Estimating and Interpreting Probability Density Functions

This paper examines two approaches to estimating implied risk-neutral probability density functions from the prices of European-style options. It sets up a monte carlo test to evaluate alternative techniques’ ability to recover simulated distributions based on Heston’s (1993) stochastic volatility model. The paper tests both for the accuracy and stability of the estimated summary statistics from RNDs. We find that a method based on interpolating the volatility smile outperforms the commonly used parametric approach that uses a mixture of lognormals.