Term Structure Of Forward Rates Research Articles

Using extracted forward rate term structure information to forecast foreign exchange rates

Abstract The difficulty of beating the random walk in forecasting spot foreign exchange rates is well documented. In this paper, we propose a functional principal component-based scalar response model which we benchmark versus leading VECM frameworks. Our approach leads to near systematic outperformance in terms of a comparison of performance measures, and to multiple instances of statistically significant improvements in forecast accuracy. Overall, our results provide evidence that the forward rate term structure contains substantial information about the evolution of the spot exchange rate. Finally, a stylised trading strategy is employed to demonstrate the potential economic benefits of our approach.

A Unified Willow Tree Framework for One-Factor Short-Rate Models

The familiar binomial model allows the stock to move from the current node to just two possible prices in the next time step, which seriously limits the model’s ability to handle many realistic problems efficiently. The trinomial adds a branch and gains a lot more flexibility. The “willow tree” structure allows many branches at each node, and recent work has shown that it can produce significant improvements in performance for some classes of problems. Modeling interest rate behavior is an extremely important case. A viable short-rate model must allow stochastic volatility, and for practical use it must be arbitrage-free, meaning it can be calibrated to match the observed term structure of forward rates in the market. In this article, Wang and Xu show how to construct willow tree lattice models for eleven of the most common single-factor interest rate models, including those designed to be arbitrage-free. Unlike some of these models, the willow tree approach can handle interest rates that go negative, which is essential in the current environment.

Extracting Forward Rate Term Structure Information in Foreign Exchange

The difficulty of beating the random walk in forecasting spot foreign exchange rates is well documented, with the restricted VECM of Clarida and Taylor (1997) providing the primary challenge. We seek to extract the informational content of the forward rate term structure through the implementation of a functional principal component-based scalar response model. Our out-of-sample framework leads to near systematic outperformance in terms of a direct comparison of performance measures, versus both the VECM and random walk. The results indicate that the forward rate term structure contains statistically significant information about the evolution of the spot exchange rate.

Kernel-Correlated Lévy Field Driven Forward Rate and Application to Derivative Pricing

We propose a term structure of forward rates driven by a kernel-correlated Levy random field under the HJM framework. The kernel-correlated Levy random field is composed of a kernel-correlated Gaussian random field and a centered Poisson random measure. We shall give a criterion to preclude arbitrage under the riskneutral pricing measure. As applications, an interest rate derivative with general payoff functional is priced under this pricing measure.

On a stochastic heat equation with first order fractional noises and applications to finance

In this paper, we propose a class of stochastic heat equations with first order fractional noises. We define a first order noise through the adjoint operator of the first order operator, where the operation of the stochastic integral can be avoided. In this framework, the existence and uniqueness of the solution of the equation will be established. Further, we give the regularity of the solution. Finally, we model the term structure of forward rate with the solutions and give the conditions under which the market is arbitrary-free.

REVERSE REGRESSIONS AND LONG‐HORIZON FORECASTING

SUMMARYLong‐horizon predictive regressions in finance pose formidable econometric problems when estimated using available sample sizes. Hodrick in 1992 proposed a remedy that is based on running a reverse regression of short‐horizon returns on the long‐run mean of the predictor. Unfortunately, this only allows the null of no predictability to be tested, and assumes stationary regressors. In this paper, we revisit long‐horizon forecasting from reverse regressions, and argue that reverse regression methods avoid serious size distortions in long‐horizon predictive regressions, even when there is some predictability and/or near unit roots. Meanwhile, the reverse regression methodology has the practical advantage of being easily applicable when there are many predictors. We apply these methods to forecasting excess bond returns using the term structure of forward rates, and find that there is indeed some return forecastability. However, confidence intervals for the coefficients of the predictive regressions are about twice as wide as those obtained with the conventional approach to inference. We also include an application to forecasting excess stock returns. Copyright © 2011 John Wiley & Sons, Ltd.

The dynamics of long forward rate term structures

AbstractIn this article, we look at study the dynamics of forward rates with maturities longer than 14 years. We re‐document the phenomenon of the downward sloping long forward rate term structure using U.S. Treasury STRIPS data over the period 1988 to 2007. By calibrating Diebold F. X. and Li C.‐L.'s (2006) dynamic Nelson C. R. and Siegel A. F. (1987) and Christensen J. H. E., Diebold F. X., and Rudebusch G. D.'s (2007) arbitrage‐free Nelson‐Siegel models, we find that both models explain the empirical phenomenon very well. Out‐of‐sample comparison shows that imposing no‐arbitrage restriction indeed improves the forecasting performance. © 2010 Wiley Periodicals, Inc. Jrl Fut Mark 30:957–982, 2010

Bond risk premia and realized jump risk

We find that augmenting a regression of excess bond returns on the term structure of forward rates with an estimate of the mean realized jump size almost doubles the R 2 of the forecasting regression. The return predictability from augmenting with the jump mean easily dominates that offered by augmenting with options-implied volatility and realized volatility from high-frequency data. In out-of-sample forecasting exercises, inclusion of the jump mean can reduce the root mean square prediction error by up to 40%. The incremental return predictability captured by the realized jump mean largely accounts for the countercyclical movements in bond risk premia. This result is consistent with the setting of an incomplete market in which the conditional distribution of excess bond returns is affected by a jump risk factor that does not lie in the span of the term structure of yields.

Bond Risk Premia and Realized Jump Risk

We find that augmenting a regression of excess bond returns on the term structure of forward rates with an estimate of the mean realized jump size almost doubles the R2 of the forecasting regression. The return predictability from augmenting with the jump mean easily dominates that offered by augmenting with options-implied volatility and realized volatility from high frequency data. In out-of-sample forecasting exercises, inclusion of the jump mean can reduce the root mean square prediction error by up to 40 percent. The incremental return predictability captured by the realized jump mean largely accounts for the countercyclical movements in bond risk premia. This result is consistent with the setting of an incomplete market in which the conditional distribution of excess bond returns is affected by a jump risk factor that does not lie in the span of the term structure of yields.

Bond Risk Premia and Realized Jump Volatility

We find that adding a measure of market jump volatility risk to a regression of excess bond returns on the term structure of forward rates nearly doubles the R² of the regression. Our market jump volatility measure is based on the realized jumps identified from high-frequency stock market returns using the bi-power variation technique. The significant enhancement of bond return predictability is robust to different forecasting horizons, to using non-overlapping returns and to the choice of different window sizes in computing the jump volatility. This market jump volatility factor also crowds out the price-dividend ratio in explaining much of the countercyclical movement in bond risk premia. We argue that this finding provides support for the unspanned stochastic volatility hypothesis according to which the conditional distribution of excess bond returns is affected by state variables that are not in the span of the term structure of yields and forward rates.

Pricing of multiple defaultable bond

In this paper a generalized defaultable bond pricing formula is derived by assuming that there exists a defaultable forward rate term structure and that firms in the economy interact when default occurs. Generally, The risk-neutral default intensity λQ is not equal to the empirical or actual default intensity λ. This paper proves that multiple default intensities are invariant under equivalent martingale transformation, given a well-diversified portfolio corresponding to the defaultable bond. Thus one can directly apply default intensities and fractional losses empirically estimated to the evaluation of defaultable bonds or contingent claims.

Does Correlation Matter in Pricing Caps and Swaptions?

This paper studies the effect of forward rate correlations on caplet and swaption prices. A two-factor HJM lognormal model of forward rates that implies a realistic covariance matrix of forward rates is constructed. A one-factor lognormal model, with the same forward rate volatilities as the two-factor one, is employed for comparison purposes. The one- and two-factor models price European caplets identically. The one-factor model overprices European swaptions as expected. But the magnitude of overpricing is surprisingly small, less than three percent for at-the-money swaptions on five-year semi-annual swaps. The overpricing is less for shorter swap lengths. The surprising result is that the one-factor model underprices both American caplets and American-type swaptions. Five-year at-the-money American caplets on six-month rates are underpriced by as much as twelve percent and three-year at-the-money constant maturity Bermudan swaptions on two-year semi-annual swaps by as much as ten percent. The underpricing is relatively low for six-month and one-year options but increases with option maturity and forward rate decorrelation. Unlike constant maturity Bermudan swaptions, regular Bermudan swaptions are overpriced by the one-factor model by more than four percent in the case of three-year maturity swaptions. An intuitive explanation for the underpricing of American options under the one-factor model is offered. This explanation implies that American options on any type of interest rate security would be underpriced if perfect correlation across the forward rate term structure is assumed.

Market Rate Expectations and Forward Rates

ANTTI ILMANGN is a vice president at Salomon Brothers in fucedincome research in London, England. I hree main forces determine the term structure of forward rates: the market’s rate expectations; required bond risk premiums; and the convexity bias. Many market observers believe that the first force is the dominant one. This article focuses on the impact of the market’s rate expectations on the yield curve shape but emphasizes the consequences of ignoring the two other forces. The impact of rate expectations on today’s yield

The Efficacy of Term Structure Estimation Techniques

Business. I t is well-recognized that the term structure of defaultfree interest rates is not directly observable in a market where government obligations of various maturities bear coupons at different rates, and where ordinary income and capital gains are subject to unknown and varying effective tax rates. (See, for example, Jordan [1984], Livingston [1979], McCulloch [1975], Robicheck and Niebuhr [1970], Ronn [I 9871, Schaefer [1982], and Torous [1985].) At the same time, accurate knowledge of the term structure of spot rates and the underlying term structure of forward rates is essential for financial research and practice. This information cannot be obtained from the yield curve of Treasury strips, because those obligations are traded in a separate and distinct market. The strips market is dominated by a unique clientele of U.S. taxexempt institutions and Japanese investors who have a tax incentive to hold long-term principal (versus coupon) strips. There are unknown differences in effective tax rates between the two markets, and a drfference in liquidity in favor of the wider market for standard coupon bonds. The term structure underlying the coupon bond market must therefore be estimated from bonds traded in that market. Such estimates are required for the management of fixed-income security portfolios and for pricing interest rate-contingent claims such as fixed-income securities, options, and futures (see Ho and Lee [I9861 and Kishimot

Exchange market efficiency: An examination of speculation across forward markets

The rejection of the joint hypothesis of exchange market efficiency and no risk premium is shown to hold up all across the term structure of forward rates for the Canadian dollar/U.S. dollar exchange rate.