Economics
Term Structure Application
Term structure application refers to the use of the term structure of interest rates to analyze and make decisions about financial markets and investments. It involves examining the relationship between the yields on different maturities of fixed-income securities. By understanding the term structure, investors and policymakers can gain insights into future economic conditions and make informed decisions about borrowing, lending, and investing.
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9 Key excerpts on "Term Structure Application"
eBook - PDF- Sudipto Bhattacharya, George Michael Constantinides(Authors)
- 2005(Publication Date)
- World Scientific(Publisher)
Econometrica, Vol. 53, No. 2 (March, 1985) A THEORY OF THE TERM STRUCTURE OF INTEREST RATES' BY JOHN C. COX, JONATHAN E. INGERSOLL, JR., AND STEPHEN A. Ross This paper uses an intertemporal general equilibrium asset pricing model to study the term structure of interest rates. In this model, anticipations, risk aversion, investment alternatives, and preferences about the timing of consumption all play a role in determining bond prices. Many of the factors traditionally mentioned as influencing the term structure are thus included in a way which is fully consistent with maximizing behavior and rational expectations. The model leads to specific formulas for bond prices which are well suited for empirical testing. 1. INTRODUCTION THE TERM STRUCTURE of interest rates measures the relationship among the yields on default-free securities that differ only in their term to maturity. The determinants of this relationship have long been a topic of concern for economists. By offering a complete schedule of interest rates across time, the term structure embodies the market's anticipations of future events. An explanation of the term structure gives us a way to extract this information and to predict how changes in the underlying variables will affect the yield curve. In a world of certainty, equilibrium forward rates must coincide with future spot rates, but when uncertainty about future rates is introduced the analysis becomes much more complex. By and large, previous theories of the term structure have taken the certainty model as their starting point and have proceeded by examining stochastic generalizations of the certainty equilibrium relationships. The literature in the area is voluminous, and a comprehensive survey would warrant a paper in itself. It is common, however, to identify much of the previous work in the area as belonging to one of four strands of thought. First, there are various versions of the expectations hypothesis.
eBook - ePubThe Creators of Inside Money
A New Monetary Theory
- D. Gareth Thomas(Author)
- 2018(Publication Date)
- Palgrave Macmillan(Publisher)
The term structure of interest rates, however, recognises a common link between them all in the form of expectations of the future, whether long or short, which determines the holding of various financial assets of maturity as well as influencing the determination of aggregate demand and supply within the real economy. The term structure, therefore, is important for Central Bank ’s policymakers. If these monetary instruments affect short-term rates of interest in the first instance, which leads to the determination of long-term rates of interest, which drives capital and consumption expenditure, then analysing the term structure is crucial for understanding the transmission mechanism of monetary policy (Fender 2012). 1 Nevertheless, it is also relevant for many households in terms of the portfolio choice of assets. Suppose a family requires expenditure on private school fees in ten years’ time and decides to save now. There are a number of options. They could save by investing into a ten-year bond. Alternatively, they could purchase a short-term bill and then take the earnings into another bond each time it matures, until the ten years are up. Clearly, the important components determining the choice will be the expected return (or cost) and the risk involved, embodied in the term structure. Therefore, the analysis must consider the various theoretical models put forward in the literature to explain the relationship between interest rates on bonds (or bills) of differing maturity, although the hypothesis can applied to other assets as diverse as housing and the mortgage rate. The foremost theory of the term structure of interest rates is the so-called expectations hypothesis, which focuses on the rôle of expectations of future short-term interest rates in the determination of prices and yields on longer-term bills (or bonds). There a number of ways in which the theory in the literature differs in terms of the length of the bills (or bonds) included in the analysis
eBook - PDF- Roy E. Bailey(Author)
- 2005(Publication Date)
- Cambridge University Press(Publisher)
See the introduction to volume I of Ross (2000) and the references cited there. 328 The economics of financial markets opportunities, and (b) if the model of the term structure were correct (i.e. an acceptably close approximation to the actual evolution of bond prices). The predictions can then be compared with realized bond prices in order to inform investment strategies (i.e. to provide signals about which bonds to buy or sell) or to provide price quotations in negotiations about OTC contracts. Alternatively, from a more disinterested academic perspective, the predictions can be tested using methods similar to those described in chapter 9. Here the goal is to identify which theories of economic behaviour are more (or less) consistent with the observed patterns of bond prices and their rates of return. 13.7 Summary 1. Studies of the term structure of interest rates seek to reveal the relationship among the yields on bonds with different times to maturity. Commonly, the term structure is expressed by a yield curve, which plots yields as a function of the number of years remaining before redemption of the bonds. 2. Because the time to maturity is not the only dimension across which bonds differ, it is necessary to control for other characteristics of bonds, in particular their coupon payments. The most straightforward approach is to construct yield curves for zero-coupon bonds (bonds that promise to make a single payment at maturity). 3. Another attribute of some bonds is that the promised payments are adjusted for changes in the price level. From the observed prices (yields) of these index-linked bonds, it is possible to estimate real yield curves that express yields to maturity adjusted for future price level changes as a function of time to maturity. It then becomes possible to extract estimates of expected inflation rates, for various periods in the future, from market prices (yields) for real and nominal bonds.
eBook - PDF- Brian Kettell(Author)
- 2001(Publication Date)
- Butterworth-Heinemann(Publisher)
56 Economics for Financial Markets corresponding to a 4 per cent yield, relative eagerness to sell securities (to borrow) would drive the price of securities down, and would drive the rate of interest up. Now let us drop the assumption about a single rate of interest and consider why it is that rates of interest or yields on different financial instruments vary. Why do some borrowers pay more than others? Why are the yields on long-dated securities different from those on short-dated ones? Why do interest rates on different currency denominated assets vary? It is to these questions that we now turn. The term structure of interest rates The term structure of interest rates, or maturity structure as it is sometimes referred to, refers to the set of theories designed to explain why practically homogeneous bonds of different maturities have different interest rates. The starting point for understanding the term structure theories is the present value concept (discussed in detail in Chapter 2). Because of the time value of money, one dollar received at a future date has a present value of less than one dollar. If we denote the present (that is, time 0) value of $1 received n periods from now by D n , then the interest rate is the discount rate (denoted by R n ) that solves the following equation. D n = 1 (1 + R n ) n (3.1) D n represents both the present value of $1 received in n period and the spot price of a zero coupon bond with a par value of $1. The purchaser of this zero coupon bond pays the purchase price D n at time zero and receives the par value of $1 at time n . The rate R n is called the zero coupon discount rate or the spot interest rate. The spot market is the market for immediate delivery. Some observers call the spot market the ‘cash’ market. The spot price D n and the spot interest rate R n are inversely related. When the spot interest rate goes up, the spot price goes down because the spot interest rate is the denominator.
eBook - PDF- John Y. Campbell(Author)
- 2008(Publication Date)
- University of Chicago Press(Publisher)
5.1 Introduction Since the seminal papers by Vasicek (1977) and Cox, Ingersoll, and Ross (1985), there is a consensus in the finance literature that term structure mod-els should respond to three requirements: absence of arbitrage opportuni-ties and both econometric and numerical tractability. Models designed to meet these criteria can be useful, for instance, in the pricing of fixed income derivatives and in the assessment of the risks implied by fixed income port-folios. More recently, however, a number of requirements have been added to the modeling of the yield curve dynamics. Satisfactory models should also (1) be able to identify the economic forces behind movements in the yield curve, (2) take into account the way central banks implement their monetary policies, and (3) have a macroeconomic framework consistent with the stochastic discount factor implied by the model. In this chapter, we present a model that fulfills all of the preceding requirements and, in addi-tion, integrates learning dynamics within this macro-finance framework. The model presented in this chapter builds on recent developments (phases) in the a ffi ne term structure literature. The first phase is character-191 5 Learning, Macroeconomic Dynamics, and the Term Structure of Interest Rates Hans Dewachter and Marco Lyrio Hans Dewachter is a professor in international economics at the Catholic University of Leuven. Marco Lyrio is an assistant professor of finance at Warwick Business School. We are grateful for financial support from the FWO-Vlaanderen (Project No. G.0332.01). We thank the discussant, Jordi Galí; the organizer, John Campbell; and the participants at the National Bureau of Economic Research (NBER) Conference on Asset Prices and Monetary Policy for very helpful comments.
- Frank Skinner(Author)
- 2004(Publication Date)
- Butterworth-Heinemann(Publisher)
A third use of the term and credit risk structure of interest rates is to discover and use information embedded in these yield curves. For example, it has long been thought that the sovereign term structure of interest rates includes investors’ expectations concerning the future rate of inflation. Therefore if we measure the sovereign term structure of interest rates accurately, we may be able to forecast the market’s expectation of inflation. If we believe that the market is on average correct, then we may be able to act upon expected changes in inflation before the change occurs. Similarly changes in the credit spread , that is the difference in yield between a given credit risky bond, say triple B that underlies the triple B yield curve less the corresponding 24 Pricing and Hedging Interest and Credit Risk Sensitive Instruments maturity sovereign yield, may indicate changes in the expectation of the likelihood of recession. 2.3.1 Which yield curve? Because the term structure of interest rates can be used for a variety of purposes there are three different types of sovereign yield curves each of which is specially suited for a particular purpose. The three types of yield curves are the benchmark yield curve, the par coupon yield curve and the zero coupon yield curve. The first two are used for relative pricing. The benchmark yield curve, as the name suggests, is composed of the most frequently traded bonds in the sovereign bond market. You can readily identify the benchmark yield curve as there are only a few observations, and the points between these observations are linearly interpolated. In other words, the benchmark yield curve is a piece-wise linear curve that looks something like Figure 2.2. Yield Maturity Figure 2.2 The benchmark yield curve Here we see that there are about eight observations, and points between are simply straight lines that join them up. Obviously the interpolation is very crude and the yields indicated are not very reli-able.
eBook - PDFFixed Income Securities
Valuation, Risk, and Risk Management
- Pietro Veronesi(Author)
- 2015(Publication Date)
- Wiley(Publisher)
But the model can be useful to interpret the yield curve. For instance, according to the model, if we observe a yield curve that is relatively steep, this can be due to any of the following three reasons: 1. Market participants expected high future inflation, and thus high future spot rates. A MACROECONOMIC MODEL OF THE TERM STRUCTURE 643 Figure 18.5 Yield Curves in the Macro Economic Model 0 5 10 15 20 25 30 2 4 6 8 10 Maturity Yield (%) Panel A: Yield Curve for Three Values of Expected Inflation High Expected Inflation Average Expected Inflation Low Expected Inflation 0 5 10 15 20 25 30 0 0.5 1 1.5 Maturity Term Spread (%) Panel B: Term Spread for Three Values of Risk Aversion Low Risk Aversion Medium Risk Aversion High Risk Aversion 644 THE RISK AND RETURN OF INTEREST RATE SECURITIES 2. Market participants have a high aversion to risk, and therefore require a higher yield for longer term bonds. 3. The amount of risk is high, and therefore again market participants require a higher yield for longer term bonds. Only the first point implies that a positively sloped term structure predicts higher future spot rates, while points 2 and 3 do not. 18.4 CASE ANALYSIS: THE RISK IN THE P&G LEVERAGED SWAP In Section 17.9 of Chapter 17 we investigated the valuation of a complicated interest rate swap, whose cash flows would depend on the setting of a spread six months after the initiation of the contract according to a complicated formula. In this section, we show how we can use Monte Carlo simulations to gauge the riskiness of such an investment. To perform the risk analysis, we first need to estimate the risk natural parameters of the Vasicek model of interest rates. These parameters can be estimated by using the history of interest rates. In Section 17.9, we approximated the short-term interest rate r t with the 3-month continously compounded T-bill rate 4 and considered two samples: A 3-year sample and a 10-year sample.
eBook - ePub- Erik Lindström, Henrik Madsen, Jan Nygaard Nielsen(Authors)
- 2018(Publication Date)
- Chapman and Hall/CRC(Publisher)
Here the statistical term estimation of the term structure will be used throughout. In Section 14.11.3, the Extended Kalman filtering technique from Chapter 14 will be used, where the spot interest rate model describes the underlying process and the solution of the bond pricing equation is the measurement equation. Thus the method enables us to estimate both parameters and implied interest rates directly from observed bond prices. 11.6.1 Polynomial methods In practice it is fairly common to assume that the yield curve may be approximated by a polynomial in T of order s, i.e., Y (T) = α − 1 + α 1 T + α 2 T 2 + … + α s T s. (11.152) This is a reasonably general formulation. A number of estimation methods exist and have been implemented in statistical packages, which we shall not discuss here. A program package called RIO, which is based on cubic splines, has been developed at the Aarhus School of Business. This package is also used today in a number of financial institutions, because it allows the modeller to split the term structure into a number of segments. The package can also calculate other types of information. 11.6.2 Decay functions Decay functions are very useful for term structure estimation if the term structure should converge to a constant interest rate for T → ∞. The simplest possible decay function is Y (T) = α 0 + α 1 exp (− α 2 T). (11.153) In the next section, we discuss in some detail an extension of this model. 11.6.3 Nelson-Siegel method The relation between the price of a zero-coupon bond, P (t, T), and the instantaneous forward rate, F (t, T), is given by (11.109), i.e., P (t, T) = exp (− ∫ t T f (t, s) d s). (11.154) The yield curve follows from (11.13),. i.e., Y (t, T) = − log [ P (t, T) ] T − t = 1 T − t ∫ t T f (t, s) d s. (11.155) Today, at t = 0, we may observe the yield of a number of bonds with different maturities
eBook - PDF- (Author)
- 2022(Publication Date)
- Wiley(Publisher)
Chapter 7 The Term Structure and Interest Rate Dynamics 359 they interpreted as level, steepness, and curvature. The level movement refers to an upward or downward shift in the yield curve. The steepness movement refers to a non-parallel shift in the yield curve when either short-term rates change more than long-term rates or long-term rates change more than short-term rates. The curvature movement is a reference to movement in three segments of the yield curve: The short-term and long-term segments rise while the middle-term segment falls, or vice versa. Exhibit 11 illustrates these factors. EXHIBIT 11 Primary Yield Curve Factors: Level, Slope, and Curvature Yield (%) Term Term Slope Curvature Level In practice, the level movement factor explains most of the total changes in swap and bond market yields. This factor may be interpreted as a reflection of parallel yield curve moves in which rates move in the same direction and by a similar order of magnitude. The steepness factor addresses the shape of the curve, with short-term yields typically moving more than long-term yields. These changes take place over time and therefore explain less of the total variance in rates than the level factor. Finally, the third factor, curvature, tends to have a nega- tive impact on intermediate yields and a positive impact on short- and long-term yields. This variable explaining the “twist” in the yield curve has the smallest impact of the three. 8. THE MATURITY STRUCTURE OF YIELD CURVE VOLATILITIES AND MANAGING YIELD CURVE RISKS • explain the maturity structure of yield volatilities and their effect on price volatility 8.1. Yield Volatility Quantifying interest rate volatilities is important for fixed income managers for at least two reasons. First, most fixed-income instruments and derivatives have embedded options. Option values, and hence the values of the fixed-income instrument, crucially depend on the level of interest rate volatilities.
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