Risk Management

We Don’t Quite Know What We are Talking About When We Talk About Volatility ArXiv ID: ssrn-970480 “View on arXiv” Authors: Unknown Abstract Finance professionals, who are regularly exposed to notions of volatility, seem to confuse mean absolute deviation with standard deviation, causing an underesti Keywords: Volatility, Risk Management, Standard Deviation, Statistical Analysis Complexity vs Empirical Score Math Complexity: 3.0/10 Empirical Rigor: 8.0/10 Quadrant: Street Traders Why: The paper relies on a conceptual mathematical argument about Jensen’s inequality and the relationship between standard deviation and mean absolute deviation, but the core math is relatively simple. Empirical rigor is high due to the conducted survey (87 participants across three professional groups) with presented statistical results (frequency histograms, error ratios) and clear data collection methodology. flowchart TD A["Research Question: Do finance professionals<br>understand volatility?"] --> B["Key Methodology: Survey<br>and statistical analysis"] B --> C["Data/Inputs: Responses from<br>finance professionals"] C --> D["Computation: Calculate and compare<br>Mean Absolute Deviation vs Standard Deviation"] D --> E["Key Findings/Outcomes:<br>Confusion between MAD and SD<br>Underestimation of volatility"]

Deep Reinforcement Learning for Optimum Order Execution: Mitigating Risk and Maximizing Returns ArXiv ID: 2601.04896 “View on arXiv” Authors: Khabbab Zakaria, Jayapaulraj Jerinsh, Andreas Maier, Patrick Krauss, Stefano Pasquali, Dhagash Mehta Abstract Optimal Order Execution is a well-established problem in finance that pertains to the flawless execution of a trade (buy or sell) for a given volume within a specified time frame. This problem revolves around optimizing returns while minimizing risk, yet recent research predominantly focuses on addressing one aspect of this challenge. In this paper, we introduce an innovative approach to Optimal Order Execution within the US market, leveraging Deep Reinforcement Learning (DRL) to effectively address this optimization problem holistically. Our study assesses the performance of our model in comparison to two widely employed execution strategies: Volume Weighted Average Price (VWAP) and Time Weighted Average Price (TWAP). Our experimental findings clearly demonstrate that our DRL-based approach outperforms both VWAP and TWAP in terms of return on investment and risk management. The model’s ability to adapt dynamically to market conditions, even during periods of market stress, underscores its promise as a robust solution. ...

Wasserstein Distributionally Robust Rare-Event Simulation ArXiv ID: 2601.01642 “View on arXiv” Authors: Dohyun Ahn, Huiyi Chen, Lewen Zheng Abstract Standard rare-event simulation techniques require exact distributional specifications, which limits their effectiveness in the presence of distributional uncertainty. To address this, we develop a novel framework for estimating rare-event probabilities subject to such distributional model risk. Specifically, we focus on computing worst-case rare-event probabilities, defined as a distributionally robust bound against a Wasserstein ambiguity set centered at a specific nominal distribution. By exploiting a dual characterization of this bound, we propose Distributionally Robust Importance Sampling (DRIS), a computationally tractable methodology designed to substantially reduce the variance associated with estimating the dual components. The proposed method is simple to implement and requires low sampling costs. Most importantly, it achieves vanishing relative error, the strongest efficiency guarantee that is notoriously difficult to establish in rare-event simulation. Our numerical studies confirm the superior performance of DRIS against existing benchmarks. ...

Counterexamples for FX Options Interpolations – Part I ArXiv ID: 2512.19621 “View on arXiv” Authors: Jherek Healy Abstract This article provides a list of counterexamples, where some of the popular fx option interpolations break down. Interpolation of FX option prices (or equivalently volatilities), is key to risk-manage not only vanilla FX option books, but also more exotic derivatives which are typically valued with local volatility or local stochastic volatilility models. Keywords: FX Options, Volatility Interpolation, Local Volatility, Stochastic Volatility, Risk Management, Foreign Exchange (FX) ...

Equilibrium Liquidity and Risk Offsetting in Decentralised Markets ArXiv ID: 2512.19838 “View on arXiv” Authors: Fayçal Drissi, Xuchen Wu, Sebastian Jaimungal Abstract We develop an economic model of decentralised exchanges (DEXs) in which risk-averse liquidity providers (LPs) manage risk in a centralised exchange (CEX) based on preferences, information, and trading costs. Rational, risk-averse LPs anticipate the frictions associated with replication and manage risk primarily by reducing the reserves supplied to the DEX. Greater aversion reduces the equilibrium viability of liquidity provision, resulting in thinner markets and lower trading volumes. Greater uninformed demand supports deeper liquidity, whereas higher fundamental price volatility erodes it. Finally, while moderate anticipated price changes can improve LP performance, larger changes require more intensive trading in the CEX, generate higher replication costs, and induce LPs to reduce liquidity supply. ...

Reinforcement Learning in Financial Decision Making: A Systematic Review of Performance, Challenges, and Implementation Strategies ArXiv ID: 2512.10913 “View on arXiv” Authors: Mohammad Rezoanul Hoque, Md Meftahul Ferdaus, M. Kabir Hassan Abstract Reinforcement learning (RL) is an innovative approach to financial decision making, offering specialized solutions to complex investment problems where traditional methods fail. This review analyzes 167 articles from 2017–2025, focusing on market making, portfolio optimization, and algorithmic trading. It identifies key performance issues and challenges in RL for finance. Generally, RL offers advantages over traditional methods, particularly in market making. This study proposes a unified framework to address common concerns such as explainability, robustness, and deployment feasibility. Empirical evidence with synthetic data suggests that implementation quality and domain knowledge often outweigh algorithmic complexity. The study highlights the need for interpretable RL architectures for regulatory compliance, enhanced robustness in nonstationary environments, and standardized benchmarking protocols. Organizations should focus less on algorithm sophistication and more on market microstructure, regulatory constraints, and risk management in decision-making. ...

FX Market Making with Internal Liquidity ArXiv ID: 2512.04603 “View on arXiv” Authors: Alexander Barzykin, Robert Boyce, Eyal Neuman Abstract As the FX markets continue to evolve, many institutions have started offering passive access to their internal liquidity pools. Market makers act as principal and have the opportunity to fill those orders as part of their risk management, or they may choose to adjust pricing to their external OTC franchise to facilitate the matching flow. It is, a priori, unclear how the strategies managing internal liquidity should depend on market condions, the market maker’s risk appetite, and the placement algorithms deployed by participating clients. The market maker’s actions in the presence of passive orders are relevant not only for their own objectives, but also for those liquidity providers who have certain expectations of the execution speed. In this work, we investigate the optimal multi-objective strategy of a market maker with an option to take liquidity on an internal exchange, and draw important qualitative insights for real-world trading. ...

AI-Trader: Benchmarking Autonomous Agents in Real-Time Financial Markets ArXiv ID: 2512.10971 “View on arXiv” Authors: Tianyu Fan, Yuhao Yang, Yangqin Jiang, Yifei Zhang, Yuxuan Chen, Chao Huang Abstract Large Language Models (LLMs) have demonstrated remarkable potential as autonomous agents, approaching human-expert performance through advanced reasoning and tool orchestration. However, decision-making in fully dynamic and live environments remains highly challenging, requiring real-time information integration and adaptive responses. While existing efforts have explored live evaluation mechanisms in structured tasks, a critical gap remains in systematic benchmarking for real-world applications, particularly in finance where stringent requirements exist for live strategic responsiveness. To address this gap, we introduce AI-Trader, the first fully-automated, live, and data-uncontaminated evaluation benchmark for LLM agents in financial decision-making. AI-Trader spans three major financial markets: U.S. stocks, A-shares, and cryptocurrencies, with multiple trading granularities to simulate live financial environments. Our benchmark implements a revolutionary fully autonomous minimal information paradigm where agents receive only essential context and must independently search, verify, and synthesize live market information without human intervention. We evaluate six mainstream LLMs across three markets and multiple trading frequencies. Our analysis reveals striking findings: general intelligence does not automatically translate to effective trading capability, with most agents exhibiting poor returns and weak risk management. We demonstrate that risk control capability determines cross-market robustness, and that AI trading strategies achieve excess returns more readily in highly liquid markets than policy-driven environments. These findings expose critical limitations in current autonomous agents and provide clear directions for future improvements. The code and evaluation data are open-sourced to foster community research: https://github.com/HKUDS/AI-Trader. ...

Informative Risk Measures in the Banking Industry: A Proposal based on the Magnitude-Propensity Approach ArXiv ID: 2511.21556 “View on arXiv” Authors: Michele Bonollo, Martino Grasselli, Gianmarco Mori, Havva Nilsu Oz Abstract Despite decades of research in risk management, most of the literature has focused on scalar risk measures (like e.g. Value-at-Risk and Expected Shortfall). While such scalar measures provide compact and tractable summaries, they provide a poor informative value as they miss the intrinsic multivariate nature of risk.To contribute to a paradigmatic enhancement, and building on recent theoretical work by Faugeras and Pagés (2024), we propose a novel multivariate representation of risk that better reflects the structure of potential portfolio losses, while maintaining desirable properties of interpretability and analytical coherence. The proposed framework extends the classical frequency-severity approach and provides a more comprehensive characterization of extreme events. Several empirical applications based on real-world data demonstrate the feasibility, robustness and practical relevance of the methodology, suggesting its potential for both regulatory and managerial applications. ...

The Interplay between Utility and Risk in Portfolio Selection ArXiv ID: 2509.10351 “View on arXiv” Authors: Leonardo Baggiani, Martin Herdegen, Nazem Khan Abstract We revisit the problem of portfolio selection, where an investor maximizes utility subject to a risk constraint. Our framework is very general and accommodates a wide range of utility and risk functionals, including non-concave utilities such as S-shaped utilities from prospect theory and non-convex risk measures such as Value at Risk. Our main contribution is a novel and complete characterization of well-posedness for utility-risk portfolio selection in one period that takes the interplay between the utility and the risk objectives fully into account. We show that under mild regularity conditions the minimal necessary and sufficient condition for well-posedness is given by a very simple either-or criterion: either the utility functional or the risk functional need to satisfy the axiom of sensitivity to large losses. This allows to easily describe well-posedness or ill-posedness for many utility-risk pairs, which we illustrate by a large number of examples. In the special case of expected utility maximization without a risk constraint (but including non-concave utilities), we show that well-posedness is fully characterised by the asymptotic loss-gain ratio, a simple and interpretable quantity that describes the investor’s asymptotic relative weighting of large losses versus large gains. ...