Tails of option-implied probability distributions

Abstract

This thesis builds on and contributes to work in the field of financial risk management, specifically option-implied probability distributions. Although a number of studies have examined estimating the middle portion of probability distributions, there has not been a strong focus on the tails of the distribution, which are of particular importance in a risk management setting. As such, this study provides additional insights about these tails, by horse-racing four different tail-fitting methods. This research differs from previous studies by introducing a new, non-parametric, heuristic tail-fitting method that is similar in methodology to the consensus, most-often used method to estimate the middle portion of the probability distribution; and, by identifying which tail fitting method produces the most stable estimate with the least tail-option pricing error. In short, the non-parameterized, heuristic method, similar to the fast and stable method most commonly used to estimate the middle portion of the probability distribution, is also stable, with the least option pricing bias in the tails of the distribution.