Shape Invariant Modeling of Pricing Kernels and Risk Aversion

The pricing kernel puzzle: survey and outlook

“…Similarly, but using a slightly different technique, Grith, Haerdle, and Park (2013) The authors conclude that the locally risk loving behavior is pro-cyclical as the hump of the empirical pricing kernel seems to be more pronounced in calm periods.…”

Reference Dependent Preferences and the EPK Puzzle

“…Several studies report the shape of the pricing kernel as being hump-shaped for most months between 2004 and 2007. This holds for both the German DAX 30 index Giacomini and Härdle (2008); Grith et al (2012) and the American S&P 500 index Barone-Adesi et al (2013); Beare and Schmidt (2012); Polkovnichenko and Zhao (2012).…”

“…In this sense the authors find that the hump-shaped pricing kernel stems from a mix of optimistic overconfident and pessimistic underconfident agents. Grith et al (2012) use the shape invariant model, a semi-parametric approach for multiple curves with shape-related nonlinear variation, to model the dynamics of the empirical pricing kernel (EPK) based on the hump feature. The approach allows to summarize the nonlinear variability with a few interpretable parameters that can be used to conduct a further analysis that links the shape of the pricing kernel to the business condition.…”

Pricing the (European) option to switch between two energy sources: An application to crude oil and natural gas

“…It is well known that historical and risk neutral densities of probability differ by a pricing kernel (Barone-Adesi et al, 2013;Campbell and Cochrane, 1999;Christoffersen et al, 2013). Such pricing kernel reflects agents' risk aversion (Bliss and Panigirtzoglou, 2004;Grith et al, 2013). Moreover, the risk neutral density of proability often exhibits fatter tail than the historical probability density (Abken et al, 1996;Ait-Sahalia and Lo, 1998;Bates, 2000Bates, , 2003.…”