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.

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Identifiers

ORCID for Maria Kyriacou: orcid.org/0000-0001-7996-2015

ORCID for Jose Olmo: orcid.org/0000-0002-0437-7812

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