Evolution of forward curves in the Heath–Jarrow–Morton framework by cubature method on Wiener space

Abstract

ABSTRACT The multi-curve extension of the Heath–Jarrow–Morton framework is a popular method for pricing interest rate derivatives and overnight indexed swaps in the post-crisis financial market. That is, the set of forward curves is represented as a solution to an initial boundary value problem for an infinite-dimensional stochastic differential equation. In this paper, we review the post-crisis market proxies for interest rate models. Then, we consider a simple model that belongs to the above framework. This model is driven by a single Wiener process, and we discretize the space of trajectories of its driver by cubature method on Wiener space. After that, we discuss possible methods for numerical solution of the resulting deterministic boundary value problem in the finite-dimensional case. Finally, we compare the obtained numerical solutions of cubature method with the classical Monte Carlo simulation.