Abstract
Based on the consumption-based model, if we have asset’s payoff function and a stochastic discount factor or called it pricing kernel, the expectation of product of payoff and pricing kernel is our asset price. General speaking, there are two methods to estimate pricing kernel: one is inter-temporal marginal rate of substitution, and the other is probability density function that is usually employed in empirical research. However, empirical research suggests that pricing kernel is U-shaped or negative on certain condition, which violates the characteristics of marginal rate of substitution. Researchers call this “pricing kernel puzzle.” Jackwerth (2004) thought the pricing kernel puzzle was attributed to incorrect belief from investors or called it market sentiment, So Barone-Adesi, Mancini and Shefrin (2012) explained the puzzle with market sentiment in inter-temporal marginal rate of substitution method. In this paper, we try to explain the puzzle with market sentiment in probability density function method. We employ mixture lognormal distribution proposed by Ritchy (1990) as risk-neutral density to obtain the pricing kernel with market sentiment, and we find out VIX is a good representative market sentiment proxy to explain the puzzle.