A Quantum Field Theory Term Structure Model Applied to Hedging

TL;DR

This paper introduces a quantum field theory extension of the HJM model for describing forward rate evolution, providing computational tools for hedging and demonstrating empirical effectiveness of low-dimensional hedge portfolios.

Contribution

It applies quantum field theory to term structure modeling, enabling efficient computation and improved hedging strategies compared to traditional models.

Findings

Field theory generalization describes imperfectly correlated forward rates.

Hedge parameters reduce to HJM counterparts under certain conditions.

Empirical data shows low-dimensional hedge portfolios are effective.

Abstract

A quantum field theory generalization, Baaquie, of the Heath, Jarrow, and Morton (HJM) term structure model parsimoniously describes the evolution of imperfectly correlated forward rates. Field theory also offers powerful computational tools to compute path integrals which naturally arise from all forward rate models. Specifically, incorporating field theory into the term structure facilitates hedge parameters that reduce to their finite factor HJM counterparts under special correlation structures. Although investors are unable to perfectly hedge against an infinite number of term structure perturbations in a field theory model, empirical evidence using market data reveals the effectiveness of a low dimensional hedge portfolio.