Efficient simulation and calibration of general HJM models by splitting schemes

TL;DR

This paper presents high-order weak approximation schemes for HJM interest rate models that enable efficient simulation and calibration, leveraging QMC methods and weighted function spaces to handle real-world complexities.

Contribution

Introduces novel splitting schemes for HJM models that improve computational efficiency and enable practical calibration using QMC and weighted spaces.

Findings

Reduced computational complexity compared to multi-level Monte Carlo methods.

Effective calibration of HJM models to caplet data.

Applicable to unbounded payoffs and characteristics in real-world scenarios.

Abstract

We introduce efficient numerical methods for generic HJM equations of interest rate theory by means of high-order weak approximation schemes. These schemes allow for QMC implementations due to the relatively low dimensional integration space. The complexity of the resulting algorithm is considerably lower than the complexity of multi-level MC algorithms as long as the optimal order of QMC-convergence is guaranteed. In order to make the methods applicable to real world problems, we introduce and use the setting of weighted function spaces, such that unbounded payoffs and unbounded characteristics of the equations in question are still allowed. We also provide an implementation, where we efficiently calibrate an HJM equation to caplet data.