Single stock call options as lottery tickets

This paper investigates whether the overpricing of out-of-the money single stock calls can be explained by Tversky and Kahneman's (1992) cumulative prospect theory (CPT). We argue that these options are overpriced because investors' overweight small probability events and overpay for such positively skewed securities, i.e., characteristics of lottery tickets. We match a set of subjective density functions derived from risk-neutral densities, including the CPT with the empirical probability distribution of U.S. equity returns. We find that overweighting of small probabilities embedded in the CPT explains on average the richness of out-of-the money single stock calls better than other utility functions. The degree that agents overweight small probability events is, however, strongly time-varying and has a horizon effect, which implies that it is less pronounced in options of longer maturity. We also find that time-variation in overweighting of small probabilities is strongly explained by market sentiment, as in Baker and Wurgler (2007).