Market Implied Probability Distributions and Bayesian Skew Estimation

TL;DR

This paper explores how the volatility smile reflects market-implied probability distributions, examines the impact of smile changes, and introduces Bayesian methods and fuzzy skew visualization for better modeling with sparse data.

Contribution

It introduces Bayesian techniques for estimating skew distributions from limited market data and visualizes skew using fuzzy smile concepts.

Findings

Volatility smile translates into market-implied probability distributions.

Bayesian methods effectively estimate skew with sparse data.

Fuzzy smile provides a visual representation of skew distributions.

Abstract

We review and illustrate how the volatility smile translates into a probability distribution, the market-implied probability distribution representing believes priced in. The effects of changes in the smile are examined. Special attention is given to the effects of slope, which might appear at first counter-intuitive. We then show how Bayesian methods can be used to deal with sparse real market data. With each skew in a parametric model we associate a probability. This is illustrated with an example, for which multivariate parameter distributions are derived. We introduce the fuzzy smile (or fuzzy skew) as a visual illustration of the skew distribution.