A Theory of Equivalent Expectation Measures for Contingent Claim Returns

Abstract

This paper introduces a dynamic change of measure approach for computing the analytical solutions of expected future prices (and therefore, expected returns) of contingent claims over a finite horizon. The new approach constructs hybrid probability measures called the “equivalent expectation measures” (EEMs), which provide the physical expectation of the claim’s future price until before the horizon date, and serve as pricing measures on or after the horizon date. The EEM theory can be used for empirical investigations of both the cross-section and the term structure of returns of contingent claims, such as Treasury bonds, corporate bonds, and financial derivatives.

Keywords: Dynamic change of measure, Equivalent expectation measure, Expected returns, Risk-neutral valuation, Contingent claims

JEL Classification: G12, G13