Affine term structure models

As aforementioned, it can be shown that the expectation Yi zm ) is determined by an exponential affine form fulfilling the martingale condition. Now, postulating a multiple-Field term structure model the bond price dynamics are given by... 

The implications of this new model class are in contrast to most term structure models discussed in the literature, which assume that the bond markets are complete and fixed income derivatives are redundant securities. Collin-Dufresne and Goldstein [ 18] and Heiddari and Wu [36] show in an empirical work, using data of swap rates and caps/floors that there is evidence for one additional state variable that drives the volatility of the forward rates. Following from that empirical findings, they conclude that the bond market do not span all risks driving the term structure. This framework is rather similar to the affine models of equity derivatives, where the volatility of the underlying asset price dynamics is driven by a subordinated stochastic volatility process (see e.g. Heston [38], Stein and Stein [71] and Schobel and Zhu [69]). 

Again, we start with a one-factor term structure model with USV and show that the exponential affine guess... 

The traditional one-, two- and multi-factor equilibrium models, known as ajfine term structure models (see James and Webber, 2000 or Duffie, 1996, p. 136). These include Gaussian affine models such as Vasicek, Hull-White and Steeley, where the model describes a process with constant volatility and models that have a square-root volatility such as Cox-Ingersoll-Ross (CIR) ... 

A function SH — SH is affine if there are constants a and b such that for all values of x, H x) = a+bx. This describes certain term structure models drift and diffusion functions. 

As discussed in Section 15.1, numerous protein systems have been observed to behave in a manner consistent with a structural-mechanical basis of allosteric control between coupled sites, in which the sites are connected structurally by a network of interactions or pathways [14,15]. In these systems, allostery typically has been presented in terms of the Monod-Wyman-Changeux (MWC) [8] and Koshland-Nemethy-Filmer (KNF) [9] models, both of which are special cases of a more general model [61]. Briefly, the MWC model describes allostery as originating from the equilibria between two macroscopic states, each of which can bind ligand with different affinities. In this model, the equilibrium is driven toward the high-affinity state by mass action. The KNF model, however, relies on an induced fit ... 

Head et al. developed a PLS-based model VALIDATE [47] to scale the relative contributions of entropy and enthalpy to binding affinity for a variety of complexes whose crystal structures had been determined. Molecular mechanics were used to calculate several parameters most correlated with enthalpy of binding, while changes in surface area, number of rotatable bonds fixed upon binding and other parameters more related to the entropy of binding were also included in the model. Of interest was that the principal components of the model were dominated by two terms (AH and AS,... 

Dewar and Maitlis143 discussed quite successfully the course of nitration in series of pyridine-like heterocycles in terms of the Dewar reactivity numbers. There is a continuing interest in the electronic structure of pyridine65, 144-140 a model of this compound has been studied by the ASP MO LCAO SCF (antisymmetrized products) method in the 77-electron approxition.146 The semi-empirical parameters146 were obtained from the most recent values of ionization potentials and electron affinities, and bicentric repulsion integrals were computed theoretically. 

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