proposes a generalized variant of the CES production function that allows for various input effects on the probability distribution of output. Failure to allow for this possible input-output risk structure is indeed one of the limitations of the conventional form of the CES production function. This limitation may result in false inferences about input-driven output risk. In light of this, the present paper proposes a solution to this problem. First, it is shown that the familiar CES formulation suffers from very restrictive structural assumptions regarding risk considerations, and that such restrictions may lead to biased and inefficient estimates of production quantity and production risk. Following the general theme of Just and Pope's approach, a CES-based production-function specification that overcomes this shortcoming of the original CES production function is introduced, and a three-stage Nonlinear Least-Squares (NLS) estimation procedure for the estimation of the proposed functional form is presented. To illustrate the proposed approaches in this paper, two empirical applications in irrigation and fertilizer response using the famous Hexem-Heady experimental dataset are provided. Finally, implications for modeling input-driven production risks are discussed. |
| Date: | 2025–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2512.20910 |
| By: | Zongxiao Wu; Ran Liu; Jiang Dai; Dan Luo |
| Abstract: | Credit risk assessment increasingly relies on diverse sources of information beyond traditional structured financial data, particularly for micro and small enterprises (mSEs) with limited financial histories. This study proposes a multimodal framework that integrates structured credit variables, climate panel data, and unstructured textual narratives within a unified learning architecture. Specifically, we use long short-term memory (LSTM), the gated recurrent unit (GRU), and transformer models to analyse the interplay between these data modalities. The empirical results demonstrate that unimodal models based on climate or text data outperform those relying solely on structured data, while the integration of multiple data modalities yields significant improvements in credit default prediction. Using SHAP-based explainability methods, we find that physical climate risks play an important role in default prediction, with water-logging by rain emerging as the most influential factor. Overall, this study demonstrates the potential of multimodal approaches in AI-enabled decision-making, which provides robust tools for credit risk assessment while contributing to the broader integration of environmental and textual insights into predictive analytics. |
| Date: | 2026–01 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2601.00478 |
| By: | Siqi Shao; Arshia Ghasemi; Hamed Farahani; R. A. Serota |
| Abstract: | We argue that negative skew and positive mean of the distribution of stock returns are largely due to the broken symmetry of stochastic volatility governing gains and losses. Starting with stochastic differential equations for stock returns and for stochastic volatility we argue that the distribution of stock returns can be effectively split in two - for gains and losses - assuming difference in parameters of their respective stochastic volatilities. A modified Jones-Faddy skew t-distribution utilized here allows to reflect this in a single organic distribution which tends to meaningfully capture this asymmetry. We illustrate its application on distribution of daily S&P500 returns, including analysis of its tails. |
| Date: | 2025–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2512.23640 |