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on Risk Management |
| By: | Jose Da Fonseca; Patrick Wong |
| Abstract: | This study introduces a new analytical framework for quantifying multivariate risk measures. Using the Wishart process, which is a stochastic process with values in the space of positive definite matrices, we derive several conditional tail risk measures which, thanks to the remarkable analytical properties of the Wishart process, can be explicitly computed up to a one- or two-dimensional integration. These quantities can also be used to solve analytically a capital allocation problem based on conditional moments. Exploiting the stochastic differential equation property of the Wishart process, we show how an intertemporal (i.e., time-lagged) view of these risk measures can be embedded in the proposed framework. Several numerical examples show that the framework is versatile and operational, thus providing a useful tool for risk management. |
| Date: | 2026–02 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2602.06401 |
| By: | Du-Yi Wang; Guo Liang; Kun Zhang; Qianwen Zhu |
| Abstract: | Rapidly evolving market conditions call for real-time risk monitoring, but its online estimation remains challenging. In this paper, we study the online estimation of one of the most widely used risk measures, Value at Risk (VaR). Its accurate and reliable estimation is essential for timely risk control and informed decision-making. We propose to use the quantile regression forest in the offline-simulation-online-estimation (OSOA) framework. Specifically, the quantile regression forest is trained offline to learn the relationship between the online VaR and risk factors, and real-time VaR estimates are then produced online by incorporating observed risk factors. To further ensure reliability, we develop a conformalized estimator that calibrates the online VaR estimates. To the best of our knowledge, we are the first to leverage conformal calibration to estimate real-time VaR reliably based on the OSOA formulation. Theoretical analysis establishes the consistency and coverage validity of the proposed estimators. Numerical experiments confirm the proposed method and demonstrate its effectiveness in practice. |
| Date: | 2026–02 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2602.01912 |
| By: | Tomasz Kania |
| Abstract: | We develop a non-standard analysis framework for coherent risk measures and their finite-sample analogues, coherent risk estimators, building on recent work of Aichele, Cialenco, Jelito, and Pitera. Coherent risk measures on $L^\infty$ are realised as standard parts of internal support functionals on Loeb probability spaces, and coherent risk estimators arise as finite-grid restrictions. Our main results are: (i) a hyperfinite robust representation theorem that yields, as finite shadows, the robust representation results for coherent risk estimators; (ii) a discrete Kusuoka representation for law-invariant coherent risk estimators as suprema of mixtures of discrete expected shortfalls on $\{k/n:k=1, \ldots, n\}$; (iii) uniform almost sure consistency (with an explicit rate) for canonical spectral plug-in estimators over Lipschitz spectral classes; (iv) a Kusuoka-type plug-in consistency theorem under tightness and uniform estimation assumptions; (v) bootstrap validity for spectral plug-in estimators via an NSA reformulation of the functional delta method (under standard smoothness assumptions on $F_X$); and (vi) asymptotic normality obtained through a hyperfinite central limit theorem. The hyperfinite viewpoint provides a transparent probability-to-statistics dictionary: applying a risk measure to a law corresponds to evaluating an internal functional on a hyperfinite empirical measure and taking the standard part. We include a standardd self-contained introduction to the required non-standard tools. |
| Date: | 2026–01 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2602.00784 |
| By: | Tim Leung; Matthew Lorig |
| Abstract: | We price European options in a class of models in which the volatility of the underlying risky asset depends on the short rate of interest. Our study results in an explicit pricing formula that depends on knowledge of a characteristic function. We provide examples of models in which the characteristic function can be computed analytically and, thus, the value of European options is explicit. Numerical implementation to produce the implied volatility is also presented. |
| Date: | 2026–01 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2602.00858 |
| By: | Heather N. Fogarty; Sooie-Hoe Loke; Nicholas F. Marshall; Enrique A. Thomann |
| Abstract: | This paper studies decentralized risk-sharing on networks. In particular, we consider a model where agents are nodes in a given network structure. Agents directly connected by edges in the network are referred to as friends. We study actuarially fair risk-sharing under the assumption that only friends can share risk, and we characterize the optimal signed linear risk-sharing rule in this network setting. Subsequently, we consider a special case of this model where all the friends of an agent take on an equal share of the agent's risk, and establish a connection to the graph Laplacian. Our results are illustrated with several examples. |
| Date: | 2026–02 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2602.05155 |
| By: | Giovanni Bonaccolto (Department of Economics and Law, ``Kore" University of Enna, Piazza dell'Universita, 94100 Enna, Italy); Massimiliano Caporin (Department of Statistical Sciences, University of Padova, Via Cesare Battisti 241/243, Padova, Italy); Oguzhan Cepni (Ostim Technical University, Ankara, Turkiye; University of Edinburgh Business School, Centre for Business, Climate Change, and Sustainability; Department of Economics, Copenhagen Business School, Denmark); Rangan Gupta (Department of Economics, University of Pretoria, Private Bag X20, Hatfield 0028, South Africa) |
| Abstract: | We investigate whether sentiment innovations help forecast realized volatility in U.S. state-level stock markets. We combine 5-minute intraday data for 50 U.S. states with a daily state-level Twitter-based sentiment index over the period August 2011 to August 2024. Realized variance, skewness, and kurtosis are constructed using intermittency-adjusted estimators that account for sparse trading and zero returns. We adopt a Heterogeneous Autoregressive framework and enrich it with higher-order realized moments and changes in state-level sentiment, estimating the models via weighted least squares to mitigate heteroskedasticity effects. Out-of-sample performance is assessed in a rolling-window forecasting design for daily, weekly, and monthly horizons, and formal forecast comparisons are conducted using Diebold-Mariano and Clark-West tests. Our results confirm that the Heterogeneous Autoregressive components remain the dominant drivers of realized volatility dynamics across all horizons. Importantly, tail-risk information, proxied by realized kurtosis, delivers the most systematic and economically meaningful improvements in predictive accuracy, particularly at short horizons. Sentiment changes exhibit an episodic but non-negligible predictive foot-print: while their average in-sample contribution is limited, they enhance forecast performance for a subset of states, especially when combined with higher-moment information in richer specifications. Overall, our findings highlight that integrating in-traday distributional characteristics and sentiment innovations can improve volatility forecasting at the regional level, albeit in a state- and horizon-dependent manner. |
| Keywords: | State-level stock markets, Sentiment, HAR-RV, Realized moments, Forecast evaluation |
| JEL: | C53 C58 G11 G17 |
| Date: | 2026–02 |
| URL: | https://d.repec.org/n?u=RePEc:pre:wpaper:202603 |
| By: | Sasha Stoikov; Aadityaa Singla; Umu Cetin; Luis Alonso Cendra Villalobos |
| Abstract: | In the streaming era, music revenues distributed to rights holders have become more transparent. However, it is not yet clear how to quantify the risk and return characteristics of music royalty assets, as is done with equities. In this paper, we fit three discounted cashflow models to transactions on the Royalty Exchange platform. We use our best model to backtest the one year and five year performance of music royalty assets, after transaction costs. We find that Life of Rights (LOR) music assets had risk and return characteristics comparable to stocks in the S\&P500, when held over 5 years. Since the performance of stocks and music assets are likely to be uncorrelated, this result may help investors assess this asset class within the context of a more traditional stock and bond portfolio. |
| Date: | 2026–02 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2602.05007 |
| By: | Irma Alonso-Alvarez (BANCO DE ESPAÑA); Ekaterina Bukina (BANCO DE ESPAÑA); Marina Diakonova (BANCO DE ESPAÑA); Nino Khitarishvili (BANCO DE ESPAÑA); Javier J. Pérez (BANCO DE ESPAÑA); Pedro Piqueras (BANCO DE ESPAÑA) |
| Abstract: | This paper presents a comprehensive database of geopolitical risk (GPR) indices for 34 countries, constructed using a standardized textual analysis methodology applied to national news sources. Building on the framework introduced in Alonso-Alvarez et al. (2025), we calculate both general and bilateral GPR indices that reflect the intensity and origin of geopolitical tensions as perceived in domestic media narratives. The indices are derived from a dictionary-based approach applied to press articles accessed via the Factiva platform, with queries translated into 15 languages to ensure linguistic and cultural relevance. Bilateral indices focus on four key regions – Russia, China, the Middle East and North Africa (MENA), and the Western Bloc – capturing how each country perceives external geopolitical threats. The resulting high-frequency dataset is validated through statistical robustness checks and narrative analysis of index peaks. Our work contributes to the literature by offering a scalable, globally representative tool for analyzing geopolitical risk, complementing existing measurements such as the Caldara-Lacoviello GPR index and enabling new empirical applications in macroeconomics, finance and international relations. |
| Keywords: | geopolitical risk, geopolitical tensions, textual analysis |
| JEL: | C43 E32 F51 F52 H56 |
| Date: | 2026–02 |
| URL: | https://d.repec.org/n?u=RePEc:bde:opaper:2603e |
| By: | Chiheb Ben Hammouda; Truong Ngoc Nguyen |
| Abstract: | Multivariate shortfall risk measures provide a principled framework for quantifying systemic risk and determining capital allocations prior to aggregation in interconnected financial systems. Despite their well established theoretical properties, the numerical estimation of multivariate shortfall risk and the corresponding optimal allocations remains computationally challenging, as existing Monte Carlo based approaches can be numerically expensive due to slow convergence. In this work, we develop a new class of single and multilevel numerical algorithms for estimating multivariate shortfall risk and the associated optimal allocations, based on a combination of Fourier inversion techniques and randomized quasi Monte Carlo (RQMC) sampling. Rather than operating in physical space, our approach evaluates the relevant expectations appearing in the risk constraint and its optimization in the frequency domain, where the integrands exhibit enhanced smoothness properties that are well suited for RQMC integration. We establish a rigorous mathematical framework for the resulting Fourier RQMC estimators, including convergence analysis and computational complexity bounds. Beyond the single level method, we introduce a multilevel RQMC scheme that exploits the geometric convergence of the underlying deterministic optimization algorithm to reduce computational cost while preserving accuracy. Numerical experiments demonstrate that the proposed Fourier RQMC methods outperform sample average approximation and stochastic optimization benchmarks in terms of accuracy and computational cost across a range of models for the risk factors and loss structures. Consistent with the theoretical analysis, these results demonstrate improved asymptotic convergence and complexity rates relative to the benchmark methods, with additional savings achieved through the proposed multilevel RQMC construction. |
| Date: | 2026–02 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2602.06424 |
| By: | Jamel Saadaoui |
| Abstract: | This paper constructs a new identification method to quantify bilateral geopolitical shocks-geopolitical turning points- i.e., abrupt, unforeseen state-to-state political turning points. Geopolitical shocks are captured by the second difference of the Political Relationship Index (Δ²PRI), a monthly narrative-based index constructed from Chinese government and media coverage. Unlike conventional global geopolitical risk indicators, Δ²PRI separates sudden departures from bilateral diplomatic paths so causal estimation is possible in a comparative cross-national context. Quantile instrumental variable local projections (IV-LP) are applied in the paper to estimate the dynamic and asymmetric geopolitical shock impact on world oil prices. It is estimated that US-China relational improvements lower oil prices by 0.2% in the short run and increase them by 0.3% in the medium run, with larger effects at the distribution boundaries of oil prices. Replication from Japan-China data establishes external validity. The paper adds a replicable analysis framework to explain how political shocks for dyads with heterogeneous institutional history and strategic rivalry spill over into global economic instability. |
| Keywords: | geopolitical risk, oil prices, quantile local projections, instrumental variables |
| JEL: | C26 C32 F51 Q41 |
| Date: | 2026–02 |
| URL: | https://d.repec.org/n?u=RePEc:een:camaaa:2026-08 |
| By: | Mahmood Alaghmandan; Meghal Arora; Olga Streltchenko |
| Abstract: | In this paper, we present a methodology for measuring the impact of scenarios on the expected losses of exposures by leveraging the existing provisioning infrastructure within financial institutions, where scenario effects are captured through changes in probabilities of default. We then describe how to design and implement a scenario test where risk drivers are given for standardized groupings of exposures, and the groupings are defined based on common features of the exposures. The methodology presented served as a theoretical foundation for the standardized climate scenario exercise conducted in 2024 by the Office of the Superintendent of Financial Institutions of Canada and Quebec's Autorite des Marches Financiers. |
| Date: | 2026–02 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2602.01361 |
| By: | Ilias Aarab; Thomas Gottron; Andrea Colombo; J\"org Reddig; Annalauro Ianiro |
| Abstract: | Micro-structural models of contagion and systemic risk emphasize that shock propagation is inherently multi-channel, spanning counterparty exposures, short-term funding and roll-over risk, securities cross-holdings, and common-asset (fire-sale) spillovers. Empirical implementations, however, often rely on stylized or simulated networks, or focus on a single exposure dimension, reflecting the practical difficulty of reconciling heterogeneous granular collections into a coherent representation with consistent identifiers and consolidation rules. We close part of this gap by constructing an empirically grounded multilayer network for euro area significant banking groups that integrates several supervisory and statistical datasets into layer-consistent exposure matrices defined on a common node set. Each layer corresponds to a distinct transmission channel, long- and short-term credit, securities cross-holdings, short-term secured funding, and overlapping external portfolios, and nodes are enriched with balance-sheet information to support model calibration. We document pronounced cross-layer heterogeneity in connectivity and centrality, and show that an aggregated (flattened) representation can mask economically relevant structure and misidentify the institutions that are systemically important in specific markets. We then illustrate how the resulting network disciplines standard systemic-risk analytics by implementing a centrality-based propagation measure and a micro-structural agent-based framework on real exposures. The approach provides a data-grounded basis for layer-aware systemic-risk assessment and stress testing across multiple dimensions of the banking network. |
| Date: | 2026–02 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2602.10960 |
| By: | Masaaki Fukasawa |
| Abstract: | The skew stickiness ratio is a statistic that captures the joint dynamics of an asset price and its volatility. We derive a representation formula for this quantity using the It\^o-Wentzell and Clark-Ocone formulae, and we apply it to analyze its asymptotics under Bergomi-type stochastic volatility models. |
| Date: | 2026–02 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2602.05241 |
| By: | Luttini, Emiliano Evaristo; Mekonnen, Dawit Kelemework; Mercer-Blackman, Valerie; Sorensen, Bent |
| 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. The findings show that 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. |
| Date: | 2026–01–14 |
| URL: | https://d.repec.org/n?u=RePEc:wbk:wbrwps:11297 |
| By: | Evgeny Kagan; Kyle Hyndman; Andrew Davis |
| Abstract: | We use a series of pre-registered, incentive-compatible online experiments to investigate how people evaluate and choose among different waiting time distributions. Our main findings are threefold. First, consistent with prior literature, people show an aversion to both longer expected waits and higher variance. Second, and more surprisingly, moment-based utility models fail to capture preferences when distributions have thick-right tails: indeed, decision-makers strongly prefer distributions with long-right tails (where probability mass is more evenly distributed over a larger support set) relative to tails that exhibit a spike near the maximum possible value, even when controlling for mean, variance, and higher moments. Conditional Value at Risk (CVaR) utility models commonly used in portfolio theory predict these choices well. Third, when given a choice, decision-makers overwhelmingly seek information about right-tail outcomes. These results have practical implications for service operations: (1) service designs that create a spike in long waiting times (such as priority or dedicated queue designs) may be particularly aversive; (2) when informativeness is the goal, providers should prioritize sharing right-tail probabilities or percentiles; and (3) to increase service uptake, providers can strategically disclose (or withhold) distributional information depending on right-tail shape. |
| Date: | 2026–02 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2602.06263 |
| By: | Keywan Christian Rasekhschaffe |
| Abstract: | We study whether generative AI can automate feature discovery in U.S. equities. Using large language models with retrieval-augmented generation and structured/programmatic prompting, we synthesize economically motivated features from analyst, options, and price-volume data. These features are then used as inputs to a tabular machine-learning model to forecast short-horizon returns. Across multiple datasets, AI-generated features are consistently competitive with baselines, with Sharpe improvements ranging from 14% to 91% depending on dataset and configuration. Retrieval quality is pivotal: better knowledge bases materially improve outcomes. The AI-generated signals are weakly correlated with traditional features, supporting combination. Overall, generative AI can meaningfully augment feature discovery when retrieval quality is controlled, producing interpretable signals while reducing manual engineering effort. |
| Date: | 2026–01 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2602.00196 |