Recovering Risk-Neutral Probability Density Functions Using Gaussian Mixture Distributions

摘要

This paper presents a new approach to recover the implied risk-neutral probability density Junction (PDF) using Gaussian mixture distribution from options prices. Suppose the risk-neutral PDF is subjected to Gaussian mixture distribution, by minimizing the distance between the risk-neutral PDF and the physical PDF, the risk-neutral PDF is obtained. This method can avoid non-negative of the implied distribution. We test our approach using options prices data and prove the effectiveness of our methodology. The results show that the risk-neutral PDF has excess kurtosis, and a bimodal feature; a smaller peak of the left tail suggests that the approximation of lognormal distribution of underlying assets will underestimate the possibility of the loss.