Hedging in Field Theory Models of the Term Structure

TL;DR

This paper applies quantum field theory methods to the HJM term structure model to evaluate hedge parameters and effectiveness, demonstrating that low-dimensional hedge portfolios can be highly effective.

Contribution

It introduces a quantum field theory approach to the HJM model, providing a novel way to calculate hedge parameters and assess hedging effectiveness.

Findings

Low-dimensional hedge portfolios are quite effective.

Path integrals facilitate hedge parameter calculations.

Hedging effectiveness is demonstrated over finite periods.

Abstract

We use path integrals to calculate hedge parameters and efficacy of hedging in a quantum field theory generalization of the Heath, Jarrow and Morton (HJM) term structure model which parsimoniously describes the evolution of imperfectly correlated forward rates. We also calculate, within the model specification, the effectiveness of hedging over finite periods of time. We use empirical estimates for the parameters of the model to show that a low dimensional hedge portfolio is quite effective.