Uncovering the Distribution of Option Implied Risk Aversion ()
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.
Share and Cite:
Kyriacou, M. , Olmo, J. and Strittmatter, M. (2019) Uncovering the Distribution of Option Implied Risk Aversion.
Journal of Mathematical Finance,
9, 81-104. doi:
10.4236/jmf.2019.92006.
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