Stock returns revisited and variances hedged by machine learning
利用绝对变差主导二次变差的性质，构建收益百分比绝对值有界的模型，通过逆逻辑变换改进估计，并用机器学习方法降低动态对冲的波动性，保留方差支付作为残差。
The empirically supported property of absolute variations dominating quadratic variations are employed to motivate the construction of models with percentage returns bounded by unity in absolute value. Characteristic functions are developed for the log price relative for the new return models. The models are estimated on time series and option data and demonstrate improvements delivered by the inverse logistic transformation. Applications to pricing return variations and options on them are developed. Hedging strategies use Machine Learning methods on simulated sample spaces. It is observed that the log contract hedge introduces a high volatility dynamic hedge that theoretically may be compensated by the log contract leaving the variance contract as a residual. The Machine Learned hedge works with other functions estimated here by a Gaussian Process Regression that substantially reduces the volatility of the dynamic hedge and yet leaves, approximately, the variance payout as the residual.