Why Does Implied Risk Aversion Smile?

A multi-horizon comparison of density forecasts for the S&P 500 using index returns and option prices

“…Ziegler (2007) provides a detailed theoretical analysis of several potential explanations of this empirical conclusion. 19 Consequently, all our transformations from risk-neutral to real-world densities can be reinterpreted as methods that jointly estimate risk premia and remove the systematic overpricing of option contracts.…”

“…They find that ex post, real-world densities for the S&P 500 and FTSE 100 indices are a significant improvement upon their risk-neutral densities; Anagnou-Basioudis et al (2005), Kang and Kim (2006) and Liu et al (2007) provide further utility-based results for these markets. However, as empirical estimates of implied risk aversion are incompatible with a standard consumption-based framework (Jackwerth, 2000;Rosenberg and Engle, 2002;Ziegler, 2007), standard utility transformations are unlikely to provide completely satisfactory real-world densities. Liu et al (2007) estimate the two parameters of a more flexible transformation, by maximizing the ex post likelihood of the index levels on monthly, option expiry dates.…”

Option-implied risk preferences: An extension to wider classes of utility functions

“…The first method is to derive the risk aversion functions by joint estimation of risk neutral PDFs (RN-PDFs) and subjective PDFs. Most research on option-implied risk preferences including Jackwerth (2000), Ait-Sahalia and Lo (2000), Coutant (1999), Luis (2001), Perignon and Villa (2002), Rosenberg and Engle (2002), Kliger and Levy (2002), Giamouridis (2003) and Ziegler (2003) falls into this category. When using this method, subjective PDFs are mostly estimated from historical time series of underlying asset returns under stationary assumptions or stochastic process assumptions.…”

Market pricing of executive stock options and implied risk preferences

“…This is justified by Ziegler (2007). He shows that if traders have homogenous beliefs, implied risk aversion at market level is the weighted harmonic mean of individual preferences, and the weights are determined by individual consumption shares.…”

“…(3.11), which in turn gives the Aït-Sahalia and Lo (2000) estimator (3.12). Ziegler (2007) shows that risk aversion estimates are quite sensitive to errors in density estimation. In his example a small error in estimated standard deviation leads to a large perturbation in risk aversion estimates.…”