A Note on Real-World and Risk-Neutral Dynamics for Heath-Jarrow-Morton Frameworks

TL;DR

This paper explores the relationship between real-world and risk-neutral interest rate dynamics within the Heath-Jarrow-Morton framework, providing verifiable deterministic conditions for their connection.

Contribution

It introduces Lipschitz-type deterministic conditions that relate real-world and risk-neutral dynamics in a general HJM model driven by Hilbert space Brownian motion and Poisson measures.

Findings

Derived verifiable conditions for measure change between dynamics

Applicable to models driven by Hilbert space-valued processes

Facilitates risk management and derivative pricing

Abstract

As a consequence of the financial crises, risk management became more important and real-world dynamics of interest-rate models moved into the focus of interest. Since risk-neutral dynamics are classically important to compute prices of financial derivatives, it is interesting when real-world dynamics can be related to risk-neutral dynamics via an equivalent change of measures. In this article we give deterministic conditions in a general Heath-Jarrow-Morton framework driven by a Hilbert space valued Brownian motion and a Poisson random measure. Our conditions are of Lipschitz type and therefore easy to verify.