Stable distributions and the term structure of interest rates

In an abundance of cases asset returns fit stable distributions better than normal distributions. We examine a model where the term structure of interest rates follows a subordinate process directed by a stable process and indicate how to fix the parameters of the model.     

Estimating VAR models for the term structure of interest rates

In this paper we follow the work of Evans and Marshall and propose new approaches for modelling the joint development of macro variables and the returns of government bond yields of several maturities. The models are estimated and compared with other forecasting schemes previously proposed in the literature, especially those relying on univariate, VAR and error correction methods. The models are then used to judge the hypothesis that the information content of macro variables and the term structure of interest rates as a whole help improving forecasting performance. Our main conclusion is quite simple: if one is interested in computing short-term forecasts, then there is no significant improvement in incorporating information other than the one already present in past observations of the yield at hand; however, if one worries about long-term forecasts (which is frequently the case with pension insurance companies), then the information content of macro variables and the term structure can improve forecasting performance.     

Term structure of interest rates and the expectation hypothesis: The euro area

This paper investigates the informational content of the yield curve in the European market using data on the Italian term structures. According to the expectation hypothesis theory (EHT) the current forward rate equals the future short rate plus a constant risk premium that is time invariant but maturity dependent. This theory has been widely tested in the empirical literature providing various findings according to the country where it has been applied and to the segment of the yield curve examined or the period under study. The standard approach to test the EHT uses the regression techniques assuming data on spot rates and their first differences to be stationary. Recently an increasing number of studies evidenced the non stationarity of interest rates time series and some tests of the EHT are formulated using term spread and forward-spot spread which are stationary. A new strand of literature suggests to investigate the EHT using a restricted VAR framework. In this paper, following [Jondeau, E., Ricart, R., 1999. The expectations hypothesis of the term structure: tests on us, german, french and uk euro-rates. Journal of International Money and Finance 18, 725–750, Ghazali, N.A. Low, S.W., 2002. The expectations hypothesis in emerging financial markets: the case of malaysia. Applied Economics 34, 1147–1156 and Seo, B., 2003. Non linear mean reversion in the term structure of interest rates. Journal of Economic Dynamics and Control 27, 2243–2265], we test if the expectation hypothesis holds using cointegration and error correction analysis. For the period under study results suggest that the long and short term interest rates are cointegrated and therefore subject to a long equilibrium path, providing evidence that the EHT holds for the Italian and the European market.     

利率期限结构的主成分分析

本文采用主成分分析的方法对我国的利率期限结构进行了研究。在采用这种方法的同时,结合非线性变换BOX—COX得出了我国的利率期限结构具有代表性的三个主成分:利率期限结构曲线的平移、斜率的变化以及曲率的变化。同时通过实证分析证实了这种方法的有效性。     

A Bayesian approach to term structure modeling using heavy‐tailed distributions

In this paper, we introduce a robust extension of the three‐factor model of Diebold and Li (J. Econometrics, 130: 337–364, 2006) using the class of symmetric scale mixtures of normal distributions. Specific distributions examined include the multivariate normal, Student‐t, slash, and variance gamma distributions. In the presence of non‐normality in the data, these distributions provide an appealing robust alternative to the routine use of the normal distribution. Using a Bayesian paradigm, we developed an efficient MCMC algorithm for parameter estimation. Moreover, the mixing parameters obtained as a by‐product of the scale mixture representation can be used to identify outliers. Our results reveal that the Diebold–Li models based on the Student‐t and slash distributions provide significant improvement in in‐sample fit and out‐of‐sample forecast to the US yield data than the usual normal‐based model. Copyright © 2011 John Wiley & Sons, Ltd.     

A note on the Flesaker-Hughston model of the term structure of interest rates

A term structure model proposed by Flesaker and Hughston (1996a,b) is analysed within the general framework of arbitrage-free term structure modelling. Basic valuation formulae for caps and swaptions are presented.     

A cyclical square-root model for the term structure of interest rates

This paper presents a cyclical square-root model for the term structure of interest rates assuming that the spot rate converges to a certain time-dependent long-term level. This model incorporates the fact that the interest rate volatility depends on the interest rate level and specifies the mean reversion level and the interest rate volatility using harmonic oscillators. In this way, we incorporate a good deal of flexibility and provide a high analytical tractability. Under these assumptions, we compute closed-form expressions for the values of different fixed income and interest rate derivatives. Finally, we analyze the empirical performance of the cyclical model versus that proposed in Cox et al. (1985) and show that it outperforms this benchmark, providing a better fitting to market data.     

Some results on strong solutions of SDEs with applications to interest rate models

In this work, we investigate SDEs whose coefficients may depend on the entire past of the solution process. We introduce different Lipschitz-type conditions on the coefficients. It turns out that for existence and uniqueness of a strong solution it suffices to have Lipschitz continuity in mean, in a sense to be made precise. We then investigate when it suffices to have local Lipschitz conditions. Furthermore we consider the case of drift coefficients which are locally Lipschitz in mean. Finally we show how these results can be applied to prove existence and uniqueness of solutions in interest rate term structure models.     

Term structure extrapolation and asymptotic forward rates

We investigate different inter- and extrapolation methods for term structures under different constraints in order to generate market-consistent estimates which describe the asymptotic behavior of forward rates. Our starting point is the method proposed by Smith and Wilson, which is used by the European insurance supervisor EIOPA. We use the characterization of the Smith–Wilson class of interpolating functions as the solution to a functional optimization problem to extend their approach in such a way that forward rates will converge to a value which is an outcome of the optimization process. Precise conditions are stated which guarantee that the optimization problems involved are well-posed on appropriately chosen function spaces. As a result, a well-defined optimal asymptotic forward rate can be derived directly from prices and cashflows of traded instruments. This allows practitioners to use raw market data to extract information about long term forward rates, as we will show in a study which analyzes historical EURIBOR swap data.     

Approximating term structure of interest rates using cubic L1 splines

Classical spline fitting methods for estimating the term structure of interest rates have been criticized for generating highly fluctuating fitting curves for bond price and discount function. In addition, the performance of these methods usually relies heavily on parameter tuning involving human judgement. To overcome these drawbacks, a recently developed cubic L₁ spline model is proposed for term structure analysis. Cubic L₁ splines preserve the shape of the data, exhibit no extraneous oscillation and have small fitting errors. Cubic L₁ splines are tested using a set of real financial data and compared with the widely used B-splines.     

Lognormality of rates and term structure models

A term structure model with lognormal type volatility structure is proposed. The Heath, Jarrow and Morton (HJM) framework, coupled with the theory of stochastic evolution equations in infinite dimensions, is used to show that the resulting instantaneous rates are well defined (they do not explode) and remain positive, contrary to those derived in [2]. They are also bounded from below and above by lognormal processes. The model can be used to price and hedge caps, swaptions and other interest rate and currency derivatives including the Eurodollar futures contract, which requires integrability of one over zero coupon bond. This extends results obtained by Sandmann and Sondermann in [22] and [23] for Markovian lognormal short rates to (non-Markovian) lognormal forward rates. We show also existence of invariant measures for the proposed term structure dynamics     

The role of the dependence between mortality and interest rates when pricing Guaranteed Annuity Options

In this paper we investigate the consequences on the pricing of insurance contingent claims when we relax the typical independence assumption made in the actuarial literature between mortality risk and interest rate risk. Starting from the Gaussian approach of Liu et al. (2014), we consider some multifactor models for the mortality and interest rates based on more general affine models which remain positive and we derive pricing formulas for insurance contracts like Guaranteed Annuity Options (GAOs). In a Wishart affine model, which allows for a non-trivial dependence between the mortality and the interest rates, we go far beyond the results found in the Gaussian case by Liu et al. (2014), where the value of these insurance contracts can be explained only in terms of the initial pairwise linear correlation.     

Estimation and empirical evaluation of the time-dependent Extended-CIR term structure model

Email: ym{at}onetel.net.uk Empirical study of 25 years US Treasury bills data shows thateven when the spot interest rate remains fixed, its volatilityvaries significantly over time. Constant-coefficient modelscannot capture these changes as they give rise to time-homogeneousdistributions. Maximum likelihood fitting of a one-factor time-dependentExtended-CIR model of the term structure, whose closed-formsolution was previously obtained by the author, shows that itcan capture these changes, as well as achieve significantlyhigher likelihood value. It is shown that exploitation of theclosed-form solutions substantially improves the accuracy andefficiency of Monte Carlo simulations over high-order discretizationalgorithms. It is also shown that the feasibility of exact one-to-onecalibration of the model to any continuous yield curve allowsvaluation of bond options significantly more accurately andefficiently.     

Sequential Arbitrage Measurements and Interest Rate Envelopes

This paper proposes new measures that provide us with the level of sequential arbitrage in bond markets. All the measures vanish in an arbitrage-free market and all of them are positive otherwise. Each measure is generated by a dual pair of optimization problems. Primal problems permit us to compute optimal sequential arbitrage strategies, if available. Each dual problem generates a concrete proxy for the term structure of interest rates. The set of proxies allows us to obtain the exact market price of any bond and may measure several effects. For instance, the credit risk spread of nondefault free bonds, or the embedded option price of callable or extendible bonds. The developed theory has been tested empirically.     

Valuation and hedging of contingent claims in the HJM model with deterministic volatilities

The aim of the present paper is mostly expository, namely, we intend to provide a concise presentation of arbitrage pricing and hedging of European contingent claims within the Heath, Jarrow and Morton frame-work introduced in Heath et al. (1992) under deterministic volatilities. Such a special case of the HJM model, frequently referred to as the Gaussian HJM model, was studied among others in Amin and Jarrow (1992), Jamshidian (1993), Brace and Musiela (1994a, 1994b). Here, we focus mainly on the partial differential equations approach to the valuation and hedging of derivative securities in the HJM framework. For the sake of completeness, the risk neutral methodology (more specifically, the forward measure technique) is also exposed.     

Ruin probability in the presence of interest earnings and tax payments

In this paper we investigate the ruin probability in a general risk model driven by a compound Poisson process. We derive a formula for the ruin probability from which the Albrecher–Hipp tax identity follows as a corollary. Then we study, as an important special case, the classical risk model with a constant force of interest and loss-carried-forward tax payments. For this case we derive an exact formula for the ruin probability when the claims are exponential and an explicit asymptotic formula when the claims are subexponential.     

The determination of quasistationary distributions directly from the transition rates of an absorbing Markov chain

There are many stochastic systems arising in areas as diverse as wildlife management, chemical kinetics and reliability theory, which eventually “die out,” yet appear to be stationary over any reasonable time scale. The notion of a quasistationary distribution has proved to be a potent tool in modelling this behaviour. In finite-state systems the existence of a quasistationary distribution is guaranteed. However, in the infinite-state case this may not always be so and the question of whether or not quasistationary distributions exist requires delicate mathematical analysis. The purpose of this paper is to present simple conditions for the existence of quasistationary distributions for continuous-time Markov chains and to demonstrate how these can be applied in practice.     

A note on immunization under a general stochastic equilibrium model of the term structure

The paper investigates the actuarial immunization problem under recent stochastic equilibrium models for the term structure of interest rates developed in the theory of finance, thereby generalizing results of Boyle (1978, 1980).     

The consumption-based determinants of the term structure of discount rates

The rate of return of a zero-coupon bond with maturity T is determined by our expectations about the mean (+), variance (-) and skewness (+) of the growth of aggregate consumption between 0 and T. The shape of the yield curve is thus determined by how these moments vary with T. We first examine growth processes in which a higher past economic growth yields a first-degree dominant shift in the distribution of the future economic growth, as assumed for example by Vasicek (J. Financ. Econ. 5, 177–188, 1977). We show that when the growth process exhibits such a positive serial dependence, then the yield curve is decreasing if the representative agent is prudent (), because of the increased risk that it yields for the distant future. A similar definition is proposed for the concept of second-degree stochastic dependence, as observed for example in the Cox–Ingersoll–Ross model, with the opposite comparative static property holding under temperance (), because the change in downside risk (or skweness) that it generates. Finally, using these theoretical results, we propose two arguments in favor of using a smaller rate to discount cash-flows with very large maturities, as those associated to global warming or nuclear waste management. An earlier version of this paper was entitled “Transitory shocks to GNP and the consumption-based term structure of interest rates”. I am indebted to John Campbell, Martin Weitzman and to two referees for helpful comments.     

基于利率的期限结构模型的债券价格过程的分形性质(英文)

本文研究了由文[4]( KENNEDY D P.The term structure of interest rates as a Gaussian randomfield[J] .Mathematical Finance ,1994 ,4(3) :247-258 .)提出的利率期限结构模型下的债券价格过程,并获得了债券价格曲线是一条Hausdorff维数为3/2的分形曲线.