A 15-Factor Heath, Jarrow, and Morton Stochastic Volatility Model for the German Bund Yield Curve, Using Daily Data from August 7, 1997 through December 31, 2022

A 15-Factor Heath, Jarrow, and Morton Stochastic Volatility Model for the German Bund Yield Curve, Using Daily Data from August 7, 1997 through December 31, 2022

01/17/2023 10:56 AM

Daniel Dickler, Robert A. Jarrow, Stas Melnikov, Alexandre Telnov, Donald R. van Deventer, and Xiaoming Wang[1]

First Version: January 17, 2023

This Version: January 17, 2023

ABSTRACT

Please note: SAS Institute Inc. term structure models are updated monthly. For the most recent set of coefficients, contact [email protected]

This paper analyzes the number and the nature of factors driving the movements in the German government ("Bund") yield curve from August 7, 1997 through December 31, 2022. The process of model implementation reveals a number of important insights for interest rate modeling generally. First, model validation of historical yields is important because those yields are the product of a third-party curve fitting process that may produce spurious indications of interest rate volatility. Second, quantitative measures of smoothness and international comparisons of smoothness provide a basis for measuring the quality of simulated yield curves. Third, we outline a process for incorporating insights from the Japanese and European experience with negative interest rates into term structure models with stochastic volatility in Germany and other countries. Fourth, we compare data availability for Germany with broad international experience to measure the risk that a simulation beyond historical rate levels in Germany could go awry. Finally, we illustrate the process for comparing stochastic volatility and affine models of the term structure. We conclude that stochastic volatility models have a superior fit to the history of yield movements in the German Bund market.

We also recommend that Germany Bund interest rate risk analysis employ the full "World" 13-country term structure model rather than relying solely on German data alone.

The full copy of the paper is available here:

Kamakura-AnUpdatedHJMModelforGermany20221231v1

Footnotes

[1] SAS Institute Inc. and Kamakura Corporation, 2222 Kalakaua Avenue, Suite 1400, Honolulu, Hawaii, USA, 96815. E-Mail [email protected]. The authors wish to thank Prof. Robert A. Jarrow for 29 years of conversations on this topic. The authors are grateful to Daniel Dickler, Dr. Xiaoming Wang, and Theodore Spradlin for analytical and data-related assistance. The authors also wish to thank the participants at seminars organized by the Bank of Japan and the Federal Reserve Bank of San Francisco at which a paper addressing similar issues in a Japan and U.S. government bond context was presented.