Stochastic Models for the Term Structure of Interest Rates

Modelling the term structure of interest rates is a long-standing topic in financial economics. In the past several decades or so, many stochastic interest rate models have been proposed with a vie...

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

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)

An evaluator of warrant models is essential for enhancing the current procedures used in the country's stock market and economy. This would provide additional insight for investors to make informed investment decisions and help to better understand the dynamics of warrant pricing in Malaysia. It has been established that the conventional process for valuing equity warrants using call option pricing models, like the Black-Scholes model, has numerous flaws, including the presumption of constant volatility and interest rates. As a matter of fact, existing alternative models were more concerned with providing techniques for pricing than with conducting empirical tests of warrant pricing models. Consequently, it is crucial to have a mathematical model that takes into account stochastic volatility and stochastic interest rates when pricing and analyzing equity warrants. Recent research by Roslan, Ibrahim, Jameel, and Ibrahim (2020) and Roslan, Ibrahim, Karim (2020) examined the pricing of hybrid equity warrants in the presence of stochastic factors. There was no comparative analysis conducted in these studies to ascertain the relative efficacy of the two methods used. This study's main goal is to empirically investigate how well equity warrant pricing models perform in the Malaysian market. This evaluation will take into account the impact of stochastic interest rates, using the Cox-Ingersoll-Ross (CIR) stochastic interest rate model, and stochastic volatility, using the Heston stochastic volatility model. To perform the analysis, the study will make use of a number of mathematical techniques, such as partial differential equations, Fourier transform approaches, and the change of measure method. The research methodology is divided into three main phases. It is anticipated that the research's findings will provide new perspectives that go beyond the domain of warrant pricing, creating chances for more widespread applications in fields like foreign exchange, insurance, and mortgage contracts.

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 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.

New estimates of the term structure of interest rates are used to investigate movements of and along the U.S. money demand function during the period 1920-38. The entire term structureand not just its short end-is found to be important to the interwar demand for money function. Therefore, the low short-term interest rates of the early 1930s cannot be identified as evidence of easy money. Instead, the widened spread between shortand long-term interest rates is evidence of the liquidity crisis proposed by Friedman and Schwartz, F&S, (10) in their explanation of the Great Depression. This finding critically depends on use of new, correctly-measured term structures of interest rates. The received estimates, which are widely recognized to be crude approximations, mask the important role played by the term structure in the monetary dynamics of the inter-war period.

ABSTRACTOption‐pricing models that assume a constant interest rate may misprice futures options if the interest rate fluctuates significantly or if the price of the underlying asset is correlated with the interest rate. The futures option‐pricing model of Ramaswamy and Sundaresan allows for a stochastic interest rate and correlation of the underlying asset's price with the interest rate. Using a data set of daily closing prices for Comex gold futures options, this paper tests the Ramaswamy and Sundaresan model against a constant interest rate model. Results indicate that the stochastic interest rate model is a superior predictor of market prices.

This paper shows the limitation of the cost-of-carry model which is used for pricing the theoretical value of the KTB futures, and proposes an alternative pricing model based on the term structure of interest rates. Under the assumption of 1-factor term structure, this paper treats the theoretical price of KTB futures price as a risk-neutral expectation of payoff function at maturity and derives the approximated formula for pricing the KTB futures. As compared with our price of KTB futures using the term structure of interest rates, the conventional KOFEX price based on the cost-of-carry model tends to be overvalued as the time to maturity increases. This result is due to the difference between the futures and forward prices which is caused by treating the futures contract as the forward contract in the conventional KOFEX pricing model. In particular, this discrepancy becomes more significant when the price of underlying asset and the interest rates are negatively correlated and the time to maturity is longer. The bond futures contract is a typical example of financial instrument whose price has a negative correlation with interest rates

The term structure of interest rates, i.e., yield curve, has long been of interest to monetary policymakers and their advisers. The transmission of monetary is conventionally viewed as running from shortterm interest rates managed by central banks to longer-term rates that influence aggregate demand. A central bank's leverage over longer-term rates comes from fact that market determines these as average expected level of short rates over relevant horizon (abstracting from a term premium and default risk). Working in other direction, long bond rate contains a premium for expected and, thus, serves as an indicator of credibility of a central bank's commitment to low inflation.1 Different theoretical perspectives support two above-mentioned uses of term structure for monetary policy: John Hicks's (1939) expectations theory of term structure supports first, and Irving Fisher's (1896) decomposition of nominal bond rates into expected and an expected real return supports second.2 The two views are compatible in principle, although reconciling them creates difficulties of interpretation in practice. For example, does a steepening yield curve indicate a loss of confidence in central bank's commitment to low inflation, or does it indicate that markets expect tighter in form of a higher path of short rates pursued by central bank? The yield curve contains information of use to monetary policymakers, but it needs to be interpreted in light of judicious subsidiary identifying conditions, together with other data on economy. Some circumstances lend themselves to clearer interpretations than others, and there are many pitfalls. Whether or not one regards longer-term interest rates as economic indicators or as part of transmission mechanism for policy, or both, term structure plays a potentially important role in policymaking process. In spite of its complexity, term structure cannot be ignored. This article addresses some issues involved in using term structure to conduct monetary policy. I begin by discussing long bond rate as an indicator of expectations. Second, I comment on role that bond rates have played in recent U.S. monetary history. Third, I explain how information in yield curve can be used to overcome what I call policy in pipeline problem. Fourth, I review recent empirical evidence supporting two theoretical views underlying our understanding of term structure. I explain how peso problems associated with inflation scares in bond market may help to account for a serious empirical failure of expectations theory of term structure. I also discuss evidence supporting view that significant movements in long-term interest rates are largely driven by expected inflation. Finally, I point out some pitfalls of using term structure to make tactical decisions. 1. PURSUING LOW INFLATION The Chairman of Federal Reserve Board, Alan Greenspan, supports a longrun goal for price stability such that the expected rate of change of general level of prices ceases to be a factor in individual and business decisionmaking.3 The long bond rate is particularly well suited to help a central bank assess degree to which it has achieved low defined in that way. One could compare behavior of yield on a long-term nominal bond to its behavior in a past period in which was very low and public was reasonably confident that it would stay low. For instance, in United States 30-year nominal bond rate ranged from around 3 percent to a little over 4 percent from mid-1950s until mid-1960s, a period in which averaged around 1 to 2 percent, and presumably, long-term expectations were no more than that.4 One would think that if Federal Reserve (the Fed) were to achieve full credibility for low inflation, long bond rate would once again move down to 3 to 4 percent range. …

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.

The wide fluctuations in interest rates that have occurred in recent years have led to the creation of numerous instruments that serve as hedges against interest rate risk. Among them are ‘caps’, ‘floors’ and other’ swaptions’, which are all options on the term structure of interest rates. 1 When an interest rate option is exercised, it is settled in cash, which means that there is no delivery of the underlying asset; instead, a sum of money is paid by the seller (issuer) to the holder of the option. Interest rate options differ from options on government bonds (Treasury Bonds and Bills in the United States, Obligations Assimilables du Tresor (OATs) in France, and so on) for which, in the event of exercise, the seller of the option delivers the underlying asset (the bond) against the payment of the exercise price. They also differ from the option clauses tagged on to some modern forms of bond, such as callability (early repayment at the option of the issuer of the bond), or puttability (repayment at the option of the holder of the bond). These were discussed in Chapter 10. However, all these securities are contingent on the term structure of interest rates.