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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 CPT with the empirical probability distribution of U.S. equity returns. We find that overweighting of small probabilities embedded in 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 timevarying 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 (2006).
On average, "young" people underestimate whereas "old" people overestimate their chances to survive into the future. We adopt a Bayesian learning model of ambiguous survival beliefs which replicates these patterns. The model is embedded within a non-expected utility model of life-cycle consumption and saving. Our analysis shows that agents with ambiguous survival beliefs (i) save less than originally planned, (ii) exhibit undersaving at younger ages, and (iii) hold larger amounts of assets in old age than their rational expectations counterparts who correctly assess their survival probabilities. Our ambiguity-driven model therefore simultaneously accounts for three important empirical findings on household saving behavior.