Measuring expectations in options markets: An application to the SP500 index

TL;DR

This paper introduces a Bayesian nonparametric approach to extract the entire time-varying distribution of market implied asset prices from options data, providing a comprehensive view of market expectations for the SP500 index.

Contribution

It proposes a novel Bayesian nonparametric method using Dirichlet processes to analyze the evolution of implied distributions in options markets, surpassing traditional implied volatility measures.

Findings

Successful extraction of time-varying implied distributions

Enhanced understanding of market expectations over time

Application to SP500 options demonstrates method effectiveness

Abstract

Extracting market expectations has always been an important issue when making national policies and investment decisions in financial markets. In option markets, the most popular way has been to extract implied volatilities to assess the future variability of the underlying with the use of the Black and Scholes formula. In this manuscript, we propose a novel way to extract the whole time varying distribution of the market implied asset price from option prices. We use a Bayesian nonparametric method that makes use of the Sethuraman representation for Dirichlet processes to take into account the evolution of distributions in time. As an illustration, we present the analysis of options on the SP500 index.