Expectation and Price in Incomplete Markets

TL;DR

This paper introduces a novel approach to pricing in incomplete markets by minimizing the entropy of the price measure relative to the economic measure, effectively integrating market convexities and available price data.

Contribution

It proposes a new entropy-minimization framework for derivative pricing that unifies expectation-based and replication-based methods in incomplete markets.

Findings

The method accounts for market and funding convexities.

It interpolates between expectation and replication approaches.

Provides a systematic way to resolve residual ambiguity in pricing.

Abstract

Risk-neutral pricing dictates that the discounted derivative price is a martingale in a measure equivalent to the economic measure. The residual ambiguity for incomplete markets is here resolved by minimising the entropy of the price measure from the economic measure, subject to mark-to-market constraints, following arguments based on the optimisation of portfolio risk. The approach accounts for market and funding convexities and incorporates available price information, interpolating between methodologies based on expectation and replication.