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).

scholarly journals How to handle negative interest rates in a CIR framework

SeMA Journal ◽  
2021 ◽  
Author(s):  
Marco Di Francesco ◽  
Kevin Kamm
Keyword(s):  
Interest Rate ◽  
Interest Rates ◽  
Yield Curve ◽  
Analytical Formula ◽  
Market Prices ◽  
Cir Model ◽  
Term Structures ◽  
Negative Interest Rates ◽  
The Difference ◽  
Mean Variance

AbstractIn this paper, we propose a new model to address the problem of negative interest rates that preserves the analytical tractability of the original Cox–Ingersoll–Ross (CIR) model without introducing a shift to the market interest rates, because it is defined as the difference of two independent CIR processes. The strength of our model lies within the fact that it is very simple and can be calibrated to the market zero yield curve using an analytical formula. We run several numerical experiments at two different dates, once with a partially sub-zero interest rate and once with a fully negative interest rate. In both cases, we obtain good results in the sense that the model reproduces the market term structures very well. We then simulate the model using the Euler–Maruyama scheme and examine the mean, variance and distribution of the model. The latter agrees with the skewness and fat tail seen in the original CIR model. In addition, we compare the model’s zero coupon prices with market prices at different future points in time. Finally, we test the market consistency of the model by evaluating swaptions with different tenors and maturities.

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.

scholarly journals Risks and the influence of negative interest rates on economic activity: a case study of Sweden, Denmark, and Switzerland

2020 ◽  
Vol 15 (1) ◽  
pp. 30-41
Author(s):  
Liběna Černohorská ◽  
Darina Kubicová
Keyword(s):  
Time Series ◽  
Interest Rates ◽  
Granger Causality ◽  
Economic Activity ◽  
Central Banks ◽  
Time Interval ◽  
Short Term ◽  
Stock Indices ◽  
Negative Interest Rates ◽  
The Impact

The purpose of this paper is to analyze the impact of negative interest rates on economic activity in a selected group of countries, in particular Sweden, Denmark, and Switzerland, for the period 2009–2018. The central banks of these countries were among the first to implement negative interest rates to revive the economic growth. Therefore, this study analyzed long- and short-term relationships between interest rates announced by central banks and gross domestic product and blue chip stock indices. Time series analysis was conducted using Engle-Granger cointegration analysis and Granger causality testing to identify long- and short-term relationship. The first step, using the Akaike criteria, was to determine the optimal delay of the entire time interval for the analyzed periods. Time series that seem to be stationary were excluded based on the results of the Dickey-Fuller test. Further testing continued with the Engle-Granger test if the conditions were met. It was designed to identify co-integration relationships that would show correlation between the selected variables. These tests showed that at a significance level of 0.05, there is no co-integration between any time series in the countries analyzed. On the basis of these analyses, it was determined that there were no long-term relationships between interest rates and GDP or stock indices for these countries during the monitored time period. Using Granger causality, the study only confirmed short-term relationship between interest rates and GDP for all examined countries, though not between interest rates and the stock indices. Acknowledgment The paper has been created with the financial support of The Czech Science Foundation GACR 18-05244S – Innovative Approaches to Credit Risk Management.

How loan interest rate liberalization affects firms’ loan maturity structure

2014 ◽  
Vol 4 (2) ◽  
pp. 153-167 ◽  
Author(s):  
Jianfang Zhou ◽  
Jingjing Wang ◽  
Jianping Ding
Keyword(s):  
Interest Rate ◽  
Interest Rates ◽  
Manufacturing Companies ◽  
Short Term ◽  
Data Set ◽  
Content Type ◽  
Interest Rate Liberalization ◽  
Upper Limit ◽  
Maturity Structure

Purpose – After loan interest rate upper limit deregulation in October 2004, the financing environment in China changed dramatically, and the banks were eligible for risk compensation. The purpose of this paper is to focus on the influence of the loan interest rate liberalization on firms’ loan maturity structure. Design/methodology/approach – Based on Rajan's (1992) model, the authors constructed a trade-off model of how the banks choose long-term and short-term loans scales, and further analyzed banks’ loan term decisions under the loan interest rate upper limit deregulation or collateral cases. Then the authors used an unbalanced panel data set of 586 Chinese listed manufacturing companies and 9,376 observations during the period 1996-2011 to testify the theoretical conclusion. Furthermore, the authors studied the effect on firms with different characteristics of ownership or scale. Findings – The results show that the loan interest rate liberalization significantly decreases the private companies’ reliance on short-term loans and increases sensitivity to interest rates of state-owned companies’ long-term loans. But the results also show that the companies’ ownership still plays a key role on the long-term loans availability. When monetary policy tightened, small companies still have to borrow short-term loans for long-term purposes. As the bank industry is still dominated by state-owned banks and the deposit interest rate has upper limits, the effect of the loan interest rate liberalization on easing long-term credit constraints is limited. Originality/value – From a new perspective, the content and findings of this paper contribute to the study of the effect of the interest rate liberalization on China economy.

Implications of Central banks’ negative policy rates on financial stability

2018 ◽  
Vol 10 (2) ◽  
pp. 310-320
Author(s):  
Benjamin S. Kay
Keyword(s):  
Interest Rate ◽  
Interest Rates ◽  
Financial Stability ◽  
Global Economy ◽  
Content Type ◽  
Interest Rate Policy ◽  
Trade Offs ◽  
Negative Interest Rates ◽  
Rate Policy ◽  
Negative Interest Rate Policy

Purpose While central bankers have widely discussed the trade-offs of negative interest rates on monetary policy, the consequences of negative rates on financial stability are less well understood. The purpose of this paper is to examine the likely and possible financial stability consequences of a negative rates policy with particular focus on banks, short-term funding markets, foreign exchange markets, asset managers, pension funds and insurers. Design/methodology/approach It draws from international experience with negative interest rates to identify financial stability threats posed to any economy by negative interest rates, and it also highlights where the US experience is likely to differ. Findings In time, financial market threats and other logistical issues of a negative interest rate policy can be managed or overcome. Even cumulatively, these threats are likely to be small as long as the rates remain only modestly negative. However, if the rates remain negative for long periods or they become more sharply negative, the rewards of avoiding negative rates increase. Originality/value Does the negative interest rate policy directly or through these challenges of implementation present a substantial obstacle to achieving financial stability objectives? As policy rates go negative in a greater share of the global economy, the financial stability consequences remain poorly understood and under discussed.

New Zealand COVID-19 fightback prospects are positive

2020 ◽  
Keyword(s):  
New Zealand ◽  
Political Parties ◽  
Interest Rates ◽  
Financial Market ◽  
Media Coverage ◽  
Market Liquidity ◽  
Content Type ◽  
Reserve Bank ◽  
Global Demand ◽  
The Government

Significance The government has locked the country down for four weeks and legislated to borrow up 52 million dollars (30.7 million US dollars), equivalent to 17% of GDP. The Reserve Bank of New Zealand (RBNZ) is using several monetary policy tools to meet its inflation and employment targets, keep interest rates low and support financial market liquidity. Impacts Tourism, the largest export-earner, and high-earners logging and education, will suffer. Dairy, meat and horticultural exports will be shielded by continuing global demand, aided by a weak New Zealand dollar. The country heads into the COVID-19 crisis with low debt-to-GDP, but debt taken out now will take a future toll. Opposition and minor political parties will get reduced media coverage, while the September general election may be delayed.

Yen surge to question global monetary easing's effects

2016 ◽  
Keyword(s):  
Interest Rates ◽  
Central Banks ◽  
Recent Improvement ◽  
German Government ◽  
Monetary Policies ◽  
Government Bonds ◽  
Content Type ◽  
Negative Interest Rates ◽  
The Us ◽  
Fiscal Support

Significance Despite aggressive easing by both the Bank of Japan (BoJ) and the ECB, including negative interest rates, the lowering of expectations over the scale and pace of rate hikes by the US Federal Reserve (Fed) has negated their attempts to weaken their currencies and thus boost export-driven growth. This is heightening concern that ultra-loose monetary policies have passed the point where they can revive growth and inflation. Impacts Despite the recent improvement due to the oil price rebound since mid-February, sentiment towards EM currencies will remain fragile. The still strong demand for 'safe-haven' assets, such as German government bonds and gold, implies investors will remain cautious. Negative deposit rates will further undermine banks' earnings, amid persistent concerns about capital levels. Central banks will reach the limits of their capacity to promote growth without fiscal support from governments.

Weak GDP growth makes case for more easing in Japan

2016 ◽  
Keyword(s):  
Interest Rates ◽  
Public Investment ◽  
Potential Growth ◽  
Content Type ◽  
Structural Problems ◽  
Residential Investment ◽  
Negative Interest Rates ◽  
Bank Of Japan ◽  
Low Expectations ◽  
Negative Factors

Significance The previous quarter's output was revised upward to 2.0% from the original 1.7%. For the first six months, Japan has grown at a bit more than 1.1% (annualised) -- above its predicted growth trajectory, given the decline of population and workforce. The Bank of Japan (BoJ) recently estimated Japan's potential growth rate at 0.21%, and the Cabinet Office put it at 0.3%. Given such low expectations, any negative factors such as weak exports can easily cause a contraction. Impacts Higher consumption depends on higher labour income, which is undermined by the increased use of non-regular workers. Negative interest rates stimulate residential investment and a front-loaded stimulus appears to have raised public investment. Falling numbers of hours worked, while jobs increased, demonstrates structural problems in the labour market.

Mozambique’s FRELIMO will struggle to stem unrest

2018 ◽  
Keyword(s):  
Private Sector ◽  
Interest Rates ◽  
Debt Crisis ◽  
Liquefied Natural Gas ◽  
Northern Province ◽  
Local Elections ◽  
Short Term ◽  
Content Type ◽  
Democratic Movement ◽  
Private Sector Development

Significance Home to major liquefied natural gas (LNG) projects, the northern province has been beset by a spate of alleged Islamist militant attacks in recent weeks, with at least 40 people killed. While the FRELIMO government has recently trumpeted progress in the protracted peace talks with rebel movement RENAMO, worsening security problems in Cabo Delgado are threatening investments that are crucial to easing a persistent debt crisis. Impacts Private-sector development will be further hindered by high interest rates and unpaid government arrears. Cooperation between RENAMO and the Mozambique Democratic Movement (MDM) may increase ahead of the local elections. Cabo Delgado terrorism could overshadow RENAMO-linked insecurity in the short term.

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