Open Access
American Research Journal of Business and Management
ISSN (Online): 2379-1047
DOI: 10.46568/arjbm
A Mixture of Distributions Model for the Term Structure of Interest Rates with an Application to Risk Management
Accenture Consulting
Michael Jacobs, Jr. “A Mixture of Distributions Model for the Term Structure of Interest
Rates with an Application to Risk Management”, American Research Journal of Business and
Management; Volume 3, 2017; pp:1-17
Abstract
It is well known in the term structure literature that the normal and log-normal
distribution models are not consistent across high and low interest rate regimes, which creates
challenges for building models to measure and manage interest rate risk. In this paper we
outline a tractable approach to solving this problem based upon the theory of Black (1995),
which utilizes an “inverse-call transformation” methodology to derive “shadow rates” as
underlying drivers of observed yields, that have been shown in the literature to be more
appropriate than the standard models for the purposes forecasting and risk management with
respect to interest rate sensitive portfolios. We extend the literature by calibrating optimal
shadow rates, modeling them in a multivariate dynamic conditional correlation (DCC)
framework and applying the results to an interest rate risk management exercise, thereby
providing a useful risk management tool for both banks and their prudential supervisors. We
conclude that our mixture of normal and log-normal distributions model, utilizing optimally
calibrated shadow rates as drivers, produces the most reasonable set of simulated 1 year rate
distributions from the fitted DCC model as compared to the normal or log-normal model.
