The Aggregation Property and its Applications to Realised Higher Moments

TL;DR

This paper introduces a unified multivariate aggregation property enabling unbiased estimation of realized higher moments and risk premia from high-frequency financial data, extending previous models and classifications.

Contribution

It develops a general multivariate aggregation property that unifies prior versions and defines new realized higher moments for unbiased risk premia estimation.

Findings

Unified multivariate aggregation property established.

New realized third and fourth moments defined.

Efficient, unbiased measurement of long-term higher-moment risk premia.

Abstract

We develop a general multivariate aggregation property which encompasses the distinct versions of the property that were introduced by Neuberger [2012] and Bondarenko [2014] independently. This way, we classify new types of model-free realised characteristics for which risk premia may be estimated without bias. We focus on the aggregation property for multivariate martingales and log martingales, and then define realised third and fourth moments which allow long-term higher-moment risk premia to be measured, efficiently and without bias, using high-frequency returns.