A Theory of Equivalent Expectation Measures for Contingent Claim Returns

TL;DR

This paper develops a new measure change technique called equivalent expectation measures (EEMs) to analytically compute expected future prices and returns of contingent claims over finite horizons, aiding empirical analysis.

Contribution

It introduces EEMs as hybrid probability measures that unify physical and pricing expectations for contingent claims, advancing theoretical and empirical finance methods.

Findings

EEMs enable analytical solutions for expected returns.

The approach applies to various contingent claims like bonds and derivatives.

Facilitates empirical studies of return structures.

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.