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This research addresses a critical statistical error in synthetic multi-asset equity generation where naive market factor addition double-counts variance, leading to distorted risk metrics. By deriving a centering and rescaling correction for hidden Markov models with heavy-tailed emissions, the authors successfully align synthetic return distributions and volatility clustering with observed market data across hundreds of assets. The method offers a more accurate framework for stress testing and Value-at-Risk estimation without requiring separate fitting procedures for regression residuals.
Variance-Corrected Multi-Asset Equity Simulation with Hybrid Hidden Markov Marginals
arXiv:2603.10202v3 Announce Type: replace-cross Abstract: Synthetic multi-asset equity data must reproduce each asset's return distribution and its relationship with the market. Reusing a generator fitted to full asset returns creates a problem: adding its draws to a market factor counts market variance twice. We derived a correction that centers and rescales each draw over a fixed horizon before adding the market factor, allowing reuse without fitting a second generator to regression residuals. We tested the correction on 423 non-market assets in a 424-asset United States equity and exchange-traded-fund universe, using hidden Markov generators with heavy-tailed emissions. The corrected paths retained heavy tails and recovered the calibrated market loadings with low error. On 416 complete asset histories held out from 2025, the correction improved the mean Kolmogorov-Smirnov pass rate over naive composition and brought the median ratio of synthetic to observed variance close to one. Its one-day left-tail 99% Value-at-Risk exceedance rate, using thresholds pooled across separate simulated paths, was 1.12%, compared with 1.16% for the residual-fit hidden Markov comparator and a nominal rate of 1%. We also tested a jump-duration mechanism that extended visits to extreme-return states and improved volatility clustering for the broad-market exchange-traded fund with ticker SPY. The multi-asset correction remained effective with jumps enabled, but transferring the SPY jump settings improved temporal fit in training and worsened it in the 2025 holdout. The method provides a way to reuse fitted asset generators for daily-fit comparisons. Its zero-sum residual constraint removes terminal residual uncertainty, and unmodeled dependence among asset-specific residuals can lead to overstated rebalancing returns. Code, cached inputs, result summaries, and instructions for fitting the per-asset models accompany the paper.
Abstract:Synthetic multi-asset equity data must reproduce each asset's return distribution and its relationship with the market. Reusing a generator fitted to full asset returns creates a problem: adding its draws to a market factor counts market variance twice. We derived a correction that centers and rescales each draw over a fixed horizon before adding the market factor, allowing reuse without fitting a second generator to regression residuals. We tested the correction on 423 non-market assets in a 424-asset United States equity and exchange-traded-fund universe, using hidden Markov generators with heavy-tailed emissions. The corrected paths retained heavy tails and recovered the calibrated market loadings with low error. On 416 complete asset histories held out from 2025, the correction improved the mean Kolmogorov-Smirnov pass rate over naive composition and brought the median ratio of synthetic to observed variance close to one. Its one-day left-tail 99% Value-at-Risk exceedance rate, using thresholds pooled across separate simulated paths, was 1.12%, compared with 1.16% for the residual-fit hidden Markov comparator and a nominal rate of 1%. We also tested a jump-duration mechanism that extended visits to extreme-return states and improved volatility clustering for the broad-market exchange-traded fund with ticker SPY. The multi-asset correction remained effective with jumps enabled, but transferring the SPY jump settings improved temporal fit in training and worsened it in the 2025 holdout. The method provides a way to reuse fitted asset generators for daily-fit comparisons. Its zero-sum residual constraint removes terminal residual uncertainty, and unmodeled dependence among asset-specific residuals can lead to overstated rebalancing returns. Code, cached inputs, result summaries, and instructions for fitting the per-asset models accompany the paper.
Statistical Finance (q-fin.ST); Machine Learning (cs.LG); Risk Management (q-fin.RM)
arXiv:2603.10202 [q-fin.ST]
(or arXiv:2603.10202v3 [q-fin.ST] for this version)
https://doi.org/10.48550/arXiv.2603.10202 Focus to learn more arXiv-issued DOI via DataCite
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