Implied Risk Neutral Densities From Option Prices: Hypergeometric, Spline, Lognormal, and Edgeworth Functions

Abstract

This work examines the performance of four different methods to estimate the "true" Risk-Neutral Density functions (RNDs) using European options. These methods are the Mixture of Lognormal distributions (MLN), the Smoothed Implied Volatility Smile (SML), the Density Functional Based on the Confluent Hypergeometric function (DFCH), and the Edgeworth expansions (EE). The "true" RND is unknown, so it was generated using the stochastic Heston model and considering parameters that reflect the characteristics of the options market for the US dollar and Brazilian real exchange rate (USD/BRL). We find that the DFCH and MLN have the best performance in capturing the "true" RNDs.