Option Pricing with Random Risk Aversion

Luiz Vitiello, Ser-Huang Poon

Research output: Contribution to journalArticlepeer-review

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 bivariate transformed-normal distribution. Our results show that the volatility and the skewness of the risk aversion parameter change the slope of the pricing kernel, and that, 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. Also, we demonstrate that the pricing kernel may become non-monotonic for high levels of volatility and low levels of skewness of the risk aversion parameter. 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.
Original languageEnglish
Pages (from-to)1665-1684
Number of pages20
JournalReview of Quantitative Finance and Accounting
Volume58
Issue number4
DOIs
Publication statusPublished - 12 Jan 2022

Keywords

  • State-dependent risk aversion · Random risk aversion · Non-monotonic pricing kernel · Transformed normal distribution
  • State-dependent risk aversion
  • Random risk aversion
  • Transformed normal distribution
  • Non-monotonic pricing kernel

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