Risk Metrics

From fair price to fair volatility: Towards an Efficiency-Consistent Definition of Financial Risk ArXiv ID: 2508.11649 “View on arXiv” Authors: Sergio Bianchi, Daniele Angelini, Massimiliano Frezza, Augusto Pianese Abstract Volatility, as a primary indicator of financial risk, forms the foundation of classical frameworks such as Markowitz’s Portfolio Theory and the Efficient Market Hypothesis (EMH). However, its conventional use rests on assumptions-most notably, the Markovian nature of price dynamics-that often fail to reflect key empirical characteristics of financial markets. Fractional stochastic volatility models expose these limitations by demonstrating that volatility alone is insufficient to capture the full structure of return dispersion. In this context, we propose pointwise regularity, measured via the Hurst-Holder exponent, as a complementary metric of financial risk. This measure quantifies local deviations from martingale behavior, enabling a more nuanced assessment of market inefficiencies and the mechanisms by which equilibrium is restored. By accounting not only for the magnitude but also for the nature of randomness, this framework bridges the conceptual divide between efficient market theory and behavioral finance. ...

To Trade or Not to Trade: An Agentic Approach to Estimating Market Risk Improves Trading Decisions ArXiv ID: 2507.08584 “View on arXiv” Authors: Dimitrios Emmanoulopoulos, Ollie Olby, Justin Lyon, Namid R. Stillman Abstract Large language models (LLMs) are increasingly deployed in agentic frameworks, in which prompts trigger complex tool-based analysis in pursuit of a goal. While these frameworks have shown promise across multiple domains including in finance, they typically lack a principled model-building step, relying instead on sentiment- or trend-based analysis. We address this gap by developing an agentic system that uses LLMs to iteratively discover stochastic differential equations for financial time series. These models generate risk metrics which inform daily trading decisions. We evaluate our system in both traditional backtests and using a market simulator, which introduces synthetic but causally plausible price paths and news events. We find that model-informed trading strategies outperform standard LLM-based agents, improving Sharpe ratios across multiple equities. Our results show that combining LLMs with agentic model discovery enhances market risk estimation and enables more profitable trading decisions. ...