We present a two-stage lottery model with the generalized Wang transform as a probability weighting function to formally derive investors’ demand for the lottery-like security. Probability overweight on higher expected payoffs accounts for investors’ overvaluation of the security with moderately lottery-like feature, raising the demand and driving up the price. Investors’ aggressive demand is enhanced by optimistic attitude segmented from probability weighting function and weakened by probability distortion towards extreme events if considering fundamental risks. Our model predicts overpricing in small securities with optimistic investors, and implies skewness pricing and “realized kurtosis puzzle”.

我们提出了一个两阶段彩票模型，以广义 Wang 变换作为概率加权函数，以正式推导投资者对彩票类证券的需求。较高预期收益的概率超配导致投资者对具有适度彩票特征的证券估值过高，从而提高了需求并推高了价格。如果考虑基本面风险，投资者的激进需求会因概率权重函数分割的乐观态度而增强，而会因对极端事件的概率扭曲而减弱。我们的模型预测乐观投资者的小型证券定价过高，并暗示偏度定价和“已实现的峰度难题”。