TITLE:
Uncovering the Distribution of Option Implied Risk Aversion
AUTHORS:
Maria Kyriacou, Jose Olmo, Marius Strittmatter
KEYWORDS:
Simulation Based Risk-Aversion, Empirical Pricing Kernel, Index Options, Risk-Transformations
JOURNAL NAME:
Journal of Mathematical Finance,
Vol.9 No.2,
March
14,
2019
ABSTRACT: This paper explores the dynamics of risk aversion of a representative agent
with an iso-elastic utility function. In contrast to most of the existing literature,
we estimate the coefficient of relative risk aversion from option prices.
To do this, we transform the risk-neutral density function obtained from a
cross-section of option prices to an objective distribution function that reflects
individuals’ risk aversion through a CRRA utility function. The dynamics
of the relative risk-aversion coefficient are obtained by repeating the same
estimation procedure over rolling windows. This procedure uncovers strong
variation in risk aversion over time. We also propose a simulation procedure
to construct confidence intervals for the risk-aversion coefficient in each period.
We assess the robustness of these confidence intervals under different
assumptions on the data generating process of stock prices. The results imply
a strong influence of volatility on the variation of risk aversion. In an empirical
application, we compare the forecasting performance of our approach
based on our risk-aversion estimates against the method proposed in [1].
Overall, we find that our simulation based approach obtains better forecasting
results than bootstrap methods.