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

2019 ◽  
Vol 37 (2) ◽  
pp. 267-292 ◽  
Author(s):  
Giuseppe Orlando ◽  
Rosa Maria Mininni ◽  
Michele Bufalo
Keyword(s):  
Brownian Motion ◽  
Interest Rates ◽  
Arima Model ◽  
Standard Brownian Motion ◽  
Brownian Motion Process ◽  
Cir Model ◽  
Market Data ◽  
Content Type ◽  
Standardized Residuals ◽  
Motion Process

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.

Interest rates calibration with a CIR model

2019 ◽  
Vol 20 (4) ◽  
pp. 370-387 ◽  
Author(s):  
Giuseppe Orlando ◽  
Rosa Maria Mininni ◽  
Michele Bufalo
Keyword(s):  
Interest Rates ◽  
Financial Market ◽  
Short Term ◽  
New Approach ◽  
Cir Model ◽  
Market Data ◽  
Content Type ◽  
Term Structures ◽  
Negative Interest Rates ◽  
Interest Rate Dynamics

Purpose The purpose of this paper is to model interest rates from observed financial market data through a new approach to the Cox–Ingersoll–Ross (CIR) model. This model is popular among financial institutions mainly because it is a rather simple (uni-factorial) and better model than the former Vasicek framework. However, there are a number of issues in describing interest rate dynamics within the CIR framework on which focus should be placed. Therefore, a new methodology has been proposed that allows forecasting future expected interest rates from observed financial market data by preserving the structure of the original CIR model, even with negative interest rates. The performance of the new approach, tested on monthly-recorded interest rates data, provides a good fit to current data for different term structures. Design/methodology/approach To ensure a fitting close to current interest rates, the innovative step in the proposed procedure consists in partitioning the entire available market data sample, usually showing a mixture of probability distributions of the same type, in a suitable number of sub-sample having a normal/gamma distribution. An appropriate translation of market interest rates to positive values has been introduced to overcome the issue of negative/near-to-zero values. Then, the CIR model parameters have been calibrated to the shifted market interest rates and simulated the expected values of interest rates by a Monte Carlo discretization scheme. We have analysed the empirical performance of the proposed methodology for two different monthly-recorded EUR data samples in a money market and a long-term data set, respectively. Findings Better results are shown in terms of the root mean square error when a segmentation of the data sample in normally distributed sub-samples is considered. After assessing the accuracy of the proposed procedure, the implemented algorithm was applied to forecast next-month expected interest rates over a historical period of 12 months (fixed window). Through an error analysis, it was observed that our algorithm provides a better fitting of the predicted expected interest rates to market data than the exponentially weighted moving average model. A further confirmation of the efficiency of the proposed algorithm and of the quality of the calibration of the CIR parameters to the observed market interest rates is given by applying the proposed forecasting technique. Originality/value This paper has the objective of modelling interest rates from observed financial market data through a new approach to the CIR model. This model is popular among financial institutions mainly because it is a rather simple (uni-factorial) and better model than the former Vasicek model (Section 2). However, there are a number of issues in describing short-term interest rate dynamics within the CIR framework on which focus should be placed. A new methodology has been proposed that allows us to forecast future expected short-term interest rates from observed financial market data by preserving the structure of the original CIR model. The performance of the new approach, tested on monthly data, provides a good fit for different term structures. It is shown how the proposed methodology overcomes both the usual challenges (e.g. simulating regime switching, clustered volatility and skewed tails), as well as the new ones added by the current market environment (particularly the need to model a downward trend to negative interest rates).

A stochastic process approach in setting the appropriate margin level for the TAIFEX stock index futures

2006 ◽  
Vol 32 (11) ◽  
pp. 886-902
Author(s):  
Jian‐Hsin Chou ◽  
Hong‐Fwu Yu
Keyword(s):  
Brownian Motion ◽  
Value Theory ◽  
Stock Index ◽  
Stock Index Futures ◽  
Brownian Motion Process ◽  
Content Type ◽  
Index Futures ◽  
Natural Logarithm ◽  
Motion Process ◽  
Set Up

PurposeThe main purpose of this paper is to compute the appropriate margin level for the stock index futures traded on the Taiwan Futures Exchange (TAIFEX) and, then, to examine the appropriateness of the real margin requirement set by the TAIFEX.Design/methodology/approachThis paper develops a new approach assuming the future's prices follow a geometric Brownian motion process. Compared with the extreme value theory that has been intensively used to determine the appropriate futures margin levels, one of the advantages of the present model is no need to specify the frequency at which extremes are taken.FindingsThe evidences indicate that the theoretical margins obtained by the proposed model can provide a more accurate and flexible margin level in accordance with the market volatility.Research limitations/implicationsThe main limitation of this approach is that the natural logarithm of the futures prices is assumed to follow a Brownian motion process. However, such an assumption might not be practical for financial returns.Practical implicationsThe research is helpful for the clearinghouse to set up its margins policy, especially under various conditions of volatility risks.Originality/valueThis paper proposes a theoretical procedure to set an appropriate futures margin for the TAIFEX. This paper also provides a better understanding of Taiwan's futures market that is newly launched and is useful for investors to hedge and speculate.

Random Matrices and Brownian Motion

1993 ◽  
Vol 2 (2) ◽  
pp. 157-180 ◽  
Author(s):  
William M. Y. Goh ◽  
Eric Schmutz
Keyword(s):  
Stochastic Process ◽  
Brownian Motion ◽  
Random Matrices ◽  
Characteristic Polynomial ◽  
Standard Brownian Motion ◽  
Brownian Motion Process ◽  
And Brownian Motion ◽  
Motion Process ◽  
Image Position

For T ∈ GLn (Fq), let Ωn (t, T) be the number of irreducible factors of degree less than or equal to nt in the characteristic polynomial of T. Letand suppose T is chosen from G Ln(Fq) at random uniformly. We prove that the stochastic process ≺Zn(t)≻t∈[0, 1] converges to the standard Brownian motion process W(t), as n → ∞.

L'intégrale du mouvement brownien

1993 ◽  
Vol 30 (01) ◽  
pp. 17-27
Author(s):  
Aimé Lachal
Keyword(s):  
Fourier Transform ◽  
Brownian Motion ◽  
Hitting Time ◽  
First Hitting Time ◽  
Brownian Motion Process ◽  
Classical Technique ◽  
Motion Process ◽  
Mouvement Brownien ◽  
The Law ◽  
The Right

Let be the Brownian motion process starting at the origin, its primitive and Ut = (Xt+x + ty, Bt + y), , the associated bidimensional process starting from a point . In this paper we present an elementary procedure for re-deriving the formula of Lefebvre (1989) giving the Laplace–Fourier transform of the distribution of the couple (σ α, Uσa ), as well as Lachal's (1991) formulae giving the explicit Laplace–Fourier transform of the law of the couple (σ ab, Uσab ), where σ α and σ ab denote respectively the first hitting time of from the right and the first hitting time of the double-sided barrier by the process . This method, which unifies and considerably simplifies the proofs of these results, is in fact a ‘vectorial' extension of the classical technique of Darling and Siegert (1953). It rests on an essential observation (Lachal (1992)) of the Markovian character of the bidimensional process . Using the same procedure, we subsequently determine the Laplace–Fourier transform of the conjoint law of the quadruplet (σ α, Uσa, σb, Uσb ).

scholarly journals Conditional generalized analytic Feynman integrals and a generalized integral equation

2000 ◽  
Vol 23 (11) ◽  
pp. 759-776 ◽  
Author(s):  
Seung Jun Chang ◽  
Soon Ja Kang ◽  
David Skoug
Keyword(s):  
Integral Equation ◽  
Brownian Motion ◽  
Feynman Integral ◽  
Brownian Motion Process ◽  
Feynman Integrals ◽  
Motion Process ◽  
Generalized Brownian Motion Process

We use a generalized Brownian motion process to define a generalized Feynman integral and a conditional generalized Feynman integral. We then establish the existence of these integrals for various functionals. Finally we use the conditional generalized Feynman integral to derive a Schrödinger integral equation.

scholarly journals Asymptotic Behavior of the Stochastic Rayleigh-van der Pol Equations with Jumps

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
ZaiTang Huang ◽  
ChunTao Chen
Keyword(s):  
Asymptotic Behavior ◽  
Brownian Motion ◽  
Stochastic Bifurcation ◽  
Brownian Motion Process ◽  
Van Der Pol ◽  
Limit Circle ◽  
Random Attractors ◽  
Motion Process ◽  
Van Der Pol Equations ◽  
The Stability

We study the stability, attractors, and bifurcation of stochastic Rayleigh-van der Pol equations with jumps. We first established the stochastic stability and the large deviations results for the stochastic Rayleigh-van der Pol equations. We then examine the existence limit circle and obtain some new random attractors. We further establish stochastic bifurcation of random attractors. Interestingly, this shows the effect of the Poisson noise which can stabilize or unstabilize the system which is significantly different from the classical Brownian motion process.

L'intégrale du mouvement brownien

1993 ◽  
Vol 30 (1) ◽  
pp. 17-27 ◽  
Author(s):  
Aimé Lachal
Keyword(s):  
Fourier Transform ◽  
Brownian Motion ◽  
Hitting Time ◽  
First Hitting Time ◽  
Brownian Motion Process ◽  
Classical Technique ◽  
Motion Process ◽  
Mouvement Brownien ◽  
The Law ◽  
The Right

Let be the Brownian motion process starting at the origin, its primitive and Ut = (Xt+x + ty, Bt + y), , the associated bidimensional process starting from a point . In this paper we present an elementary procedure for re-deriving the formula of Lefebvre (1989) giving the Laplace–Fourier transform of the distribution of the couple (σ α, Uσa), as well as Lachal's (1991) formulae giving the explicit Laplace–Fourier transform of the law of the couple (σ ab, Uσab), where σ α and σ ab denote respectively the first hitting time of from the right and the first hitting time of the double-sided barrier by the process . This method, which unifies and considerably simplifies the proofs of these results, is in fact a ‘vectorial' extension of the classical technique of Darling and Siegert (1953). It rests on an essential observation (Lachal (1992)) of the Markovian character of the bidimensional process .Using the same procedure, we subsequently determine the Laplace–Fourier transform of the conjoint law of the quadruplet (σ α, Uσa, σb, Uσb).

Sign in / Sign up

Export Citation Format

Share Document