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Term Structure (term + structure)
Terms modified by Term Structure Selected AbstractsPRICING IN AN INCOMPLETE MARKET WITH AN AFFINE TERM STRUCTUREMATHEMATICAL FINANCE, Issue 3 2004Virginia R. Young We apply the principle of equivalent utility to calculate the indifference price of the writer of a contingent claim in an incomplete market. To recognize the long-term nature of many such claims, we allow the short rate to be random in such a way that the term structure is affine. We also consider a general diffusion process for the risky stock (index) in our market. In a complete market setting, the resulting indifference price is the same as the one obtained by no-arbitrage arguments. We also show how to compute indifference prices for two types of contingent claims in an incomplete market, in the case for which the utility function is exponential. The first is a catastrophe risk bond that pays a fixed amount at a given time if a catastrophe does not occur before that time. The second is equity-indexed term life insurance which pays a death benefit that is a function of the short rate and stock price at the random time of the death of the insured. Because we assume that the occurrence of the catastrophe or the death of the insured is independent of the financial market, the markets for the catastrophe risk bond and the equity-indexed life insurance are incomplete. [source] TERM STRUCTURES OF IMPLIED VOLATILITIES: ABSENCE OF ARBITRAGE AND EXISTENCE RESULTSMATHEMATICAL FINANCE, Issue 1 2008Martin Schweizer This paper studies modeling and existence issues for market models of stochastic implied volatility in a continuous-time framework with one stock, one bank account, and a family of European options for all maturities with a fixed payoff function h. We first characterize absence of arbitrage in terms of drift conditions for the forward implied volatilities corresponding to a general convex h. For the resulting infinite system of SDEs for the stock and all the forward implied volatilities, we then study the question of solvability and provide sufficient conditions for existence and uniqueness of a solution. We do this for two examples of h, namely, calls with a fixed strike and a fixed power of the terminal stock price, and we give explicit examples of volatility coefficients satisfying the required assumptions. [source] SEPARABLE TERM STRUCTURES AND THE MAXIMAL DEGREE PROBLEMMATHEMATICAL FINANCE, Issue 4 2002Damir Filipovi This paper discusses separablc term structure diffusion models in an arbitrage-free environment. Using general consistency results we exploit the interplay between the diffusion coefficients and the functions determining the forward curve. We introduce the particular class of polynomial term structure models. We formulate the appropriate conditions under which the diffusion for a quadratic term structure model is necessarily an Ornstein-Uhlenbeck type process. Finally, we explore the maximal degree problem and show that basically any consistent polynomial term structure model is of degree two or less. [source] Threshold Dynamics of Short-term Interest Rates: Empirical Evidence and Implications for the Term StructureECONOMIC NOTES, Issue 1 2008Theofanis Archontakis This paper studies a nonlinear one-factor term structure model in discrete time. The short-term interest rate follows a self-exciting threshold autoregressive (SETAR) process that allows for shifts in the intercept and the variance. In comparison with a linear model, we find empirical evidence in favour of the threshold model for Germany and the US. Based on the estimated short-rate dynamics we derive the implied arbitrage-free term structure of interest rates. Since analytical solutions are not feasible, bond prices are computed by means of Monte Carlo integration. The resulting term structure captures stylized facts of the data. In particular, it implies a nonlinear relation between long rates and the short rate. [source] Tax Clientele Effects in the Term Structure of UK Interest RatesJOURNAL OF BUSINESS FINANCE & ACCOUNTING, Issue 3-4 2001Eric J. Levin This paper tests for tax clientele effects in the term structure of UK interest rates. Five empirical models of the term structure of interest rates, incorporating tax effects, are estimated with daily data covering the period 31 March, 1995 to 3 August, 1995. In May 1995, the British government announced its intention to eliminate the tax exemption on capital gains from government bonds, but subsequently in July 1995 backtracked on some of its initial proposals. This period therefore forms the basis of a crude natural experiment in the sense that it provides an opportunity to examine tax clientele effects ,before' and ,after' an event which should have levelled greatly the taxing of government bonds. The empirical analysis suggests large tax clientele effects. However, there is little evidence of tax-specific term structures of interest rates. [source] New Keynesian Macroeconomics and the Term StructureJOURNAL OF MONEY, CREDIT AND BANKING, Issue 1 2010GEERT BEKAERT monetary policy; inflation target; term structure of interest rates; Phillips curve This article complements the structural New Keynesian macro framework with a no-arbitrage affine term structure model. Whereas our methodology is general, we focus on an extended macro model with unobservable processes for the inflation target and the natural rate of output that are filtered from macro and term structure data. We find that term structure information helps generate large and significant parameters governing the monetary policy transmission mechanism. Our model also delivers strong contemporaneous responses of the entire term structure to various macroeconomic shocks. The inflation target shock dominates the variation in the "level factor" whereas monetary policy shocks dominate the variation in the "slope and curvature factors." [source] Stochastic Volatility in a Macro-Finance Model of the U.S. Term Structure of Interest Rates 1961,2004JOURNAL OF MONEY, CREDIT AND BANKING, Issue 6 2008PETER D. SPENCER affine term structure model; macro finance; unit root; stochastic volatility This paper generalizes the standard homoscedastic macro-finance model by allowing for stochastic volatility, using the "square root" specification of the mainstream finance literature. Empirically, this specification dominates the standard model because it is consistent with the square root volatility found in macroeconomic time series. Thus it establishes an important connection between the stochastic volatility of the mainstream finance model and macro-economic volatility of the Okun,Friedman type. This research opens the way to a richer specification of both macro-economic and term structure models, incorporating the best features of both macro-finance and mainstream finance models. [source] Multiple Ratings Model of Defaultable Term StructureMATHEMATICAL FINANCE, Issue 2 2000Tomasz R. Bielecki A new approach to modeling credit risk, to valuation of defaultable debt and to pricing of credit derivatives is developed. Our approach, based on the Heath, Jarrow, and Morton (1992) methodology, uses the available information about the credit spreads combined with the available information about the recovery rates to model the intensities of credit migrations between various credit ratings classes. This results in a conditionally Markovian model of credit risk. We then combine our model of credit risk with a model of interest rate risk in order to derive an arbitrage-free model of defaultable bonds. As expected, the market price processes of interest rate risk and credit risk provide a natural connection between the actual and the martingale probabilities. [source] A Semiparametric Analysis of the Term Structure of the US Interest Rates,OXFORD BULLETIN OF ECONOMICS & STATISTICS, Issue 4 2009Fabrizio Iacone Abstract The short end of the US$ term structure of interest rates is analysed allowing for the possibility of fractional integration and cointegration. This approach permits mean-reverting dynamics for the data and the existence of a common long run stochastic trend to be maintained simultaneously. We estimate the model for the period 1963,2006 and find it compatible with this structure. The restriction that the data are I(1) and the errors are I(0) is rejected, mainly because the latter still display long memory. This result is consistent with a model of monetary policy in which the Central Bank operates affecting contracts with short term maturity, and the impulses are transmitted to contracts with longer maturities and then to the final goals. However, the transmission of the impulses along the term structure cannot be modelled using the Expectations Hypothesis. [source] Testing the Expectations Hypothesis of the Term Structure of Interest Rates in the Presence of a Potential Regime ShiftTHE MANCHESTER SCHOOL, Issue 2003Markku Lanne The expectations hypothesis of the term structure of interest rates is tested with monthly Eurodollar deposit rates for maturities of 1, 3 and 6 months covering the period 1983:1,1999:6. Classical regression based tests indicate rejection, while tests in a new model allowing for potential regime shifts that have not occurred in the sample period lend support to the expectations hypothesis. The results imply that the potential regime shift affected the expectations concerning the longer-term interest rate only in a short period at the beginning of the sample when the interest rates were highest. [source] Threshold Dynamics of Short-term Interest Rates: Empirical Evidence and Implications for the Term StructureECONOMIC NOTES, Issue 1 2008Theofanis Archontakis This paper studies a nonlinear one-factor term structure model in discrete time. The short-term interest rate follows a self-exciting threshold autoregressive (SETAR) process that allows for shifts in the intercept and the variance. In comparison with a linear model, we find empirical evidence in favour of the threshold model for Germany and the US. Based on the estimated short-rate dynamics we derive the implied arbitrage-free term structure of interest rates. Since analytical solutions are not feasible, bond prices are computed by means of Monte Carlo integration. The resulting term structure captures stylized facts of the data. In particular, it implies a nonlinear relation between long rates and the short rate. [source] Pricing Loans Using Default ProbabilitiesECONOMIC NOTES, Issue 2 2003Stuart M. Turnbull This paper examines the pricing of loans using the term structure of the probability of default over the life of the loan. We describe two methodologies for pricing loans. The first methodology uses the term structure of credit spreads to price a loan, after adjusting for the difference in recovery rates between bonds and loans. In loan origination, it is common practice to estimate the probability of default for a loan over a specified time horizon and the loss given default. The second methodology shows how to incorporate this information into the arbitrage free pricing of a loan. We also show how to derive an estimate of the credit spread due to liquidity risk. For both methodologies, we show how to calculate a break,even credit spread, taking into account the fee structure of a loan and the costs associated with the term structure of marginal economic capital. The break,even spread is the minimum spread for the loan to be EVA neutral in a multi,period setting. (J.E.L.: G12, G33). [source] Convergence within the EU: Evidence from Interest RatesECONOMIC NOTES, Issue 2 2000Teresa Corzo Santamaria The economic and political changes which are taking place in Europe affect interest rates. This paper develops a two-factor model for the term structure of interest rates specially designed to apply to EMU countries. In addition to the participant country's short-term interest rate, we include as a second factor a ,European' short-term interest rate. We assume that the ,European' rate follows a mean reverting process. The domestic interest rate also follows a mean reverting process, but its convergence is to a stochastic mean which is identified with the ,European' rate. Closed-form solutions for prices of zero coupon discount bonds and options on these bonds are provided. A special feature of the model is that both the domestic and the European interest rate risks are priced. We also discuss an empirical estimation focusing on the Spanish bond market. The ,European' rate is proxied by the ecu's interest rate. Through a comparison of the performance of our convergence model with a Vasicek model for the Spanish bond market, we show that our model provides a better fit both in-sample and out-of sample and that the difference in performance between the models is greater the longer the maturity of the bonds. (J.E.L.: E43, C510). [source] The Liquidity Premium in the Money Market: A Comparison of the German Mark Period and the Euro AreaGERMAN ECONOMIC REVIEW, Issue 2 2006Alain Durré Expectations hypothesis; money market; liquidity premium; cointegration analysis Abstract. This paper investigates to what extent the expectations hypothesis of the term structure (EHTS) of interest rates receives some support since the launch of the European single currency. Empirical evidence shows that in general this theory applies to most European countries, and to Germany in particular. The objective of this paper thus is twofold. First, the EHTS for the German money market and for a larger sample including the German mark period and the euro money market is tested in order to check whether the results for the former are affected by the new financial environment since January 1999. Second, the implications of the results for the monetary policy assessment are discussed. We estimate cointegrating vector autoregressive models in order to quantify the level of the liquidity premium. The results suggest that financial markets do not consider the monetary policy of the European Central Bank simply as the one prevailing during the German period. [source] Interest Rate Volatility Prior to Monetary Union under Alternative Pre-Switch RegimesGERMAN ECONOMIC REVIEW, Issue 4 2003Bernd Wilfling Interest rate volatility; term structure; exchange rate arrangements; intervention policy; stochastic processes Abstract. The volatility of interest rates is relevant for many financial applications. Under realistic assumptions the term structure of interest rate differentials provides an important predictor of the term structure of interest rates. This paper derives the term structure of differentials in a situation in which two open economies plan to enter a monetary union in the future. Two systems of floating exchange rates prior to the union are considered, namely a free-float and a managed-float regime. The volatility processes of arbitrary-term differentials under the respective pre-switch arrangements are compared. The paper elaborates the singularity of extremely short-term (i.e. instantaneous) interest rates under extensive leaning-against-the-wind interventions and discusses policy issues. [source] Australian and US interest rate swap markets: comparison and linkagesACCOUNTING & FINANCE, Issue 1 2004Francis In Abstract We investigate and compare the determinants of US and Australian interest rate swap spreads and the linkages between these markets. The slope of the risk-free term structure is the most significant determinant and its importance is greater for longer terms to maturity. Interest rate levels and, in Australia, the default premium also have some impact. The influences of interest rate volatility, the liquidity premium and (in the USA) the default premium are small or negligible. We hypothesise, and our evidence confirms, that the US swap market significantly affects the Australian swap market but not vice-versa. [source] The optimal timing of the transfer of hidden reserves in the German and Austrian tax systemsINTELLIGENT SYSTEMS IN ACCOUNTING, FINANCE & MANAGEMENT, Issue 2 2002Manfred FrühwirthArticle first published online: 16 DEC 200 The lower-of-cost-or-market principle implies that assets may be sold above book value, by which hidden reserves are disclosed. To avoid taxation of these hidden reserves, in German-speaking countries companies are allowed to transfer them to a newly purchased asset within a fixed time period. In this paper, the optimal timing of hidden reserves transfers is developed with special attention to the term structure of interest rates and interest rate risk, and using the replicating principle known from the field of finance. The paper presents one model under certainty and, as a generalization of this model, another model under interest rate risk. In both models, the criterion used for decision-making is the value of the right to transfer, which can be interpreted as the initial cost of a replicating/hedging strategy for tax payments saved/incurred. In the model under certainty, the net present value concept is used to derive the value of the right to transfer. The procedure used in the model under interest rate risk is a combination of flexible planning and the no-arbitrage approach common in derivatives pricing. It is shown that the right to transfer hidden reserves with flexible timing is equivalent to an American-style exchange option. In addition, the impact of term-structure volatility on the value of the right to transfer is analyzed. The technique presented in this paper can also be used to solve other timing problems resulting from trade-offs between early and late tax payments/tax benefits. Copyright © 2002 John Wiley & Sons, Ltd. [source] The behavior of emerging market sovereigns' credit default swap premiums and bond yield spreadsINTERNATIONAL JOURNAL OF FINANCE & ECONOMICS, Issue 1 2010Michael Adler Abstract We test whether credit risk for Emerging Market Sovereigns is priced equally in the credit default swap (CDS) and bond markets. The parity relationship between CDS premiums and bond yield spreads (BYS), that was tested and largely confirmed in the literature, is mostly rejected. Prices below par can result in positive basis, i.e. CDS premiums that are greater than BYS and vice versa. To adjust for the non-par price, we construct the BYS implied by the term structure of CDS premiums for various maturities. We are able to restore the parity relation and confirm the equivalence of credit risk pricing in the CDS and bond markets for many countries that have bonds with non-par prices and time varying credit quality. We detect non-parity even after the adjustment mainly in countries in Latin America, where the bases are larger than the bid,ask spreads in the market. We also find that the repo rates of bonds decrease around episodes of credit quality deterioration, which helps the basis remain positive. Copyright © 2009 John Wiley & Sons, Ltd. [source] Tax Clientele Effects in the Term Structure of UK Interest RatesJOURNAL OF BUSINESS FINANCE & ACCOUNTING, Issue 3-4 2001Eric J. Levin This paper tests for tax clientele effects in the term structure of UK interest rates. Five empirical models of the term structure of interest rates, incorporating tax effects, are estimated with daily data covering the period 31 March, 1995 to 3 August, 1995. In May 1995, the British government announced its intention to eliminate the tax exemption on capital gains from government bonds, but subsequently in July 1995 backtracked on some of its initial proposals. This period therefore forms the basis of a crude natural experiment in the sense that it provides an opportunity to examine tax clientele effects ,before' and ,after' an event which should have levelled greatly the taxing of government bonds. The empirical analysis suggests large tax clientele effects. However, there is little evidence of tax-specific term structures of interest rates. [source] Measures of Fit for Rational Expectations ModelsJOURNAL OF ECONOMIC SURVEYS, Issue 3 2002Tom Engsted This survey provides a detailed description of some of the recent theoretical and empirical literature on rational expectations econometrics. The survey pays special attention to non,stationarity of the data, and to the various methods for evaluating rational expectations models that have been developed as alternatives to the classical statistical approach of testing overidentifying restrictions. These methods have become very popular and widely used in empirical research. We provide an illustration using Danish stock market data, and we summarize the many results obtained recently using these measures in areas as diverse as stock prices, the term structure of interest rates, exchange rates, consumption and saving, the balance of payments, tax,smoothing, hyperinflation, and linear quadratic adjustment cost models for inventories, labour demand, and money demand. [source] Forecasting interest rate swap spreads using domestic and international risk factors: evidence from linear and non-linear modelsJOURNAL OF FORECASTING, Issue 8 2007Ilias Lekkos Abstract This paper explores the ability of factor models to predict the dynamics of US and UK interest rate swap spreads within a linear and a non-linear framework. We reject linearity for the US and UK swap spreads in favour of a regime-switching smooth transition vector autoregressive (STVAR) model, where the switching between regimes is controlled by the slope of the US term structure of interest rates. We compare the ability of the STVAR model to predict swap spreads with that of a non-linear nearest-neighbours model as well as that of linear AR and VAR models. We find some evidence that the non-linear models predict better than the linear ones. At short horizons, the nearest-neighbours (NN) model predicts better than the STVAR model US swap spreads in periods of increasing risk conditions and UK swap spreads in periods of decreasing risk conditions. At long horizons, the STVAR model increases its forecasting ability over the linear models, whereas the NN model does not outperform the rest of the models.,,Copyright © 2007 John Wiley & Sons, Ltd. [source] Term premia and the maturity composition of the Federal debt: new evidence from the term structure of interest ratesJOURNAL OF FORECASTING, Issue 7 2001Basma Bekdache Abstract This paper models bond term premia empirically in terms of the maturity composition of the federal debt and other observable economic variables in a time-varying framework with potential regime shifts. We present regression and out-of sample forecasting results demonstrating that information on the age composition of the Federal debt is useful for forecasting term premia. We show that the multiprocess mixture model, a multi-state time-varying parameter model, outperforms the commonly used GARCH model in out-of-sample forecasts of term premia. The results underscore the importance of modelling term premia, as a function of economic variables rather than just as a function of asset covariances as in the conditional heteroscedasticity models. Copyright © 2001 John Wiley & Sons, Ltd. [source] New Keynesian Macroeconomics and the Term StructureJOURNAL OF MONEY, CREDIT AND BANKING, Issue 1 2010GEERT BEKAERT monetary policy; inflation target; term structure of interest rates; Phillips curve This article complements the structural New Keynesian macro framework with a no-arbitrage affine term structure model. Whereas our methodology is general, we focus on an extended macro model with unobservable processes for the inflation target and the natural rate of output that are filtered from macro and term structure data. We find that term structure information helps generate large and significant parameters governing the monetary policy transmission mechanism. Our model also delivers strong contemporaneous responses of the entire term structure to various macroeconomic shocks. The inflation target shock dominates the variation in the "level factor" whereas monetary policy shocks dominate the variation in the "slope and curvature factors." [source] On the efficacy of simulated maximum likelihood for estimating the parameters of stochastic differential Equations*JOURNAL OF TIME SERIES ANALYSIS, Issue 1 2003A. S. Hurn C51; C52; G12 Abstract. A method for estimating the parameters of stochastic differential equations (SDEs) by simulated maximum likelihood is presented. This method is feasible whenever the underlying SDE is a Markov process. Estimates are compared to those generated by indirect inference, discrete and exact maximum likelihood. The technique is illustrated with reference to a one-factor model of the term structure of interest rates using 3-month US Treasury Bill data. [source] AN EXACT FORMULA FOR DEFAULT SWAPTIONS' PRICING IN THE SSRJD STOCHASTIC INTENSITY MODELMATHEMATICAL FINANCE, Issue 3 2010Damiano Brigo We develop and test a fast and accurate semi-analytical formula for single-name default swaptions in the context of a shifted square root jump diffusion (SSRJD) default intensity model. The model can be calibrated to the CDS term structure and a few default swaptions, to price and hedge other credit derivatives consistently. We show with numerical experiments that the model implies plausible volatility smiles. [source] PRICING EQUITY DERIVATIVES SUBJECT TO BANKRUPTCYMATHEMATICAL FINANCE, Issue 2 2006Vadim Linetsky We solve in closed form a parsimonious extension of the Black,Scholes,Merton model with bankruptcy where the hazard rate of bankruptcy is a negative power of the stock price. Combining a scale change and a measure change, the model dynamics is reduced to a linear stochastic differential equation whose solution is a diffusion process that plays a central role in the pricing of Asian options. The solution is in the form of a spectral expansion associated with the diffusion infinitesimal generator. The latter is closely related to the Schrödinger operator with Morse potential. Pricing formulas for both corporate bonds and stock options are obtained in closed form. Term credit spreads on corporate bonds and implied volatility skews of stock options are closely linked in this model, with parameters of the hazard rate specification controlling both the shape of the term structure of credit spreads and the slope of the implied volatility skew. Our analytical formulas are easy to implement and should prove useful to researchers and practitioners in corporate debt and equity derivatives markets. [source] STOCHASTIC HYPERBOLIC DYNAMICS FOR INFINITE-DIMENSIONAL FORWARD RATES AND OPTION PRICINGMATHEMATICAL FINANCE, Issue 1 2005Shin Ichi Aihara We model the term-structure modeling of interest rates by considering the forward rate as the solution of a stochastic hyperbolic partial differential equation. First, we study the arbitrage-free model of the term structure and explore the completeness of the market. We then derive results for the pricing of general contingent claims. Finally we obtain an explicit formula for a forward rate cap in the Gaussian framework from the general results. [source] QUADRATIC TERM STRUCTURE MODELS FOR RISK-FREE AND DEFAULTABLE RATESMATHEMATICAL FINANCE, Issue 4 2004Li Chen In this paper, quadratic term structure models (QTSMs) are analyzed and characterized in a general Markovian setting. The primary motivation for this work is to find a useful extension of the traditional QTSM, which is based on an Ornstein,Uhlenbeck (OU) state process, while maintaining the analytical tractability of the model. To accomplish this, the class of quadratic processes, consisting of those Markov state processes that yield QTSM, is introduced. The main result states that OU processes are the only conservative quadratic processes. In general, however, a quadratic potential can be added to allow QTSMs to model default risk. It is further shown that the exponent functions that are inherent in the definition of the quadratic property can be determined by a system of Riccati equations with a unique admissible parameter set. The implications of these results for modeling the term structure of risk-free and defaultable rates are discussed. [source] PRICING IN AN INCOMPLETE MARKET WITH AN AFFINE TERM STRUCTUREMATHEMATICAL FINANCE, Issue 3 2004Virginia R. Young We apply the principle of equivalent utility to calculate the indifference price of the writer of a contingent claim in an incomplete market. To recognize the long-term nature of many such claims, we allow the short rate to be random in such a way that the term structure is affine. We also consider a general diffusion process for the risky stock (index) in our market. In a complete market setting, the resulting indifference price is the same as the one obtained by no-arbitrage arguments. We also show how to compute indifference prices for two types of contingent claims in an incomplete market, in the case for which the utility function is exponential. The first is a catastrophe risk bond that pays a fixed amount at a given time if a catastrophe does not occur before that time. The second is equity-indexed term life insurance which pays a death benefit that is a function of the short rate and stock price at the random time of the death of the insured. Because we assume that the occurrence of the catastrophe or the death of the insured is independent of the financial market, the markets for the catastrophe risk bond and the equity-indexed life insurance are incomplete. [source] Stochastic Volatility Corrections for Interest Rate DerivativesMATHEMATICAL FINANCE, Issue 2 2004Peter Cotton We study simple models of short rates such as the Vasicek or CIR models, and compute corrections that come from the presence of fast mean-reverting stochastic volatility. We show how these small corrections can affect the shape of the term structure of interest rates giving a simple and efficient calibration tool. This is used to price other derivatives such as bond options. The analysis extends the asymptotic method developed for equity derivatives in Fouque, Papanicolaou, and Sircar (2000b). The assumptions and effectiveness of the theory are tested on yield curve data. [source] | ||||||||||||||||||||||||||||