Cointegration in continuous time for factor models

TL;DR

This paper develops a framework for cointegration in multivariate continuous-time stochastic processes, especially applied to commodity markets, incorporating factor models and operator theory for analyzing spot and forward prices.

Contribution

It introduces a novel continuous-time cointegration concept for factor models in finite and infinite dimensions, with applications to commodity markets and existing pricing models.

Findings

Provides a comprehensive framework for continuous-time cointegration.

Includes examples with popular pricing models like Heath-Jarrow-Morton.

Analyzes cointegration in both spot and forward commodity prices.

Abstract

We develop cointegration for multivariate continuous-time stochastic processes, both in finite and infinite dimension. Our definition and analysis are based on factor processes and operators mapping to the space of prices and cointegration. The focus is on commodity markets, where both spot and forward prices are analysed in the context of cointegration. We provide many examples which include the most used continuous-time pricing models, including forward curve models in the Heath-Jarrow-Morton paradigm in Hilbert space.