Volatility Of Interest Rate Changes Research Articles

Corporate Takeovers And Interest Rates

This study analyzes the effect of corporate takeover announcements on the volatility of interest rate changes and on the level of interest rates over the period 1962 through 1984. The findings suggest that intercorporate takeovers increase the volatility of interest rate changes over this period. Because the increase in volatility is concentrated around the announcement of cash takeovers, the results imply that it is the mode of financing, rather than takeovers, per se, that is important of credit markets.

Modelling and Forecasting Short-Term Interest Rate Volatility: A Semiparametric Approach

This paper employs a semiparametric procedure to estimate the diffusion process of short-term interest rate. This method is compared in its ability to capture the dynamics of short rate volatility to a class of one-factor diffusion models where the conditional variance is serially correlated and levels dependent. The Monte Carlo study shows that the semiparametric approach produces more accurate volatility estimates than models that accommodate asymmetry, levels effect and serial dependence in the conditional variance. The empirical evidence based on U.S. three-month Treasury bill rates further indicates that the semiparametric procedure is better than the widely used single-factor diffusion models in forecasting the future volatility of interest rate changes. The improvement in modelling short rate volatility using the new procedure has implications for pricing interest rate derivatives.

An Extreme Value Approach to Estimating Interest-Rate Volatility: Pricing Implications for Interest-Rate Options

This paper proposes an extreme value approach to estimating interest-rate volatility, and shows that during the extreme movements of the U.S. Treasury market the volatility of interest-rate changes is underestimated by the standard approach that uses the thin-tailed normal distribution. The empirical results indicate that (1) the volatility of maximal and minimal changes in interest rates declines as time-to-maturity rises, yielding a downward-sloping volatility curve for the extremes; (2) the minimal changes are more volatile than the maximal changes for all data sets and for all asymptotic distributions used; (3) the minimal changes in Treasury yields have fatter tails than the maximal changes; and (4) for both the maxima and minima, the extreme changes in short-term rates have thicker tails than the extreme changes in long-term rates. This paper extends the standard option-pricing models with lognormal forward rates to accommodate significant kurtosis observed in the interest-rate data. This paper introduces a closed-form option-pricing model based on the generalized extreme value distribution that successfully removes the well-known pricing bias of the lognormal distribution.

Are there nonlinearities in short-term interest rates?

The present paper investigates the characteristics of short-term interest rates in several countries. We examine the importance of nonlinearities in the mean reversion and volatility of short-term interest rates. We examine various models that allow the conditional mean (drift) and conditional variance (diffusion) to be functions of the current short rate.We find that different markets require different models. In particular, we find evidence of nonlinear mean reversion in some of the countries that we examine, linear mean reversion in others and no mean reversion in some countries. For all countries we examine, there is strong evidence of the need for the volatility of interest rate changes to be highly sensitive to the level of the short-term interest rate. Out-of-sample forecasting performance of one-factor short rate models is poor, stemming from the inability of the models to accommodate jumps and discontinuities in the time series data.

Nonlinear asymmetric models of the short-term interest rate

This study introduces a generalized discrete time framework to evaluate the empirical performance of a wide variety of well-known models in capturing the dynamic behavior of short-term interest rates. A new class of models that displays nonlinearity and asymmetry in the drift, and incorporates the level effect and stochastic volatility in the diffusion function is introduced in discrete time and tested against the popular diffusion, GARCH, and level-GARCH models. Based on the statistical test results, the existing models are strongly rejected in favor of the newly proposed models because of the nonlinear asymmetric drift of the short rate, and the presence of nonlinearity, GARCH, and level effects in its volatility. The empirical results indicate that the nonlinear asymmetric models are better than the existing models in forecasting the future level and volatility of interest rate changes. © 2006 Wiley Periodicals, Inc. Jrl Fut Mark 26:869–894, 2006

Korean Treasury Bond Futures Pricing Model

This paper proposes two alternative methods which are used for pricing the theoretical value of the KTB futures on the non-traded underlying asset; first method is to use the CKLS model, under which the volatility of interest rate changes is highly sensitive to the level of the interest rate, and then employ binomial trees to compute the theoretical value of futures, second one is to use the multifactor Vasicek model considering correlations between yields-to-maturity and then employ the Monte Carlo simulation to compute it. In the empirical study on KTB303 and KTB306, an CKLS methodology is superior to the conventional KORFX method based on the cost-of-carry model in terms of the size of difference between market price and theoretical price. However, the phenomena, the price discrepancy using the KOFEX methodology is very small for all test perlod, implies that the KOFEX one is being used for the most market participants. The reasons that an multifactor Vasicek methodlogy is performed poorly in comparison to another methods are 1) the Vasicek model might be not a good model for explaining the level of interest rates, or 2) the important point considered by the most market participants may be on the volatility or interest rate, not on the correlations between yields-to-maturity.

Quasi-maximum likelihood estimates of Kiwi short-term interest rate

This paper examines various short-term interest rate models in New Zealand. We estimate ten stochastic models of short-term interest rates using Quasi-maximum Likelihood Estimation. All models examined allow the conditional mean (drift) and conditional variance (diffusion) to be functions of the current short rate. We find no evidence of mean reversion but strong evidence of the need for the volatility of interest rate changes to be highly sensitive to the level of the Kiwi short rate. Specifically, we find the conditional volatility of the Kiwi short rate is monotonically increasing with a convex shape. We also find that the dependence of the conditional volatility of the Kiwi short rate on the level of the interest rate is significantly higher than is generally assumed by the traditional models. Finally, we find that the AS model outperforms all remaining nine models, the CKLS beats seven models, except for the CEV model, whereas the CEV beats the GBM, Dothan, and the CIR VR.

Modeling the stochastic behavior of short-term interest rates: Pricing implications for discount bonds

This paper models the stochastic behavior of short-term interest rates, and determines the correct specification of the drift and diffusion functions of the spot rate process. A wide variety of one-factor diffusion and two-factor stochastic volatility models is compared in terms of their ability to capture the dynamics of interest rate volatility. The empirical evidence on the one-, three- and six-month Eurodollar deposit rates indicates that a new class of models with stochastic volatility is better than the single-factor diffusion models in forecasting the future volatility of interest rate changes. The paper extends the one-factor BDT term structure model to a two-factor setting, and presents the pricing implications for discount bonds. Monte Carlo simulation results for the implied yields of three- and six-month zero-coupon bonds imply that incorporating the so-called level and GARCH effects in volatility improves the pricing performance of the interest rate models.

Estimating the Term Structure of Interest Rate Volatility in Extreme Values

This article proposes an extreme value approach to estimating the term structure of interest rate volatility, showing that the volatility of interest rate changes is overestimated by the standard approach that uses the thin-tailed normal distribution. The volatility of maximal and minimal changes in three-, six-, and twelve-month T-bill rates is estimated over the late 1950s through the end of 1999. The empirical results indicate that the volatility of daily changes in short rates obtained from the fat-tailed generalized error distribution is almost the same as the volatility of the extremes obtained from the generalized Pareto distribution.

New solutions to the bond-pricing equation via Lie's classical method

Using Lie's classical method of group invariants, we provide new and simple solutions to the bond-pricing partial differential equation. All of our solutions satisfy the final condition for the bond price. In finding these solutions, we used one-factor interest-rate modelling, in which our short-term interest rate follows a random walk which allows the volatility of interest rate changes to be highly sensitive to the level of riskless rate, and the market price of risk is arbitrary. As well, in one of our simple solutions, the nonlinear drift of our risk-neutral interest rate contains an arbitrary function of time, which may be freely chosen.

Testing the Empirical Performance of Stochastic Volatility Models of the Short-Term Interest Rate

I introduce two-factor discrete time stochastic volatility models of the short-term interest rate to compare the relative performance of existing and alternative empiricial specificattions. I develop a nonlinear asymmmetric framework that allows for comparisons of non-nested models featuring conditional heteoskedasticity and sensitivity of the volatility process to interest rate levels. A new class of stochastic volatility models with asymmetric GARCH models. The existing models are rejected in favor of the newly proposed models because of the asymmetric drift of the short rate, and the presence of nonlinearity, asymmetry, GARCH, and level effects in its volatility. I test the predictive power of nested and non-nested models in capturing the stochastic behavior of the risk-free rate. Empirical evidence on three-, six-, and 12-month U.S. Treasury bills indicates but that two-factor stochastic volatility models are better than diffusion and GARCH models in forecasting the future level and volatility of interest rate changes.

Dynamics of the Short-Term Interest Rate after the 1979–1982 Monetary Experiment

Most of the recent empirical studies on the dynamics of the short-term interest rate focus on a period from the 1960s to the 1990s. By and large, these studies support the conclusion that interest rate volatility is highly sensitive to interest rate levels. The 1960–1990 period, however, is characterized by several distinct monetary policy regimes. Pricing interest rate sensitive-securities using model parameters estimated from any period is inappropriate unless there is a chance the Federal Reserve may readopt some abandoned operating procedures. This study focuses on the 1982–1996 period, a relatively long and stable environment of deemphasized monetary aggregates and targeted federal fund rates. The mean reversion tendency is very strong, which is in sharp contrast to the usual findings. While there is some evidence that the volatility of interest rate changes is related to interest rate levels, the sensitivity is much lower than previously reported. Finally, the Vasicek model cannot be rejected but the monthly data and the Cox, Ingersoll, and Ross model cannot be rejected by either the monthly or weekly data.

Adjusted Forward Rates as Predictors of Future Spot Rates

Prior studies indicate that the predictive power of implied forward rates for future spot rates is weak over long sample periods and typically varies dramatically across different subperiods. Fama (1976, 1984) conjectures that the low forecast power is due to a failure to control for the term premium embedded in forward rates. We show that Fama's conjecture is consistent with the data using any of four different models of the term premium. We measure the term premium using a variety of ex ante instruments, including the junk bond premium,bid-ask spreads in Treasury bills, the Standard & Poor's 500 stock index's dividend yield and the conditional volatility of interest rate changes using an Autoregressive Conditionally Heteroscedastic (ARCH) process. Forward rates adjusted for the term premium are reliable predictors of future spot rates over the entire 1963-1993 period.

The Dynamics of Short-Term Interest Rate Volatility Reconsidered

In this paper we present and estimate a model of short-term interest rate volatility that encompasses both the level effect of Chan, Karolyi, Longstaff and Sanders (1992) and the conditional heteroskedasticity effect of the GARCH class of models. This flexible specification allows different effects to dominate as the level of the interest rate varies. We also investigate implications for the pricing of bond options. Our findings indicate that the inclusion of a volatility effect reduces the estimate of the level effect, and has option implications that differ significantly from the Chan, Karolyi, Longstaff and Sanders (1992) model. Chan, Karolyi, Longstaff and Sanders (1992, CKLS) compare a number of widely used continuous-time models of the short-term interest rate. They estimate various models and compare the models in terms of their ability to capture the actual behavior of the short-term riskless rate. issue of how these models compare is important because the models differ in their implications for valuing contingent claims and hedging interest rate risk. 1 testing approach of CKLS exploits the fact that many term structure models imply dynamics for the short-term riskless rate that can be nested in one stochastic differential equation. With respect to the most successful models they conclude: The results for the tests of the one-month Treasury Bill indicate that it is critical to model volatility correctly. models that best describe the dynamics of the interest rates over time are those that allow the conditiorial volatility of interest rate changes to be highly dependent on the

Adjusted Forward Rates as Predictors of Future Spot Rates

Prior studies indicate that the predictive power of implied forward rates for future spot rates is weak over long sample periods and typically varies dramatically across different subperiods. Fama (1976, 1984) conjectures that the low forecast power is due to a failure to control for the term premium embedded in forward rates. We show that Fama’s conjecture is consistent with the data using any of four different models of the term premium. We measure the term premium using a variety of ex ante instruments, including the junk bond premium, bid-ask spreads in Treasury bills, the Standard & Poor’s 500 stock index’s dividend yield and the conditional volatility of interest rate changes using an Autoregressiv e Conditionally Heteroscedastic (ARCH) process. Forward rates adjusted for the term premium are reliable predictors of future spot rates over the entire 1963-1993 period.

An Empirical Comparison of Alternative Models of the Short‐Term Interest Rate

ABSTRACTWe estimate and compare a variety of continuous‐time models of the short‐term riskless rate using the Generalized Method of Moments. We find that the most successful models in capturing the dynamics of the short‐term interest rate are those that allow the volatility of interest rate changes to be highly sensitive to the level of the riskless rate. A number of well‐known models perform poorly in the comparisons because of their implicit restrictions on term structure volatility. We show that these results have important implications for the use of different term structure models in valuing interest rate contingent claims and in hedging interest rate risk.

An Empirical Comparison of Alternative Models of the Short-Term Interest Rate

We estimate and compare a variety of continuous-time models of the short-term riskless rate using the Generalized Method of Moments. We find that the most successful models in capturing the dynamics of the short-term interest rate are those that allow the volatility of interest rate changes to be highly sensitive to the level of the riskless rate. A number of well-known models perform poorly in the comparisons because of their implicit restrictions on term structure volatility. We show that these results have important implications for the use of different term structure models in valuing interest rate contingent claims and in hedging interest rate risk.