Option Pricing with Random Risk Aversion

Abstract

Based on a standard general equilibrium economy, we develop a framework for pricing European options where the risk aversion parameter is state dependent and aggregate wealth and the underlying asset have a bi-variate transformed-normal distribution. Our results show that the pricing kernel may become non-monotonic for high levels of volatility and low levels of skewness of the risk aversion parameter. Also, as the volatility of the risk aversion parameter increases, the (Black and Scholes) implied volatility shifts upwards but its shape remains the same, which implies that the volatility of the risk aversion parameter does not change the shape of the risk neutral distribution. Finally, an empirical example shows that the estimated volatility of the risk aversion parameter tends to be low in periods of high market volatility and vice-versa.

Keywords: State-Dependent Risk Aversion, Random Risk Aversion, Non-Monotonic Pricing Kernel, Transformed Normal Distribution

JEL Classification: G12, G13, G22