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1 – 10 of over 37000Diandian Ma, Xiaojing Song, Mark Tippett and Thu Phuong Truong
The purpose of this study is to determine distributional properties of the accumulated rate of interest when the instantaneous rate of interest evolves in terms of the Cox et al.…
Abstract
Purpose
The purpose of this study is to determine distributional properties of the accumulated rate of interest when the instantaneous rate of interest evolves in terms of the Cox et al. (1985) square root process.
Design/methodology/approach
The law of iterated (or double) expectations is used to determine the mean and variance of the accumulated rate of interest on a cash management (or loan) account when interest accumulates at the instantaneous rates of interest implied by the square root process.
Findings
This study demonstrates how the accumulated rate of interest does not satisfy the strong mixing conditions necessary for convergence in distribution to the normal density function.
Originality/value
This study has strong educational value in determining distributional properties of the accumulated rate of interest when the instantaneous rate of interest evolves in terms of the Cox et al. (1985) square root process and demonstrating how the accumulated rate of interest does not satisfy the strong mixing conditions necessary for convergence in distribution to the normal density function.
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I review the burgeoning literature on applications of Markov regime switching models in empirical finance. In particular, distinct attention is devoted to the ability of Markov…
Abstract
I review the burgeoning literature on applications of Markov regime switching models in empirical finance. In particular, distinct attention is devoted to the ability of Markov Switching models to fit the data, filter unknown regimes and states on the basis of the data, to allow a powerful tool to test hypotheses formulated in light of financial theories, and to their forecasting performance with reference to both point and density predictions. The review covers papers concerning a multiplicity of sub-fields in financial economics, ranging from empirical analyses of stock returns, the term structure of default-free interest rates, the dynamics of exchange rates, as well as the joint process of stock and bond returns.
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Giuseppe Orlando, Rosa Maria Mininni and Michele Bufalo
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…
Abstract
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).
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Jang Koo Kang, Sung Hwan Kim and Chul Woo Han
This article uses a Kalman filter to fit yields of investment-grade corporate bonds to the model of instantaneous default risk, based on Duffee (1999. Review of Financial Studies…
Abstract
This article uses a Kalman filter to fit yields of investment-grade corporate bonds to the model of instantaneous default risk, based on Duffee (1999. Review of Financial Studies. 12. PP. 197-226). The first part of this article fits the term structure of default-free interest rates to a translated two-factor square-root diffusion model. The parameters in the two-factor model are estimated by using a quasi-maxirnum-likelihood estimator in a state-space model in the Korean treasury bond market. A Kalman filter is used to estimate the unobservable factors.
The two-factor model successfully incorporates random variations in the slope of the term structure and the level of interest rates‘ After estimating the default-free term structure of interest rates, the second part of this article extends the model to noncallable corporate bonds‘ This is done by assuming that the probability of default follows a translated square-root diffusion process with the possibility of being correlated with default-free interest rates. The parameters of the process are estimated for investment-grade corporate bonds including AM. AA, A. and BBB. Empirical results show that the default risk is negatively correlated with default-free interest rates and confirm that the default risk is greater for lower grades. In addition, the estimated model successfully produces the term structures of credit spreads for corporate bonds and show that the credit spreads for lower grade bonds are more steeply sloped than those for higher grade bonds. These results show that Duffee's model can reasonably account for the observed corporate bond prices in the Korean bond market.
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Giuseppe Orlando, Rosa Maria Mininni and Michele Bufalo
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…
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.
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DIMITRIS PSYCHOYIOS, GEORGE SKIADOPOULOS and PANAYOTIS ALEXAKIS
The volatility of a financial asset is an important input for financial decision‐making in the context of asset allocation, option pricing, and risk management. The authors…
Abstract
The volatility of a financial asset is an important input for financial decision‐making in the context of asset allocation, option pricing, and risk management. The authors compare and contrast four approaches to stochastic volatility to determine which is most appropriate to each of these various needs.
Diep Duong and Norman R. Swanson
The topic of volatility measurement and estimation is central to financial and more generally time-series econometrics. In this chapter, we begin by surveying models of…
Abstract
The topic of volatility measurement and estimation is central to financial and more generally time-series econometrics. In this chapter, we begin by surveying models of volatility, both discrete and continuous, and then we summarize some selected empirical findings from the literature. In particular, in the first sections of this chapter, we discuss important developments in volatility models, with focus on time-varying and stochastic volatility as well as nonparametric volatility estimation. The models discussed share the common feature that volatilities are unobserved and belong to the class of missing variables. We then provide empirical evidence on “small” and “large” jumps from the perspective of their contribution to overall realized variation, using high-frequency price return data on 25 stocks in the DOW 30. Our “small” and “large” jump variations are constructed at three truncation levels, using extant methodology of Barndorff-Nielsen and Shephard (2006), Andersen, Bollerslev, and Diebold (2007), and Aït-Sahalia and Jacod (2009a, 2009b, 2009c). Evidence of jumps is found in around 22.8% of the days during the 1993–2000 period, much higher than the corresponding figure of 9.4% during the 2001–2008 period. Although the overall role of jumps is lessening, the role of large jumps has not decreased, and indeed, the relative role of large jumps, as a proportion of overall jumps, has actually increased in the 2000s.
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Jens H. E. Christensen and Glenn D. Rudebusch
Recent U.S. Treasury yields have been constrained to some extent by the zero lower bound (ZLB) on nominal interest rates. Therefore, we compare the performance of a standard…
Abstract
Recent U.S. Treasury yields have been constrained to some extent by the zero lower bound (ZLB) on nominal interest rates. Therefore, we compare the performance of a standard affine Gaussian dynamic term structure model (DTSM), which ignores the ZLB, to a shadow-rate DTSM, which respects the ZLB. Near the ZLB, we find notable declines in the forecast accuracy of the standard model, while the shadow-rate model forecasts well. However, 10-year yield term premiums are broadly similar across the two models. Finally, in applying the shadow-rate model, we find no gain from estimating a slightly positive lower bound on U.S. yields.
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Interest rate risk, i.e. the risk of changes in the interest rate term structure, is of high relevance in insurers' risk management. Due to large capital investments in interest…
Abstract
Purpose
Interest rate risk, i.e. the risk of changes in the interest rate term structure, is of high relevance in insurers' risk management. Due to large capital investments in interest rate sensitive assets such as bonds, interest rate risk plays a considerable role for deriving the solvency capital requirement (SCR) in the context of Solvency II. This paper seeks to address these issues.
Design/methodology/approach
In addition to the Solvency II standard model, the author applies the model of Gatzert and Martin for introducing a partial internal model for the market risk of bond exposures. After introducing calibration methods for short rate models, the author quantifies interest rate and credit risk for corporate and government bonds and demonstrates that the type of process can have a considerable impact despite comparable underlying input data.
Findings
The results show that, in general, the SCR for interest rate risk derived from the standard model of Solvency II tends to the SCR achieved by the short rate model from Vasicek, while the application of the Cox, Ingersoll, and Ross model leads to a lower SCR. For low‐rated bonds, the internal models approximate each other and, moreover, show a considerable underestimation of credit risk in the Solvency II model.
Originality/value
The aim of this paper is to assess model risk with focus on bonds in the market risk module of Solvency II regarding the underlying interest rate process and input parameters.
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The time series of the federal funds rate has recently been extended back to 1928, now including several episodes during which interest rates remained near the lower bound of…
Abstract
The time series of the federal funds rate has recently been extended back to 1928, now including several episodes during which interest rates remained near the lower bound of zero. This series is analyzed, using the method of indirect inference, by applying recent research on bounded time series to estimate a set of bounded parametric diffusion models. This combination uncouples the specification of the bounds from the law of motion. Although Louis Bachelier was the first to use arithmetic Brownian motion to model financial time series, he has often been criticized for this proposal, since the process can take on negative values. Most researchers favor processes such as geometric Brownian motion (GBM), which remains positive. Under this framework, Bachelier's proposal remains valid when specified with bounds and is shown to compare favorably when modeling the federal funds rate.
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