Heterogeneity in Beliefs and Volatility Tail Behavior

Abstract

We propose a model of volatility tail behavior in which investors display aversion to both low-volatility and high-volatility states, and hence, the derived pricing kernel exhibits an increasing and decreasing region in the volatility dimension. The model features investors who have heterogeneity in beliefs about volatility outcomes and maximize their utility by choosing volatility-contingent cash flows. Our empirical examination suggests that the model is better suited to reproduce data features in the left tail of the volatility distribution, both qualitatively and quantitatively.

The Distribution of Uncertainty: Evidence from the VIX Options Market

“…While the right part of the volatility pricing kernel is always upward sloping, the center and the left tail show different shapes. In 2006, 2007, and 2011, Figure suggests a non‐monotonic volatility pricing kernel, which is consistent with the finding in Bakshi, Madan, and Panayotov (). In particular, 2006 was characterized by unusually low levels of the VIX.…”

“…Bakshi, Madan, and Panayotov () test the monotonicity of the volatility pricing kernel. They construct time‐series of non‐overlapping option returns for different moneyness categories and investigate whether the differences between the average returns are significant or not.…”

“…Economic intuition suggests that investors dislike economic uncertainty and thus, the pricing kernel should be increasing in the volatility dimension. Bakshi, Madan, and Panayotov () find evidence for a non‐monotonicity in the volatility pricing kernel and propose a model with heterogeneous agents that features increasing and decreasing regions of the volatility pricing kernel. We find that the overall shape of the estimated volatility pricing kernel is increasing, though some of the estimates are locally decreasing.…”

“…See, for example, Jackwerth (), Rosenberg and Engle (), Beber and Brandt (), Li and Zhao (), Bakshi, Madan, and Panayotov (), and Pan ().…”

Measuring Natural Source Dependence

“…Taking heterogeneity into account is essential because it allows us to refine our understanding of specific economic mechanisms and can lead to different predictions from the ones generated with a representative agent. For instance, heterogeneity in beliefs has been shown to explain some patterns in asset pricing (Croitoru and Lu 2014), the volatility of outcomes (Bakshi et al 2015, Li 2013, speculative bubbles (Scheinkman and Xiong 2003), and political extremism (Glaeser et al 2005).…”