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修正多资产股票模拟中的市场方差

文章 arXiv papers · 作者: Abdulrahman Alswaidan et al.
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总结

本研究处理合成多资产股票数据中的方差重复计算问题。当完整资产收益生成器与市场因子结合时，模拟收益可能会将市场方差计算两次。所提出的修正方法先在固定期限内对每个生成器的抽样结果进行中心化和缩放，再加入市场成分，因此无需为回归残差另行拟合生成器。

在美国股票和交易所交易基金范围内进行的测试发现，修正后的路径保留了厚尾特征，并以较低误差恢复了经校准的市场载荷。在留出的2025历史数据上，该方法相较于朴素组合提高了平均分布检验通过率，并使合成数据与观测数据的方差中位数接近1。报告的一日左尾风险价值超限率仍高于名义水平。在一种情形下，跳跃持续时间扩展改善了SPY的波动聚集表现，但将其设置迁移至留出数据后，时间拟合变差。模型未考虑残差依赖关系，这可能会夸大模拟的再平衡收益；零和约束也消除了终端残差不确定性。

核心观点

  • 将完整收益生成器与市场因子结合，可能导致市场方差被重复计算。
  • 该修正方法先在固定期限内对生成器抽样结果进行中心化和缩放，再加入市场因子。
  • 测试发现，该方法保留了厚尾特征和经校准的市场载荷，并改善了留出历史数据上的分布拟合。
  • 报告的尾部风险超限率高于名义水平，且迁移跳跃设置后留出数据的时间拟合变差。
  • 未建模的资产残差依赖可能会高估模拟再平衡收益。

标签

股票多资产机器学习统计学回测
全文
# Variance-Corrected Multi-Asset Equity Simulation with Hybrid Hidden Markov Marginals


# Variance-Corrected Multi-Asset Equity Simulation with Hybrid Hidden Markov Marginals









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.

在遵守原作品许可的前提下，附作者信息全文展示。 许可协议: abstract CC0

此摘要由 Stratmill 研究智能体根据原文撰写，并非原文副本。