Forecasting interest rates through Vasicek and CIR models: A partitioning approach

• Published date: 01 July 2020
• Author: Giuseppe Orlando,Rosa Maria Mininni,Michele Bufalo
• Date: 01 July 2020
• DOI: http://doi.org/10.1002/for.2642

Received: 22 January 2019 Revised: 19 August 2019 Accepted: 25 November 2019

DOI: 10.1002/for.2642

RESEARCH ARTICLE

Forecasting interest rates through Vasicek and CIR models:

A partitioning approach

Giuseppe Orlando1,2 Rosa Maria Mininni3Michele Bufalo4

1Department of Economics and Finance,

Università degli Studi di Bari Aldo Moro,

Bari, Italy

2School of Science and Technologies,

Università degli Studi di Camerino,

Camerino, Italy

3Department of Mathematics, Università

degli Studi di Bari Aldo Moro,, Bari, Italy

4Department of Methods and Models for

Economics, Territory and Finance,

Università degli Studi di Roma La

Sapienza, Rome, Italy

Correspondence

Giuseppe Orlando, Department of

Economics and Finance, Università degli

Studi di Bari “Aldo Moro”, Via C. Rosalba

53, Bari I-70124, Italy.

Email: giuseppe.orlando@uniba.it

The aim of this paper is to propose a new methodology that allows forecasting,

through Vasicek and CIR models, of future expected interest rates based on

rolling windows from observed financial market data. The novelty, apart from

the use of those models not for pricing but for forecasting the expected rates

at a given maturity, consists in an appropriate partitioning of the data sample.

This allows capturing all the statistically significant time changes in volatility

of interest rates, thus giving an account of jumps in market dynamics. The new

approach is applied to different term structures and is tested for both models. It

is shown how the proposed methodology overcomes both the usual challenges

(e.g., simulating regime switching, volatility clustering, skewed tails) as well as

the new ones added by the current market environment characterized by low to

negative interest rates.

KEYWORDS

CIR model, interest rates, forecasting and simulation, Vasicekmodel

1INTRODUCTION

This paper has the objective of forecasting interest rates

(by maturity) from observed financial market data through

a new approach that preserves the analytical tractabil-

ity of the stochastic models describing the dynamics of

real market interest rates proposed by Vasicek (1977)

and Cox–Ingersoll–Ross (CIR; Cox, Ingersoll, & Ross,

1985). This is because of their popularity within the

financial community given their simplicity (unifacto-

rial, mean-reverting models) and their ability to provide

closed-form solutions for pricing interest rate derivatives

(Zeytun & Gupta, 2007). The idea of this work was to

overcome both the usual challenges imposed by regime

switching, volatility clustering, skewed tails, etc., as well

as the new ones added by the current market environ-

ment (particularly the need to model a downward trend

to negative interest rates). This is to be achieved by

proposing a new methodology that allows forecasting of

future expected interest rates by an appropriate partition

of the dataset and assuming that the dynamic of each

rate is represented by the Vasicek or CIR model. The

effect of partitioning the available market data into sub-

samples with an appropriately chosen probability distri-

bution is twofold: (1) to improve the calibration of the

Vasicek/CIR model's parameters in order to capture all

the statistically significant changes of variance in mar-

ket spot rates, and so to give an account of jumps;

(2) to consider only the most relevant historical period.

The distributions herein considered for the dataset par-

tition are the normal and noncentral chi-square distri-

bution. These distributions have been chosen by anal-

ogy with the steady (respectively conditional) distribution

of the interest rate process in the Vasicek (resp. CIR)

model. The performance of the new approach, tested on

weekly EUR data on bonds with different maturities,

has been carried out for both Vasicek and CIR model,

and compared with the exponentially weighted moving

average (EWMA) model in terms of forecasting error.

The error analysis highlighted a better performance of

Journal of Forecasting. 2020;39:569–579. wileyonlinelibrary.com/journal/for © 2019 John Wiley & Sons, Ltd. 569