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.
Highlights
Recent research suggests that the level of risk aversion of investors is not constant (Barseghyan et al 2011; Guiso et al 2018), possibly due to changing inflation rates, equity premium, long-term bond risk premia, and credit spread amongst others (Brandt and Wang 2003; Danthine et al 2004; Bekaert et al 2010, 2019)
For a fixed level of the risk aversion parameter, the volatility and the skewness of the risk aversion parameter change the slope of the pricing kernel
This article develops a general equilibrium framework for pricing European options when risk aversion is random while aggregate wealth and the underlying asset have a bivariate transformed-normal distribution
Summary
Recent research suggests that the level of risk aversion of investors is not constant (Barseghyan et al 2011; Guiso et al 2018), possibly due to changing inflation rates, equity premium, long-term bond risk premia, and credit spread amongst others (Brandt and Wang 2003; Danthine et al 2004; Bekaert et al 2010, 2019). Attempts to estimate the (implicit) level of risk aversion using the option markets suggest a non-constant level of risk aversion (Jackwerth 2000; Bliss and Panigirtzoglou 2004 amongst others). In this paper we relax this assumption by deriving a general equilibrium European option pricing model where the risk aversion parameter (the curvature of the utility function) is stochastic.. (2) and (3), provided that the investor’s utility function and the distribution followed by the relevant random variables are specified These are provided, where we discuss two different scenarios: one where the distribution of the risk aversion parameter is not specified whilst in the second scenario we let the risk aversion parameter have a transformed-normal distribution
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