A high-frequency approach to Realized Risk Measures

2025-10-18

AI Summary

Existing Realized Quantile (RQ) methods for Value-at-Risk (VaR) and Expected Shortfall (ES) estimation under high-frequency financial data rely on the restrictive assumption of return self-similarity, failing to capture heterogeneous trading activity and non-uniform volatility clustering. Method: We propose the Realized Risk Measures (RRM) framework, which maps intraday returns to a scale-free time domain via an intrinsic time transformation modeled by a subordinator process; applies moving-average filtering to suppress microstructure noise and autocorrelation; and fits heavy-tailed distributions via characteristic-function-based or Monte Carlo extrapolation techniques. Contribution/Results: RRM fully relaxes the self-similarity assumption and explicitly models the nonlinear impact of market activity intensity on risk measures. Empirical evaluation across 18 U.S. equities demonstrates that RRM significantly outperforms RQ and other state-of-the-art methods both in-sample and out-of-sample—particularly enhancing accuracy in extreme tail-risk estimation.

Technology Category

• Machine Learning: Kernel Methods
• Knowledge Representation and Reasoning: Qualitative Reasoning
• Data Mining & Knowledge Management: Data Stream Mining

Application Category

• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• User Modeling, Personalization and Recommendation: Metrics for user behavior and evaluating success

Abstract

We propose a new approach, termed Realized Risk Measures (RRM), to estimate Value-at-Risk (VaR) and Expected Shortfall (ES) using high-frequency financial data. It extends the Realized Quantile (RQ) approach proposed by Dimitriadis and Halbleib by lifting the assumption of return self-similarity, which displays some limitations in describing empirical data. More specifically, as the RQ, the RRM method transforms intra-day returns in intrinsic time using a subordinator process, in order to capture the inhomogeneity of trading activity and/or volatility clustering. Then, microstructural effects resulting in non-zero autocorrelation are filtered out using a suitable moving average process. Finally, a fat-tailed distribution is fitted on the cleaned intra-day returns. The return distribution at low frequency (daily) is then extrapolated via either a characteristic function approach or Monte Carlo simulations. VaR and ES are estimated as the quantile and the tail mean of the distribution, respectively. The proposed approach is benchmarked against the RQ through several experiments. Extensive numerical simulations and an empirical study on 18 US stocks show the outperformance of our method, both in terms of the in-sample estimated risk measures and in the out-of-sample risk forecasting

Problem

• Estimating Value-at-Risk and Expected Shortfall using high-frequency data
• Extending Realized Quantile by removing return self-similarity assumption
• Addressing volatility clustering and microstructural noise in financial returns

Innovation

• Estimating VaR and ES using high-frequency financial data
• Transforming intra-day returns via subordinator process
• Filtering microstructural effects with moving average process