Option Pricing in an Imperfect World

TL;DR

This paper explores asset pricing without a fixed probability measure, characterizing coherent prices, their relation to bubbles, and how to extract implied probabilities from options, supported by empirical testing.

Contribution

It introduces a framework for coherent pricing without assuming a probability measure and links it to bubbles and implied probabilities, with empirical validation.

Findings

Coherent prices are equivalent to the existence of a set of pricing measures.

Decomposition of prices reveals the role of bubbles.

Empirical non-parametric approach successfully extracts implied probabilities.

Abstract

In a model with no given probability measure, we consider asset pricing in the presence of frictions and other imperfections and characterize the property of coherent pricing, a notion related to (but much weaker than) the no arbitrage property. We show that prices are coherent if and only if the set of pricing measures is non empty, i.e. if pricing by expectation is possible. We then obtain a decomposition of coherent prices highlighting the role of bubbles. eventually we show that under very weak conditions the coherent pricing of options allows for a very clear representation from which it is possible, as in the original work of Breeden and Litzenberger, to extract the implied probability. Eventually we test this conclusion empirically via a new non parametric approach.