Term-structure modeling selection

Selecting the appropriate term-structure model is more of an art than a science, depending on the particular application involved and the users individual requirements. The Ho-Lee and BDT versions, for example, are arbitrage, or arbitrage-free, models, which means that they are designed to match the current term structure. With such models—assuming, of course, that they specify the evolution of the short rate correctly—the law of noarbitrage can be used to determine the price of interest rate derivatives. 

In mathematics a spline is a piecewise polynomial function, made up of individual polynomial sections or segments that are joined together at (user-selected) points known as knot points. Splines used in term structure modeling are generally made up of cubic polynomials. The reason they are often cubic polynomials, as opposed to polynomials of order, say, two or five, is explained in straightforward fashion by de la Grandville (2001). A cubic spline is a function of order three and a piecewise cubic polynomial that is twice differentiable at each knot point. At each knot point the slope and curvature of the curve on either side must match. The cubic spline approach is employed to fit a smooth curve to bond prices (yields) given by the term discount factors. 

Thermodynamics describes the behaviour of systems in terms of quantities and functions of state, but cannot express these quantities in terms of model concepts and assumptions on the structure of the system, inter-molecular forces, etc. This is also true of the activity coefficients thermodynamics defines these quantities and gives their dependence on the temperature, pressure and composition, but cannot interpret them from the point of view of intermolecular interactions. Every theoretical expression of the activity coefficients as a function of the composition of the solution is necessarily based on extrathermodynamic, mainly statistical concepts. This approach makes it possible to elaborate quantitatively the theory of individual activity coefficients. Their values are of paramount importance, for example, for operational definition of the pH and its potentiometric determination (Section 3.3.2), for potentiometric measurement with ion-selective electrodes (Section 6.3), in general for all the systems where liquid junctions appear (Section 2.5.3), etc. 

For kriging models, the structure is defined by the set of independent variables selected - including quadratic terms - and the selection of the correlation model. The parameter estimation is performed by a maximum likelihood procedure. For neural nets, the activation function to be used is defined a priori. The structure is completed by the selection of the number of neurons in the hidden layer. A backpropagation procedure has been used for training. 

Figure 11 Structural models of CNG channels in the closed and open states. The helix S6 and of the pore lumen of the transmembrane domain along with the N-term position of their C-linker are shown. Only the C alpha atoms of two opposite subunits (out of four) are shown forthe sake of clarity. Selected residues, for which experimental measurements were carried out, are shown, d is the shortest distance between opposite C alpha atoms in the pore. The blue box indentifies the narrowest region of the pore.

QSAR - Quantitative Structure Activity Relationships - in general terms denotes models, which, based on the variation in structural and/or electronic features in series of selected, molecules, describe variation in a given end-point of these molecules. These end-points may be, e.g., biological effects or physical-chemical parameters, which experimentally can be verified. Based on the developed QSAR model end-points of new, structurally related compounds, hitherto not being experimentally studied, may be predicted. 

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