Extraction of market expectations from risk-neutral density

Abstract

The purpose of this paper is to investigate which of the proposed parametric models for extracting risk-neutral density; among Black-Scholes Merton, mixture of two log-normals and generalized beta; give the best fit. The model that fits sample data better is used to describe different characteristics (moments) of the ex ante probability distribution. The empirical findings indicate that no matter which parametric model is used, the best fit is always obtained for short maturity horizon, but when comparing models in short-run, the mixture of two log-normals gives statistically significant smaller MSE. According to the pair-wise comparison results, the basic conclusion is that the mixture of two log-normals is superior to the other parametric models and has proven to be very flexible in capturing commonly observed characteristics of the underlying financial assets, such as asymmetries and “fat-tails” in implied probability distribution.

Keywords

• market expectation
• risk-neutral density
• mixture of log-normals