This paper gives a new taxonomy of dynamic term structure models that classifies all existing TSMs as either fundamental models or preference-free single-plus, double-plus, and triple-plus models. We exemplify the new taxonomy by considering preference-free versions of some well-known fundamental short rate models. Single-plus extensions of the fundamental models are shown to be both time-homogeneous and preference-free - two characteristics which do not simultaneously hold under any existing class of TSMs. Though the analytical apparatus for pricing fixed income securities is identical under fundamental models and single-plus models, the latter models are consistent with general non-linear forms of MPRs which may also depend upon an arbitrary set of state variables, leading to better estimates of risk-neutral parameters. The preference-free double-plus and triple-plus extensions of the fundamental models are similar to the Heath, Jarrow, and Morton [1992] models, in that time-inhomogeneous drifts and volatilities are used as quot;smoothing variablesquot; to fit the initial bond prices and initial term structure of volatilities, respectively.

Praise for Dynamic Term Structure Modeling "This book offers the most comprehensive coverage of term-structure models I have seen so far, encompassing equilibrium and no-arbitrage models in a new framework, along with the major solution techniques using trees, PDE methods, Fourier methods, and approximations. It is an essential reference for academics and practitioners alike." --Sanjiv Ranjan Das Professor of Finance, Santa Clara University, California, coeditor, Journal of Derivatives "Bravo! This is an exhaustive analysis of the yield curve dynamics. It is clear, pedagogically impressive, well presented, and to the point." --Nassim Nicholas Taleb author, Dynamic Hedging and The Black Swan "Nawalkha, Beliaeva, and Soto have put together a comprehensive, up-to-date textbook on modern dynamic term structure modeling. It is both accessible and rigorous and should be of tremendous interest to anyone who wants to learn about state-of-the-art fixed income modeling. It provides many numerical examples that will be valuable to readers interested in the practical implementations of these models." --Pierre Collin-Dufresne Associate Professor of Finance, UC Berkeley "The book provides a comprehensive description of the continuous time interest rate models. It serves an important part of the trilogy, useful for financial engineers to grasp the theoretical underpinnings and the practical implementation." --Thomas S. Y. Ho, PHD President, Thomas Ho Company, Ltd, coauthor, The Oxford Guide to Financial Modeling

In this note we consider a classical term structure model framework, that is, a HJM framework on a time-discrete tenor, like the LIBOR market model, using a sequence of tenor discretization, where the tenors are valid for a specific simulation time interval.The setup then allows to model dynamic refinements of the tenor structure and, as a special case, a quasi time-homogenous tenor structure.A time-homogenous tenor structure has some relevance in exposure simulations, where two requirements come together: it is desirable to model a finer tenor structure on the short end of the rate curve compared to the long end of the rate curve and, this property should persist in the simulation at a future time.The property is easily fulfilled by models, which uses an equally fine discretization at all times, e.g., a short rate model, where simulation time discretization and tenor time discretization coincide.As we will demonstrate, a refinement of the tenor structure via a simple interpolation of forward rates would either introduce a strong restriction on the model's volatility structure (as it is the case for a classical fixed tenor LIBOR market model) or introduce an arbitrage violation. The challenge in the refinement is to simulate the right stochastic drifts. Under a (milder) condition on the model's volatility structure, the drifts can be reconstructed using a single additional state variable. The additional state variable is only needed on the coarse discretization tenors, limiting the computational resources needed to implement the model.In a limit case, the approach can be used to glue together a short rate model for the short end of the rate curve and a term-structure model for the long end of the rate curve in a time-homogenous way.

Dai and Singleton (2000) introduced a typology of affine diffusion models when the domain of admissible values of the factors is an intersection of half planes and under some additional constraints on the parameters. This condition on the domain and the additional sufficient constraints are restrictive and can considerably diminish the practical interest of affine models. In this article we successfully address the research agenda sketched by Duffie, Filipovic, Schachermayer (2003, section 12.2, p. 1042). A systematic investigation is performed and our article provides a complete typology in the two-factor case, without prior restrictions on the domain and on the parameters.

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