Asset Pricing in an Imperfect World

TL;DR

This paper develops a framework for asset pricing without a fixed probability measure, incorporating market frictions and imperfections, and characterizes when prices are coherent and how they relate to bubbles and implied probabilities.

Contribution

It introduces the concept of coherent pricing in an environment without a predefined probability measure, linking it to the existence of pricing measures and option implied probabilities.

Findings

Prices are coherent iff the set of pricing measures is non-empty.

Decomposition of prices reveals the role of bubbles.

Coherent option prices enable extraction of 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 which allows, as in Breeden and Litzenberger, to extract the implied probability.