# Top PDF Bootstrapping the interest-rate term structure ### Bootstrapping the interest-rate term structure

• Solve for the appropriate forward rate that give null NPV to the given swap.. QuantLib: forward curve[r] ### Bootstrapping the interest-rate term structure

Consistent interest-rate curve We need a consistent interest-rate curve in order to • Understand the current market conditions (e.g. forward rates) • Compute the at-the-money strikes for Caps, Floor, and Swaptions • Compute the NPV of exotic derivatives ### What moves the interest rate term structure?

changes perceptions of economic fundamentals and affects rates at different horizons. Specifically, changes in the term structure show whether policy actions directly affect distant forward rates or whether the effects die after medium horizons. An important difference exists between macroeconomic news and monetary policy news. We can quantify economic surprises, but we do not have a measure that satisfactorily captures all aspects of policy surprises. The language of FOMC statements and speeches cannot easily be quantified. To capture the surprise component, researchers have focused on how policy actions affect financial markets (see Kuttner 2001). Thus, to assess the effects of policy actions, I employ the same model-based methodology I used with employment and inflation news, examining changes across the entire term structure of interest rates as policy surprises were made public. ### Uncovered Interest Rate Parity and the Term Structure

This Table provides the empirical distributions of various economic statistics for the UIRP regressions under the null that the exchange rate process and the short rate processes are random walks with a drift. IMPLIED refers to the implied regression slope coeÆcients. CORR refers to the correlation statistic. VR refers to the variance ratio statistic. SD refers to the standard deviation of the risk premium. EVR refers to the Fama excess variance ratio statistic. \Data" refers to ### 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. ### 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] ### 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). ### 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. ### A ffine Regime-Switching Models for Interest Rate Term Structure

structure models under regime shifts. The main difference between the current pa- per and the previous studies is that the risk of regime shifts is explicitly priced in our model. The previous studies have all ignored the regime shift risk premiums except the recent paper by Dai and Singleton . Here we show that closed-form solution can be obtained using log-linear approximation for both affine- and quadratic-type term structure models which also price the regime shifting risk. Our model implies that bond risk premiums include two components under regime shifts in general. ### Calibration of interest rate term structure and derivative pricing models

In chapter 5 we show the Duffle and Kan model is unlikely to be used much in practice because it is exceedingly difficult to specify parameters for the model such that the state variable[r] ### The information in term structure interest rate spreads: the Irish case

"The Information Content of the Term Structure of Interest Rates: Theory and Practice"', Paper presented at Money Study Group Annual Conference, September 1989.. "The Inter[r] ### The effect of interest rate options hedging on term-structure dynamics

We interpret the observed behavior of five-year interest rates as the product of short-term liquidity effects. This conclusion is based on several findings. First, the predicted relationship between forward rates and spot rates does not persist beyond a few weeks, nor can it be profitably exploited in a systematic way. Both results suggest that short-term liquidity forces rather than economic fundamentals are likely to be driving the results. In addition, and in contrast to the behavior of medium-maturity rates, shorter maturity interest rates show no evidence of such feedback effects. The ample liquidity of the markets for short-term interest rate products, where market turnover is large relative to hedging demands, makes them an unlikely site for any evidence of positive-feedback effects. Finally, forward rates predict spot rates in the medium-term segment of the yield curve only in the weeks when rate changes are relatively large. This finding is also consistent with liquidity effects, since large interest rate changes cause large adjustments to options hedges, which in turn induce trading flows that will be large relative to normal market turnover. ### ON A MODEL FOR THE TERM STRUCTURE OF INTEREST RATE PROCESSES OF STABLE TYPE

1. Introduction As is well known, an interest rate process describes the profitability of a financial instrument, such as stock, bond or option. Hence if the price change is given by the sequence X = (X n ) n≥0 , then the interest rate process has in the simplest case the form ### Combining term structure of interest rate forecasts: The Brazilian case

JEL classiﬁcation: C53; E43; E47; G17 Keywords: Interest rate; Forecast model; Combined forecast Resumo Problemas como quebras estruturais e vieses causados por má-especificac¸ão dificultam achar um modelo de previsão de estrutura a termo de taxa de juros que domine todos os competidores. Esse artigo tem como objetivo identificar a existência de métodos de combinac¸ão que produzam resultados de previsão superiores a modelos individuais no caso Brasileiro. Resultados empíricos confirmam que não é possível determinar um modelo individual que consistentemente produza previsões superiores. Além disso, o desempenho desses modelos varia temporalmente. Os problemas encontrados nos modelos individuais podem ser reduzidos aplicando esquemas de combinac¸ão de previsão. Os resultados mostram consistentemente ganhos de previsão nos esquemas de combinac¸ão para o período considerado. Em particular, quanto maior o horizonte de previsão, maior a contribuic¸ão do esquema. ### The Term Structure of Interest Rates and Monetary Policy during a Zero Interest Rate Period

This figure shows that ex post return data are at less than zero percent at the beginning of the implementation of the monetary policies, and thus the zero interest rate and quantitative easing policies were initially perceived as credible and were expected to last for some considerable time. However, this phenomenon changes over time. Apparently, there is usually an increasing trend in the ex post short-term rates during low interest rate periods, but this trend was absent during the quantitative easing policy. This indicates that, while it is statistically insignificant, some investors anticipated a change in the zero interest rate policy. This finding is consistent with Marumo et al. (2003), who calculate the probability of the zero interest rate policy being removed, and conclude that after August 2000 a shift occurred in the distribu- tion of expectations; investors indeed had anticipated a policy change. In contrast, the relatively constant ex post rate during the quantitative easing policy would suggest that this measure was expected to last some time. This latter observation is generally consistent with previous research (Okina and Shiratsuka ). ### 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. ### the term structure of interest rates

A framework for estimating and extrapolating the term structure of interest rates Version <1.0>, September 2008 Page 3 Executive summary Is there any more fundamental valuation challenge than placing a value on a known cash flow at some time in the future? Risk-free yield curves are the basic building blocks for the valuation of future financial claims and long-term risk management work. Despite their fundamental importance, it turns out that measuring and estimating suitable risk-free interest rates presents some major challenges for analysts. In highly-developed fixed income markets we may be able to observe bonds or interest rate swap contracts with maturities of up to 50 years. In less developed markets liquid bond quotations might be limited to only a few years. In exceptional circumstances there may be no traded risk-free instruments at all. Of course, the liabilities of long-term financial institutions frequently extend beyond the term of available market instruments. In order to value these ultra long-term claims and assess risk, practitioners must extrapolate yield curves to generate a set of „pseudo-prices‟ for the assumed, inferred prices of discount bonds beyond the term of the longest available traded cash flow. A good yield curve estimation method must deliver extrapolated curves that are credible at a single point in time and where changes over time in extrapolated rates can be justified. ### Term Structure of Interest Rates

After the first question, he states another one: “Even if these two episodes can be seen as reflecting similar correlations between the bond rate and the short rate, is there any reason to expect the correlation to be stable in the future?” The answer for this question is no. In the low-inflation 1950 and 1969 period, long rates are varied relatively little with short rates. Then inflation expectations were anchored securely, and the range in which the Fed varied short rates to stabilize the economy was smaller in this period than it was in the 1970s, ’80s, and ’90s. Here, if the Fed succeeds in getting full credibility for low inflation in these years, short and long rates should once again co-vary which was in the earlier period. Thus, the late 1980s and mid-1990s can be seen as a transition period because short and long rates continued to exhibit the kind of covariation that observed in the period of high inflation. 