Monotonicity of the Stochastic Discount Factor and Expected Option Returns
研究发现，随机贴现因子作为个股收益的函数通常是向下倾斜的，但作为指数收益的函数并非总是如此。一个跳跃扩散模型可以解释这些发现，并推导出期权交易策略平均收益的单调性检验。
Evidence shows that the stochastic discount factor (SDF) is not always a downward-sloping function of S&P 500 returns when estimated using options data. In contrast, our results suggest that SDFs as functions of individual stock returns are generally downward sloping. A simple jump-diffusion model can reconcile these empirical findings. The same model also implies a steeper implied-volatility curve for the index than for the typical stock, a well-known empirical fact from the options literature. Both the SDF and volatility-curve results can be explained by a common source of jump risk among stocks, together with diversification of Brownian risk in the index. We also devise novel empirical tests of SDF monotonicity based on average returns of option trading strategies, thus avoiding the estimation of the return density functions.