# Term Structure of Interest Rate

## Top PDF Term Structure of Interest Rate: ### Valuation of Interest Rate Options in a Two-Factor Model of the Term Structure of Interest Rate.

factor model which can be interpreted as a random volatility specification because the volatility of the instantaneous interest rate is a function of the two factors. They obtain closed-form formulas for discount bond options which depend on investors' preferences. Chen (1994) develops a three-factor model of the term structure of interest rates. In this model the current short rate, the short term mean and the current volatility of the short rate follow a square-root process. Chen obtains a general formula for valuing interest rate derivatives that requires the computation of high-dimensional integrals. Two-factor models developed, for instance, by Richard (1978) who argues that the instantaneous interest rate is the sum of the real rate of interest and the inflation rate. Chen and Scott (1993) decompose the instantaneous interest rate into two unspecified factors each of which follows a square root process. A common characteristic of these two models is that there is little theoretical support to the choice of the factors 1 . Note that the models of the first approach mentioned above are all preference-dependent. In the framework of the second approach, we derive simple formulas for interest rate contingent claims. ### Term structure of interest rate. european financial integration.

United Kingdom and United States. However, United Kingdom used the Svensson model from January of 1982 to April of 1998. The purpose of the paper is to obtain the term structures of interest rates with a theNS model to analyze the term structure of interest rate of the last decade. The objective is to obtain the parameters (level, slope and curvature) of the model and compare the evolution of theses curves in the Monetary Union. The study include a period of thirteen years, from 1992 to 2004 and we have analyzed the evolution of these term structures in six different countries: Spain, France, Germany, Italy, United Kingdom and United States. The first four countries are members of the European Monetary Union (EMU). Germany, France and Italy already participated in the creation of the European Monetary System (EMS). Although Spain didn’t adhere to the EMS up to 198686, it is interesting to see that, as Italy, from an economic situation very different from France and Germany, it was able to reach the approaches settled down by Maastricht. Moreover, both Italy and Spain are able to be part of the Economic and Monetary Union on first ofst January in 1999. The evolution of Germany, France, Italy and Spain allows us to analyze the process of convergence of the single currency countries versus United Kingdom and United States, which are a reference to contrast the differences. ### Fiscal Policy and Term Structure of Interest Rate in Nigeria

Theoretically, the expectation theory argues that the shape of the yield can be explained by investors’ expectations about future interest rates. The liquidity preference theory states that short term bonds are more desirable than long term bonds because former are more liquid. The preferred habitat theory elucidates the shape of the term structure by the assumptions that if an investor is risk averse and such investor can draw out of his preferred habitats only with the promise of a higher yield while market segmentation theory assumes that there are two distinct markets for the short and long term bonds. The demand and supply in the long term bond market determines the long term yield while short rate is determined in the short term bond market by the forces of demand and supply. This means that the expected future rates have little to do with the shape of the yield curve. Basically, the factors that affect terms of structure of interest rate include the monetary policy, the fiscal policy, taxation and inflation. The monetary policy is used by the government to control the supply of money in the economy. When supply of money in the economy is low then the interest rates are expected to be high and vice versa while volatility in money supply growth may lead to higher interest rates. Under the fiscal policy, the government hypothetically finance all expenditure for the economy. In cases of budget deficit, the government is forced to borrow from the local markets. This in turn affects the supply of money in the economy which in turn affects the trend of interest rates (Olweny, 2011). ### A ffine Regime-Switching Models for Interest Rate Term Structure

∆ s B 6= 0), there is an additional source of risk due to regime shifts and it should also be priced (λ S (z, r t )) in the term structure model. Introducing the regime switching risk not only can add more flexibilities to the specification of time-varying bond risk premiums, but also can be potentially important in understanding the bond risk premiums over different holding periods. Wu and Zeng  use a general equilibrium model to introduce the systematic risk of regime shift in the term structure of interest rate and further estimate the model by Efficient Method of Moments. They find that the market price of the regime-switching risk is not only statistically significant, but also economically important, accounting for a significant portion of the term premiums for long-term bonds. Ignoring the regime- switching risk leads to underestimation of long-term interest rates and therefore flatter yield curves. ### Combining term structure of interest rate forecasts: The Brazilian case

The term structure of interest rates is of crucial importance for a variety of economic agents. For central banks, the yield curve helps to explain how monetary policy is implemented. For national treasuries, it indicates the yields for which public debt management should pay for issuing fixed rate bonds. For financial institutions, the term structure determines the allocation and exposure limits of different bonds maturities. For macroeconomists, it is an important leading indicator of economic activity and inflation. For firms, the term structure affects investments decisions. For households, the yield curve influences consuming and savings decisions. ### Quantitative Easing, Credibility and the Time-Varying Dynamics of the Term Structure of Interest rate in Japan

Contrary to the results of standard term-structure models with a time-invariant term pre- mium, our results show that the expectations hypothesis of the term structure of interest rates is generally supported, even during the QEMP period. Empirical results from a macro-finance model show that the relationship between the macroeconomic and financial variables has changed significantly over time. There is hardly any relationship at the zero lower bound on interest rates and deflation, and especially during the quantitative easing period. The structural decomposi- tion of the yield curve into its macroeconomic components shows that, by contrast with conven- tional wisdom, inflation, activity and monetary policy play a less prominent role in explaining the yield curve. They play no role at all particularly during quantitative easing. The variance decomposition of the level factor indicates that the main part of the variation in this factor comes from the yield curve factors, limiting the contribution of macroeconomic variables. Conversely, the relative importance of yield curve factors in the variation of inflation is relatively small and even inexistent during quantitative easing. A more pronounced effect of yield curve factors on the output gap is detected during the period of high interest rates, and this effect disappears during quantitative easing. Moreover, the increasing contribution of the level factor in the vari- ation of the call rate during quantitative easing reflects the increasing importance attributed by monetary policy to long-term interest rates. These finding are corroborated by impulse response results. ### Quantitative Easing, Credibility and the Time-Varying Dynamics of the Term Structure of Interest rate in Japan

Contrary to the results of standard term-structure models with a time-invariant term pre- mium, our results show that the expectations hypothesis of the term structure of interest rates is generally supported, even during the QEMP period. Empirical results from a macro-finance model show that the relationship between the macroeconomic and financial variables has changed significantly over time. There is hardly any relationship at the zero lower bound on interest rates and deflation, and especially during the quantitative easing period. The structural decomposi- tion of the yield curve into its macroeconomic components shows that, by contrast with conven- tional wisdom, inflation, activity and monetary policy play a less prominent role in explaining the yield curve. They play no role at all particularly during quantitative easing. The variance decomposition of the level factor indicates that the main part of the variation in this factor comes from the yield curve factors, limiting the contribution of macroeconomic variables. Conversely, the relative importance of yield curve factors in the variation of inflation is relatively small and even inexistent during quantitative easing. A more pronounced effect of yield curve factors on the output gap is detected during the period of high interest rates, and this effect disappears during quantitative easing. Moreover, the increasing contribution of the level factor in the vari- ation of the call rate during quantitative easing reflects the increasing importance attributed by monetary policy to long-term interest rates. These finding are corroborated by impulse response results. ### What moves the interest rate term structure?

However, there is more to interest rate changes than direction and magnitude. Bonds that mature at different time horizons do not move in lockstep. Much can be learned by looking at changes in the term structure of interest rates, that is, the entire range of rates from short maturities to long. Sometimes short- term interest rates move strongly and the long end of the term structure barely shifts. At other times, the short end remains anchored and the action is only in medium- and long-term rates. Identifying changes in interest rates across the maturity spectrum can be useful when assessing the impact of news on market expectations about the macroeconomy and future monetary policy. This Economic Letter looks at how different types of news affect interest rates across maturities. ### Uncovered Interest Rate Parity and the Term Structure

JEL No. F3 ABSTRACT This paper examines uncovered interest rate parity (UIRP) and the expectations hypotheses of the term structure (EHTS) at both short and long horizons. The statistical evidence against UIRP is mixed and is currency- not horizon-dependent. Economically, the deviations from UIRP are less pronounced than previously documented. The evidence against the EHTS is statistically more uniform, but, economically, actual spreads and theoretical spreads (spreads constructed under the null of the EHTS) do not behave very differently, especially at long horizons. Partly because of this, the deviations from the EHTS only play a minor role in explaining deviations from UIRP at long horizons. A random walk model for both exchange rates and interest rates fits the data marginally better than the UIRP-EHTS model. ### Exchange rate dynamics and the term structure of interest rates

It follows that any empirical test of the relationship between the exchange rate and the term structure of interest rates necessitates the utilisation of a measure of the yield curve wh[r] ### Interest Rate Term Structure Decomposition: An Axiomatic Structural Approach

Keywords: term structure decomposition, optimization, market efficiency 1. Introduction The use of forward interest rates has long been standard in financial analysis, for instance in pricing new financial instruments and in discovering arbitrage possibilities (Svensson, 1994). Bolder and Gusba (2002) note the fundamental aspect and importance of risk-free interest rates: In the world of fixed-income, it is difficult to find a more fundamental object than a riskless pure discount bond or, as it is equivalently called, a zero-coupon bond. This is because the price of a pure discount bond represents the current value of one currency paid with complete certainty at some future point in time. Abstracting from the idea of risk premia for longer-term bond holdings, it is essentially a representation of the time value of money. A trivial transformation of the bond price is the rate of return on this simple instrument or, as it is more commonly termed, the zero-coupon interest rate. These building blocks of fixed-income finance are tremendously important for a wide array of different purposes, including bond pricing, discounting future cash flows, pricing fixed- income derivative products, constructing forward interest rates, and determining risk premia associated with holding bonds of different maturities. ### The Term Structure of Interest Rates and Monetary Policy during a Zero Interest Rate Period

Interbank Offered Rate (TIBOR) data. 23 This data set covers maturities of one, two, three, six, nine, and 12 months, and enables us to analyze the performance of the short end of the term structure. The results from the TIBOR data are reported in Tables 7–9, where those during transition period A are not included due to the lack of adequate sample size. (The TIBOR data are available from 1995 onward.) Table 7 shows the poor performance of the term-structure model regardless of the combination of interest rates used to calculate the yield spreads. This result is in sharp contrast to that obtained from the long end of the term-structure model using gensaki rates and JGBs, but is consistent with previous findings obtained elsewhere that the short end of the term-structure model performs less well than the long-end model. ### International Interest-Rate Risk Premia in Affine Term Structure Models

The absence of arbitrage says that it is not possible to design a risk-free self-financing portfolio that yields more than the instantaneously return of the risk-free (short) rate within a time interval. Expected excess returns, then, are the result of explicit risk- taking. This means that arbitrage opportunities exists unless long-term bond yields are equal to risk-adjusted expectations of future short-term yields. The assumption of ab- sence of arbitrage opportunities seems quite logical in bond markets in which arbitrage opportunities are traded away immediately and markets can be characterized as highly liquid. The so called affine dynamic term structure models (ATSM) are the most popular among the class of no-arbitrage term structure models. They are best tractable since they assume bond yields to be affine functions of a set of risk factors driving the whole yield curve. They enable to get closed-form solutions for interest rates and such models are maximally flexible to reproduce the moments of bond yields and excess returns. The pioneering work by Vasicek (1977) and Cox et al. (1985) consists of a particular simple form of an affine term structure model where the short-term interest rate is the single factor that drives the whole yield curve at one moment in time and where it describes comovements of bond yields of different maturities. ### Banks' exposure to interest rate risk, their earnings from term transformation, and the dynamics of the term structure

Nearly all of the banks will gain if the term structure shifts downward and lose if the term structure moves upward, because banks tend to grant long-term loans and take in short-term deposits. For the few banks for which the 190-bp-upward shift is the relevant shock we proceed as follows: Their exposure is multiplied by -130/190 to account for their negative term transformation and to rescale their exposure. Observations of parallel shifts of other than 130 basis points are rescaled accordingly. When calculating the eﬀects of the interest rate shock, banks have to include all on-balance and all oﬀ-balance positions in their banking book. ### Estimating Nominal Interest Rate Expectations: Overnight Indexed Swaps and the Term Structure

ahead). OIS rates, on the other hand, are available at a daily frequency and have a horizon that aligns exactly with those of the zero-coupon nominal government bonds used in the estimation of GADTSMs. The term structure of OIS rates can therefore be readily added to a GADTSM for nominal government bond yields. I show that augmenting the GADTSM with OIS rates provides additional information, specifically related to future interest rate expectations, that can help better identify the evolution of these expectations. Using 3 to 24-month OIS rates in an arbitrage-free GADTSM enables the estimation of future short-term interest rate expectations for the whole term structure — from 3 months to 10 years. Estimates of interest rate expec- tations from OIS-augmented GADTSMs are superior to those from existing GADTSMs. In particular, short and long-horizon in-sample OIS-augmented risk-neutral yields match patterns in federal funds futures rates and survey expectations. These time series also match qualita- tive daily patterns exhibited by financial market instruments. This implies that OIS-augmented GADTSMs are well suited for daily frequency policy analysis. Thus, OIS-augmented GADTSMs provide reliable and policy-relevant estimates of interest rate expectations along the whole term structure. ### Analyzing Interest Rate Risk: Stochastic Volatility in the Term Structure of Government Bond Yields

Finally, h C t captures uncertainties associated with the curvature of the yield curve, which can vary between convex, linear and concave forms. Obviously, such variations mainly stem from time-varying volatility in bonds with mid-term maturities. An alternative way to capture time-varying volatility in the term structure of inter- est rates would be to allow Σ itself to be time-varying. However, this would result in an N -dimensional MGARCH or SV model which is not very tractable if the cross-sectional dimension N is high. Therefore, we see our approach as a parsimonious alternative to capture interest rate risk. Note that the slope and curvature factors can be interpreted as particular (linear) combinations of yields associated with factor portfolios mimick- ing the steepness and convexity of the yield curve. 4 Then, the corresponding slope and ### Analyzing the Effect of Changes in the Benchmark Policy Interest Rate Using a Term Structure Model

This paper estimates the term structure of interest rates with the setup of 3-factor no arbitrage model and investigates the trend of term premia and the effectiveness of changes in policy interest rates. The term premia are found to be high in a three-year medium term objective, which can be interpreted as reflecting the recognition of investors who expect a higher uncertainty in real activities for the coming three years than for a longer term. Then, in order to look into the effect of policy interest rates after the recent change of benchmark interest rate, this paper analyzes the effects of the changes in short-term interest rates of the financial market on the yield curve of the bond market at time of change. Empirical results show that the discrepancy between call rate, short-term rate in money market, and instantaneous short rate, short-term rate in the bond market, is found to be significantly widened, comparing to the periods before the change in benchmark interest rate. It is not easy to conclude clearly for now whether such a widening gap is caused by the lack of experiences with managing new benchmark interest rate or is just an exceptional case due to the recent turmoil in the global financial market. However, monetary policy needs to be operated in a manner that could reduce the gap to enhance its effectiveness. ### A generalized one-factor term structure model and pricing of interest rate derivative securities

of risk, nonparametric estimation allows data to speak for themselves. The model precludes arbitrage opportunities, preserves a simple structure and the computational tractability, and at the same time allows for maximal flexibility in fitting into the data. The paper is organized as follows. Section 2 outlines the spot rate approach of mod- eling term structure dynamics; Section 3 summarizes two well known one-factor models, i.e., the Vasicek (1977) model and the CIR (1985) model, and examines the behavior of these models and their closed form solutions for bond and bond option prices; In Section 4, consistent estimators of the nonparametric drift func- tion, diffusion function and market price of risk are proposed. Procedures to obtain nonparametric prices of interest rate derivative securities by either solving the PDE numerically or performing Monte Carlo simulations along the risk-neutral process are proposed as well. In Section 5, the nonparametric model is implemented using historical Canadian interest rate term structure data. Empirical results not only pro- vide strong evidence that the traditional spot interest rate models and market price of interest rate risk are misspecified but also suggest that different model specifications have significant impact on the term structure dynamics and prices of interest rate derivative securities. A brief conclusion is contained in Section 6.  