Volatility structures of forward rates and the dynamics of the term structure: a multifactor case

This paper considers the modelling of collateralized debt obligations (CDOs). We propose a top-down model via forward rates generalizing Filipović, Overbeck and Schmidt (2009) to the case where the forward rates are driven by a finite dimensional Lévy process. The contribution of this work is twofold: we provide conditions for absence of arbitrage in this generalized framework. Furthermore, we study the relation to market models by embedding them in the forward rate framework in spirit of Brace, Gatarek and Musiela (1997).

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A Quantum Field Theory Term Structure Model Applied to Hedging

International Journal of Theoretical and Applied Finance ◽

10.1142/s0219024903001980 ◽

2003 ◽

Vol 06 (05) ◽

pp. 443-467 ◽

Cited By ~ 5

Author(s):

Belal E. Baaquie ◽

Marakani Srikant ◽

Mitch C. Warachka

Keyword(s):

Field Theory ◽

Quantum Field Theory ◽

Term Structure ◽

Theory Model ◽

Forward Rate ◽

Quantum Field ◽

Structure Model ◽

Term Structure Model ◽

Forward Rates ◽

Low Dimensional

A quantum field theory generalization, Baaquie [1], of the Heath, Jarrow and Morton (HJM) [10] term structure model parsimoniously describes the evolution of imperfectly correlated forward rates. Field theory also offers powerful computational tools to compute path integrals which naturally arise from all forward rate models. Specifically, incorporating field theory into the term structure facilitates hedge parameters that reduce to their finite factor HJM counterparts under special correlation structures. Although investors are unable to perfectly hedge against an infinite number of term structure perturbations in a field theory model, empirical evidence using market data reveals the effectiveness of a low dimensional hedge portfolio.

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ADAPTIVE AND MONOTONE SPLINE ESTIMATION OF THE CROSS-SECTIONAL TERM STRUCTURE

International Journal of Theoretical and Applied Finance ◽

10.1142/s0219024903001840 ◽

2003 ◽

Vol 06 (02) ◽

pp. 195-212 ◽

Cited By ~ 6

Author(s):

ALESSANDRO RAMPONI

Keyword(s):

Interest Rates ◽

Term Structure ◽

Piecewise Polynomial ◽

Discount Function ◽

Cross Sectional ◽

Piecewise Polynomial Approximation ◽

Forward Rates ◽

Regression Spline ◽

Adaptive Regression ◽

Spline Estimation

A number of numerical methods based on a piecewise polynomial approximation have been proposed for the estimation of the term structure of interest rates. Some drawbacks have been pointed out, such as a possible non monotonic estimated discount function and a highly fluctuating spot and forward rates. In order to overcome these kind of problems, we study the feasibility of an adaptive regression spline technique which use a monotone basis together with two alternative knot location procedures: a deterministic greedy algorithm and its randomized version in a simulated annealing framework. The features of the proposed method are tested on a set of data.

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A Review of Term-Structure Models and Their Applications: [forms Part Of: Report of the Fixed-Interest Working Group, B.A.J. 4, II Pg.213–383]

British Actuarial Journal ◽

10.1017/s1357321700000052 ◽

1998 ◽

Vol 4 (2) ◽

pp. 323-383 ◽

Cited By ~ 1

Author(s):

G.B. Chaplin

Keyword(s):

Term Structure ◽

Risk Measures ◽

Evolutionary Models ◽

Forward Rates ◽

Term Structure Models ◽

Accurate Indication ◽

Descriptive Approach ◽

Polynomial Models ◽

Superior Approach ◽

Selection Of

ABSTRACTThe literature on ‘Term-Structure Models’ is extensive with many contributions from financial economists over the last twenty years. This paper reviews examples of term-structure models from different categories (‘equilibrium’, ‘evolutionary’ and ‘descriptive’) with particular emphasis on their intended application. The Vasicek (one-factor equilibrium), Richard (two-factor), and Hull & White (evolutionary) models are discussed in some detail.The paper reviews a particular class of descriptive polynomial models which is flexible and in widespread use both in the academic and the practitioner community. The model is cast in terms of forward rates, applied to the gilt market, and techniques are used to determine how many terms in the polynomial expansion are statistically required in order to describe the market accurately. The model is a linear model of forward and spot rates and is stable; this allows the calculation of risk measures for each bond which give a superior approach, in principle, to portfolio hedging.Selection of model should be driven by its application. If the objective is a reasonably accurate description of the curve and, by implication, an accurate indication of yields which can be obtained in the market, then a model which fits the market accurately is preferable. The ‘descriptive’ approach is therefore most appropriate in this context.

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Tax-induced bias in forward rates, term premiums, and the term structure of interest rates

Economics Letters ◽

10.1016/0165-1765(90)90241-r ◽

1990 ◽

Vol 34 (2) ◽

pp. 183-189 ◽

Cited By ~ 1

Author(s):

Seokchin Kim

Keyword(s):

Interest Rates ◽

Term Structure ◽

Forward Rates

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Forward Rates and Future Policy: Interpreting the Term Structure of Interest Rates

Brookings Papers on Economic Activity ◽

10.2307/2534355 ◽

1983 ◽

Vol 1983 (1) ◽

pp. 173 ◽

Cited By ~ 273

Author(s):

Robert J. Shiller ◽

John Y. Campbell ◽

Kermit L. Schoenholtz ◽

Laurence Weiss

Keyword(s):

Interest Rates ◽

Term Structure ◽

Forward Rates ◽

Future Policy

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MODELING TERM STRUCTURE DYNAMICS: AN INFINITE DIMENSIONAL APPROACH

International Journal of Theoretical and Applied Finance ◽

10.1142/s0219024905003049 ◽

2005 ◽

Vol 08 (03) ◽

pp. 357-380 ◽

Cited By ~ 23

Author(s):

RAMA CONT

Keyword(s):

Interest Rates ◽

Term Structure ◽

Yield Curve ◽

Dimensional Space ◽

Forward Rate ◽

Model Parameters ◽

Stochastic Pde ◽

Forward Rates ◽

Infinite Dimensional ◽

Average Shape

Motivated by stylized statistical properties of interest rates, we propose a modeling approach in which the forward rate curve is described as a stochastic process in a space of curves. After decomposing the movements of the term structure into the variations of the short rate, the long rate and the deformation of the curve around its average shape, this deformation is described as the solution of a stochastic evolution equation in an infinite dimensional space of curves. In the case where deformations are local in maturity, this equation reduces to a stochastic PDE, of which we give the simplest example. We discuss the properties of the solutions and show that they capture in a parsimonious manner the essential features of yield curve dynamics: imperfect correlation between maturities, mean reversion of interest rates, the structure of principal components of forward rates and their variances. In particular we show that a flat, constant volatility structures already captures many of the observed properties. Finally, we discuss parameter estimation issues and show that the model parameters have a natural interpretation in terms of empirically observed quantities.

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Information Content of Implied Forward Exchange Rates

Journal of Derivatives and Quantitative Studies ◽

10.1108/jdqs-01-2003-b0001 ◽

2003 ◽

Vol 11 (1) ◽

pp. 1-23

Author(s):

Seong Hun Kim ◽

Dong Se Cha

Keyword(s):

Exchange Rates ◽

Interest Rates ◽

Error Correction ◽

Information Content ◽

Term Structure ◽

Error Correction Model ◽

Fisher Effect ◽

Interest Rate Parity ◽

Correction Model ◽

Forward Rates

This paper analyzes the information content of the forward exchange rates implied by the interest rate parity, using the Korea and U.S. interest rates and Won/dollar exchange rates observed during the period of March 1991 to December 2002. First, we test the cointegration between implied forward exchange rates and future spot exchange rates to examine their longrun relationship, and find the existence of cointegration. Next, we examine the international Fisher effect and estimate an error correction model for their shortrun relationship. Our analysis supports the international Fisher effect for longer maturities. Our result also supports the error correction model that states that the future spot exchange rates will be adjusted reflecting the information contained in the past-period implied forward rates which is not fully reflected to current spot rates. Finally, we also find that the term structure of implied forward exchange rates is associated with the changes in future spot rates for longer maturities. Based on our findings, we conclude that the longrun relationship exists between the implied forward exchange rates and future spot exchange rates, and the shortrun deviation from the relationship tend to disappear as they return to the longrun relationship in the course of time.

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