Expectation and Price in Incomplete Markets

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 minimizing the entropy of the price measure from the economic measure, subject to mark-to-market constraints, following arguments based on the optimization of portfolio risk. The approach accounts for market and funding convexities and incorporates available price information, interpolating between methodologies based on expectation and replication.

Keywords: Derivative Pricing, Funding, Discounting, Incomplete Markets, Portfolio Optimization, Entropy, Levy-Khintchine Representation

JEL Classification: G11, G12, G13, G14