The Pricing Kernel Puzzle: Reconciling Index Option Data and Economic Theory

Abstract

One of the central questions in financial economics is the determination of asset prices, such as the value of a stock. Over the past three decades, research on this topic has converged on a concept called the "state-price density". However, a puzzle has arisen. On the one hand, Cox, Ingersoll, and Ross (1985) and others argue that the ratio of the state-price density to the statistical probability density, which is commonly known as the pricing kernel, should decrease monotonically as the aggregate wealth of an economy rises. On the other hand, recent empirical work on options on the S&P 500 index suggests that, for a sizable range of index levels, the pricing kernel is increasing instead of decreasing. We investigate theoretical explanations to this puzzle. Our existing work has ruled out some alternative hypotheses, such as data imperfections and methodological problems. We provide a representative agent model where volatility is a function of a second momentum state variable. This model is capable of generating the empirical patterns in the pricing kernel. We estimate the model through GMM.

Keywords: Derivatives, Asset Pricing, Option Pricing, Empirical Studies