A new approach to forecast market interest rates through the CIR model

Abstract

Purpose The purpose of this study is to suggest a new framework that we call the CIR#, which allows forecasting interest rates from observed financial market data even when rates are negative. In doing so, we have the objective is to maintain the market volatility structure as well as the analytical tractability of the original CIR model. Design/methodology/approach The novelty of the proposed methodology consists in using the CIR model to forecast the evolution of interest rates by an appropriate partitioning of the data sample and calibration. The latter is performed by replacing the standard Brownian motion process in the random term of the model with normally distributed standardized residuals of the “optimal” autoregressive integrated moving average (ARIMA) model. Findings The suggested model is quite powerful for the following reasons. First, the historical market data sample is partitioned into sub-groups to capture all the statistically significant changes of variance in the interest rates. An appropriate translation of market rates to positive values was included in the procedure to overcome the issue of negative/near-to-zero values. Second, this study has introduced a new way of calibrating the CIR model parameters to each sub-group partitioning the actual historical data. The standard Brownian motion process in the random part of the model is replaced with normally distributed standardized residuals of the “optimal” ARIMA model suitably chosen for each sub-group. As a result, exact CIR fitted values to the observed market data are calculated and the computational cost of the numerical procedure is considerably reduced. Third, this work shows that the CIR model is efficient and able to follow very closely the structure of market interest rates (especially for short maturities that, notoriously, are very difficult to handle) and to predict future interest rates better than the original CIR model. As a measure of goodness of fit, this study obtained high values of the statistics R2 and small values of the root of the mean square error for each sub-group and the entire data sample. Research limitations/implications A limitation is related to the specific dataset as we are examining the period around the 2008 financial crisis for about 5 years and by using monthly data. Future research will show the predictive power of the model by extending the dataset in terms of frequency and size. Practical implications Improved ability to model/forecast interest rates. Originality/value The original value consists in turning the CIR from modeling instantaneous spot rates to forecasting any rate of the yield curve.

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

“…and Najafi, Mehrdoust, and Shirinpour (2017) proposed some extensions of the CIR framework where a mixed fractional Brownian motion is added to account for the random part of the model. Finally, Orlando, Mininni, and (Orlando, Mininni, & Bufalo, 2019a, 2019b.…”

Interest rates forecasting: Between Hull and White and the CIR#—How to make a single‐factor model work

“…Note that the elements s in Equations (2) and (3) are the Gaussian standardized residuals of an “optimal” ARIMA model suitable chosen as follows. Consider the following set, for : where represents the Johnson transformation (1949), is the estimate of by a ARIMA( p j , i j , q j ) from a set of candidate models satisfying some conditions (see Orlando et al, 2019b, section 4.4.1), and μ j and η j are, respectively, the mean and the standard deviation of...…”

“…To forecast the next interest rates, we have to first calibrate the model, that is, the six parameters ( k , θ , σ , p , i , q ) as described above, on a fixed rolling window w of length m of historical data, say , and then, the future interest rate value , can be computed by the steps described in Orlando et al (2019b).…”

How to handle negative interest rates in a CIR framework

“…Orlando et al suggest in several papers (cf. [22][23][24]) a new framework, which they call CIR# model, that fits the term structure of interest rates. Additionally, it preserves the market volatility, as well as the analytical tractability of the original CIR model.…”