A cyclical square-root model for the term structure of interest rates

Fixed rate endowment mortgages differ from fixed rate repayment mortgages primarily because, in the event of early termination, the amount owed by the borrower is a function of the evolution of the term structure of interest rates, whereas for a repayment mortgage it is pre-determined. We use a contingent claims framework for valuing the embedded options in certain British fixed-rate endowment mortgages, with a (capped) mortgage indemnity guarantee (MIG). We assume a mean-reverting interest rate and a lognormal house price diffusion process to arrive at a partial differential equation as the basis of the contingent claims and include conventional mortgage terms such as arrangement fees and prepayment penalties. This methodology provides a template for the borrower, lender and insurer to compare mortgage terms, including the fairness of contract rates, fees and any MIG premiums required, when borrowing more than 75% of the house value at origination. Given the conventional terms and the diffusion processes, we assume the parties have common expectations for some diffusion parameters, including expected future rate and price volatilities. Also we assume that borrowers are 'economic actors' regarding default and prepayment options, and that factors such as mobility, divorce, unemployment, and transaction costs are deterministic and can be ignored in this model, along with moral hazard problems between the insurer and the lender. Since the partial differential equation incorporating the general features of these mortgage contracts does not have a closed-form solution, an explicit finite difference method is used for the valuation (and sensitivity) results. We provide graphical representations (and interpretations) of each mortgage component as a function of house prices and interest rate levels. After empirical studies on the input parameters, each mortgage component may be compared with 'market values'. This model may also be useful as a 'mark-to-value' proxy for all parties, as expected parameters change (especially interest rate and house price levels, and expected future volatilities), for purposes of determining 'value added accounting', appropriate reserves, and indeed for setting premiums and business decisions. Finally, we compare endowment and repayment mortgages for different levels of loan-to-value ratios, interest rate and house price volatility.

Short‐term interest rate processes determine the term structure of interest rates in an arbitrage‐free market and are central to the valuation of interest rate derivatives. We obtain parameter estimates and compare the empirical fit of alternative one‐factor continuous‐time processes for the South African short‐term interest rate (and hence of arbitrage‐free term structure models) using Gaussian estimation methods. We find support only for diffusions where the interest rate volatility is moderately sensitive to the level of the interest rate. Other common models with restrictions that either preclude this effect, or restrict it to be too high, do not fit the data. Differences in the specification of the drift function have no evident effect on model performance.

This chapter is devoted to stochastic interest rate models. Since the 1970s stochastic interest rate models have played a central role in Finance, not only in research but also in practical applications. These models were immediately implemented by practitioners to accurately price financial securities, like interest rate derivatives. Their pricing, however, was mathematically far more demanding than equity pricing, due to the fact that the whole term structure of interest rates and its development over time was required.

PurposeAims to investigate whether the level and volatility of interest rates affect the excess returns of major Asian listed property markets within a time‐varying risk framework.Design/methodology/approachA three‐factor model is employed with excess return volatility, interest rate level and interest rate volatility as its factors. The generalized autoregressive conditionally heteroskedasticity in the mean (GARCH‐M) analyzes are undertaken on monthly excess returns of property stock indexes for the period 1987‐2003.FindingsProperty stocks are generally sensitive to changes in the long‐term and short‐term interest rates and to a lesser extent, their volatility. Moreover, there are disparities in the magnitude as well as direction of sensitivities in interest rate level and volatility across the listed property markets and under different market conditions. Overall, results indicate changes in the ARCH parameter, risk premia, volatility persistence and interest rate level and volatility effects before and after the 1997 Asian financial crisis. However, these noted changes are not uniform and depend on the individual listed property markets.Originality/valueThe findings enhance investors' understanding in financial asset pricing and complement existing evidence in international real estate. With the increasing significance of property stocks as real estate investment vehicles for international investors to gain property exposure in Asia and internationally, the paper is timely and provides the basis for more advanced research in international real estate investment strategies and capital asset pricing.

We examine and test the validity of the expectation hypothesis of the term structure (EHTS) of interest rates in Saudi Arabia using the traditional single equation approach, Campbell and Shiller methodology, Error Correction Model, and monthly data over the period June 1983 to December 2014. The results of the single equation approach indicate that the test of validity of the expectation hypothesis cannot be rejected for all maturities. We also find that the validity of the EHTS of interest rates is supported through the stationarity of the term spreads between short- and long-term interest rates. Moreover, the cointegration test reveals the existence of a cointegration relationship between short- and long-term interest with ( 1 − 1 ) $\left(1-1\right)$ cointegrating vector, suggesting the validity EHTS of interest rates. Policy implications based on the empirical results suggest that the transparency of monetary policy in Saudi Arabia and the effective role of the Saudi Arabian Monetary Authority (SAMA) in conducting monetary policy increase the predictive power of market participants of future movements of short-term interest rates.

Government Bonds and the Term Structure of Interest Rates

The aim of this paper is twofold; first we concentrate on the work of Vasicek (1977) and Cox, Ingersoll and Ross (1985). We examine and test empirically each model and discuss its performance in predicting the term structure of interest rates using a parametric estimating approach GMM (Generalized Moments Method). Second we estimate the term structure of interest rate dynamics using a nonparametric approach ANN (Artificial Neural Network). Two neural network models are performed. The first model uses spreads between interest rates of 10 different maturities as the only explanatory variable of interest rate changes. The second model introduces two factors, spreads and interest rates' levels. Using historical U.S. Treasury bill rates and Treasury bond yields, we compare the ability of each model to predict the term structure of interest rates. Data are daily and cover the period from 3 January 1995 to 29 December 2000. Results suggest that neural network, Vasicek (1977) and Cox, Ingersoll and Ross (1985) models generate different yield curves. Neural network models outperform the parametric standard models. The most successful forecast is obtained with a two factors neural network model.

Term Structure of Interest Rates. Review of a Theory of the Term Structure of Interest Rates (CIR)

Most reported stochastic volatility (SV) model for interest rates only deals with an AR specification for the latent factor process. We show in this paper the technical details for specifying the SV model for interest rates that includes an ARMA structure, a jump component and additional exogenous variables for the latent factor process. We demonstrate the efficacy of this approach with an application to the US short-term interest rate data. We find that the elasticity parameter of the variance is closer to 0.5, i.e., similar to that of the Cox–Ingersoll–Ross (1985) model of interest rates. This is quite a contrast to the finding Chan et al. [Chan, KC, GA Karolyi, F Longstaff and A Sanders (1992). The volatility of short-term interest rates: An empirical comparison of alternative models of term structure of interest rates, Journal of Finance, 47, 1209–1227]. who found the elasticity to be close to 1.5.

Dai and Singleton (2002) and Duffee (2002) show that there is a tension in affine term structure models between matching the mean and the volatility of interest rates. This article examines whether this tension can be solved by an alternative parametrization of the price of risk. The empirical evidence suggests that, first, the examined parametrization is not sufficient to solve the mean-volatility tension. Second, the usual result in the estimation of affine models, indicating that some of the state variables are extremely persistent, may have been caused by the lack of flexibility in the parametrization of the price of risk. Term structure models have several uses, including pricing fixed-income derivatives, managing the risk of fixed-income portfolios, and detecting relationships between the term structure of interest rates and macrovariables such as inflation and consumption. To perform well in these tasks, term structure models must be numerically and econometrically tractable while matching the empirical properties of the term structure movements. At least two empirical properties of the term structure of interest rates have been well established by financial economists over the years [see Dai and Singleton (2003) for a survey]. First, the term premium, or the expected excess return of Treasury bonds, has a high time variability. Second, the volatility of interest rates is time varying. These two properties are so prominent in the data that they will be referred to as stylized facts. While these two stylized facts are very well established in the empirical literature, affine term structure models are thoroughly discussed in the theoretical literature. Affine models are those in which the yield of zero coupon bonds are affine functions of the model state variables. Classic

On the Information in the Interest Rate Term Structure and Option Prices

At present, China is in the critical stage of transforming from a quantitative monetary policy to a price-based monetary policy. The implementation of a quantitative-price mixed monetary policy can further improve the effect of monetary policy and interest rate regulation and maintain the stable operation of the macro economy. Based on the current economic situation, this article conducts experiments to prove the relationship between its monetary policy and the term structure of interest rates. To this end, this article first analyzes and compares the final effects of monetary policy on regional economies with the aid of an analysis framework that can simultaneously take into account the individuality of regional economies, the spillover effects between regional economies and the overall nature of monetary policy. Then, this article further combines the current background of interest rate marketization and monetary policy from quantity-oriented price-oriented changes. Focusing on the interest rate channel, it deeply analyzes the regional effects and formation of China's monetary policy under the new situation. First of all, on the basis of combing and summarizing relevant literature, find the expansion space for evaluating the regional effect of China's monetary policy. Experimental research results show that the term structure of interest rates is playing an increasingly important role in monetary policy. Combining the study of the term structure of interest rates with monetary policy and examining the relationship between them can not only promote the role of interest rates in macro-control, but also have important implications for improving the forward-looking and effectiveness of monetary policy.

This article presents empirical evidence on the effect of regular Central Bank of Brazil (CBB) communication on volatility and the direction of the interest rates futures market. The volatility of interest rates in the financial market is observed before and after publication of regular CBB communication. Moreover, the period without publication (purdah period) is also considered. Hence, this article combines, in an original manner, the idea presented by Ehrmann and Fratzscher for evaluation of the impact of communication on financial market expectation, and the model developed by Kuttner, for analysis concerning the expectations hypothesis of the term structure of interest rate. The findings support the idea that CBB communication has an effect on expectations of changes in the interest rates and in the expected direction. Furthermore, CBB communication is more effective when made in the periods before meetings of the Monetary Policy Committee and publication of the respective minutes.

This paper examines the predictive ability of the expectations hypothesis of the term structure of interest rates in the BRICS and G7 countries by relating each country’s monthly 3‑month Treasury bill rate to 10‑year government bond rates, from May 2003 to May 2018. The panel ARDL model, applying the mean group (MG), pooled mean group (PMG), and dynamic fixed effects (DFE) estimators, is employed to compare the short‑ and long‑run relationships in both groups of countries. The results show that the expectations hypothesis holds in both BRICS and G7 country groups. In the long run, the short‑term interest rate is able to predict the long-term interest rate in both the BRICS and G7 countries. Interest rates in BRICS indicate rapid adjustment back to the long‑run equilibrium, while the adjustment is sluggish in the G7 block. Based on the findings of the study, the sluggish adjustment to the equilibrium in the G7 gives the impression that the financial crisis had an impact on the term structure of interest rates as the G7 countries were directly affected by the crisis.

Significant amount of research has been dedicated to explaining property yields. Long term interest rate is usually identified as one of the key determinants, and property yields are often benchmarked to long term government bonds, which are considered to represent the closest alternative to property investments. However, empirical evidence provides a mixed picture indicating that the link is less than straightforward even when allowing for a time-varying risk premium. We argue that the relationship between interest rates and property yields is not just contemporaneous and expectations about future interest rates need to be accounted for in order to fully understand the link between these variables. Since real estate is illiquid and involves significant transaction cost, investors are effectively locked in for many years once they commit to a project. An interest rate increase during that period would expose them to a valuation risk. Moreover, when benchmarking to liquid bonds, the opportunity cost is not only the interest they can earn today but also the interest they could expect in the near future. Fundamentally, the term structure of interest rates (yield curve) contains information about the expected future interest rate. Therefore, we would expect that a steeper curve should result in higher property yields. We test this hypothesis using prime office yields in the key centres in Europe and Australia and find convincing evidence that the shape of the yield curve indeed affects property yields.