基于市场的股票收益概率
Market-Based Probability of Stock Returns
AI总结：
本文提出通过市场基于的统计矩预测股票收益概率，利用统计矩和相关性推导特征函数和概率近似，以提高宏观经济模型的可靠性。
摘要：
本文描述了市场基于的收益统计矩对当前和过去交易值的统计矩和相关性的依赖性。我们使用马科维茨对投资组合的价值加权收益的定义作为平均交易期间的市场基于的平均收益的定义。然后我们推导了市场基于的波动性和收益更高统计矩对当前和过去交易值的统计矩、波动性和相关性的依赖性。我们通过有限数量q的市场基于的统计矩来推导特征函数和收益概率的近似值。为了预测时间跨度T的市场基于的平均和波动性，应该预测相同时间跨度的当前和过去交易值的前两个统计矩和相关性。我们讨论了经济原因，这些原因限制了通过前两个统计矩预测收益统计矩的数量。这限制了通过高斯近似值的准确性来预测收益概率的准确性。为了提高大型宏观经济和市场模型如BlackRock的Aladdin、摩根大通和美国联邦储备系统的可靠性，开发人员应使用基于市场的收益统计矩。
英文摘要：
This paper describes the dependence of market-based statistical moments of returns on statistical moments and correlations of the current and past trade values. We use Markowitz's definition of value weighted return of a portfolio as the definition of market-based average return of trades during the averaging period. Then we derive the dependence of market-based volatility and higher statistical moments of returns on statistical moments, volatilities, and correlations of the current and past trade values. We derive the approximations of the characteristic function and the probability of returns by a finite number q of market-based statistical moments. To forecast market-based average and volatility of returns at horizon T, one should predict the first two statistical moments and correlation of current and past trade values at the same horizon. We discuss the economic reasons that limit the number of predicted statistical moments of returns by the first two. That limits the accuracy of the forecasts of probability of returns by the accuracy of the Gaussian approximations. To improve the reliability of large macroeconomic and market models like BlackRock's Aladdin, JP Morgan, and the U.S. Fed., the developers should use market-based statistical moments of returns.
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