Revealing the Parameter of Risk-Aversion from Option Prices when Markets are Incomplete: Theory and Evidence

Abstract

A standing assumption in the literature concerning the estimation of the parameter of relative risk aversion from option prices is that a representative investor exists. This thus assumes that markets are complete. We suggest a new methodology in order to extract the parameter of risk aversion from option prices when markets are possibly incomplete. Our estimates of the parameter of relative risk aversion ranges from 1.6 to 3.1. When it is time varying and only Calls are used, the parameter of risk aversion is shown to vary pro-cyclically with the market while the pricing kernel varies counter-cyclically. When estimated using only Puts, the parameter of risk aversion is show to vary counter-cyclically with respect to the market while the pricing kernel vary pro-cyclically. As a consequence, separating Calls from Puts help understand that the so-called Pricing Kernel Puzzle may not be a puzzle. Finally, since we took all the moneyness range available each day, the reasonable values obtained for the parameter of relative risk aversion show that puts in general, and deep-out of the money Puts in particular, are not mispriced. Market incompleteness provides a relevant explanation of their price behavior.