A New Approach to CIR Short-Term Rates Modelling

Orlando, Giuseppe; Mininni, Rosa Maria; Bufalo, Michele

doi:10.1007/978-3-319-95285-7_2

Cited by 18 publications

(17 citation statements)

References 14 publications

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“…In Orlando, Mininni, and Bufalo () we carried out a qualitative analysis of a dataset based on monthly observed spot rates and showed that the most challenging task is to fit money market interest rates, due to the largest presence of close‐to‐zero and/or negative spot rate values. For this reason, we start to examine samples of interest rates with maturity from Dataset II.…”

Section: Methodsmentioning

confidence: 99%

“…In Orlando et al () we hypothesized the empirical distribution of the observed data sample to be a mixture of normal distributions for the presence of negative interest rate values. This hypothesis is appropriate because in the Vasicek model the interest rate process

r

has a steady normal distribution, as already observed in Section .…”

Section: The Model: Procedures and Accuracymentioning

confidence: 99%

“…In the present work, among many approaches existing in the literature to estimate the parameters of a SDE (see, for instance, Poletti Laurini & Hotta, , and references therein), we applied the estimating function approach for ergodic diffusion models introduced in Bibby, Jacobsen, and Sørensen (), which turned out to be very useful in obtaining optimal estimators for the parameters of discretely sampled ergodic Markov processes, whose likelihood function is usually not explicitly known. In Orlando et al () a better performance of the latter method is shown by comparing its efficiency with the maximum likelihood estimation routine implemented in MATLAB for the CIR process by Kladívko (). In (Bibby et al, ), example 5.4 the authors constructed an approximately optimal estimating function for the CIR model, from which they derived the following explicit estimators of the three parameters

κ, θ, σ

based on a sample of

n

observed market spot rates

false(r_{1}, \dots, r_{n} false)

\begin{matrix} right {\hat{κ}}_{n} & left = - \ln (\frac{(n - 1) \sum_{i = 2}^{n} r_{i} / r_{i - 1} - (\sum_{i = 2}^{n} r_{i}) (\sum_{i = 2}^{n} r_{i - 1}^{- 1})}{{(n - 1)}^{2} - (\sum_{i = 2}^{n} r_{i - 1}) (\sum_{i = 2}^{n} r_{i - 1}^{- 1})}), & right \\ right {\hat{θ}}_{n} & left = \frac{1}{(n - 1)} \end{matrix}

…”

Section: The Model: Procedures and Accuracymentioning

confidence: 99%

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

Orlando

Mininni

Bufalo

2020

Journal of Forecasting

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The aim of this paper is to propose a new methodology that allows forecasting, through Vasicek and CIR models, of future expected interest rates (for each maturity) 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 performance of the new approach is carried out for 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, etc.) as well as the new ones added by the current market environment characterized by low to negative interest rates.

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Section: Methodsmentioning

confidence: 99%

r

has a steady normal distribution, as already observed in Section .…”

Section: The Model: Procedures and Accuracymentioning

confidence: 99%

κ, θ, σ

based on a sample of

n

observed market spot rates

false(r_{1}, \dots, r_{n} false)

\begin{matrix} right {\hat{κ}}_{n} & left = - \ln (\frac{(n - 1) \sum_{i = 2}^{n} r_{i} / r_{i - 1} - (\sum_{i = 2}^{n} r_{i}) (\sum_{i = 2}^{n} r_{i - 1}^{- 1})}{{(n - 1)}^{2} - (\sum_{i = 2}^{n} r_{i - 1}) (\sum_{i = 2}^{n} r_{i - 1}^{- 1})}), & right \\ right {\hat{θ}}_{n} & left = \frac{1}{(n - 1)} \end{matrix}

…”

Section: The Model: Procedures and Accuracymentioning

confidence: 99%

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

Orlando

Mininni

Bufalo

2020

Journal of Forecasting

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“…In the Orlando et al (2018b) we performed a qualitative analysis on these data sets. We found that the most challenging task was to fit interest rates from Dataset I for both currencies, because of the presence of next-to-zero and/or negative rates values.…”

Section: The Cir# Modelmentioning

confidence: 99%

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

Orlando

Mininni

Bufalo

2019

SEF

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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.

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“…For each maturity, interest rates are recorded on monthly basis from 31 December 2010 to 29 July 2016 for a total number of 68 datapoints. In the book [30](2018) we performed a qualitative analysis on this dataset. We found that the most challenging task was to fit short-term interest rates with maturity 1/360A, 30/360A, 60/360A, 90/360A, 120/360A,..., 360/360A, respectively, due to the presence of next-to-zero and/or negative spot rate values.…”

Section: The Datasetmentioning

confidence: 99%

On The Calibration of Short-Term Interest Rates Through a CIR Model

Orlando,

Mininni,

Bufalo

2018

Preprint

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It is well known that the Cox-Ingersoll-Ross (CIR) stochastic model to study the term structure of interest rates, as introduced in 1985, is inadequate for modelling the current market environment with negative short interest rates. Moreover, the diffusion term in the rate dynamics goes to zero when short rates are small; both volatility and long-run mean do not change with time; they do not fit with the skewed (fat tails) distribution of the interest rates, etc. The aim of the present work is to suggest a new framework, which we call the CIR# model, that well fits the term structure of short interest rates so that the market volatility structure is preserved as well as the analytical tractability of the original CIR model.

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A New Approach to CIR Short-Term Rates Modelling

Cited by 18 publications

References 14 publications

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

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

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

On The Calibration of Short-Term Interest Rates Through a CIR Model

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