Option smiling when investors’ estimates of asset volatility disagree

Abstract

This study sheds light on why heterogeneous beliefs in volatility manifest the smile effect of options and how the degree of belief disagreement influences option-implied volatility. It is found that when investors’ level of heterogeneous beliefs increases, agents who over estimate volatility raise their subjective probability about those outer dividend states and hence increase more consumption to those states. As a result, an increase of consumption causes a decrease of their marginal rate of transformation in outer states. The raising subjective probability increases the prices of outer states, while the lower marginal rate of transformation decreases the prices of that. However, the influence of the former dominates the latter, causing a fatter tail of the state-price density. As a consequence, the values increase for those call options with high strike prices and put options with low strike prices, leading to a U-shaped implied volatility and hence causes a smell effect.

Keywords:

• heterogeneous beliefs
• smile effect
• option price
• volatility
• state-price density

JEL Classification:

• G12
• G19

Notes

¹ Percentage of institutional trading = 1/2(Total institutional buying volume + Total institutional selling volume)/Total trading volume.