A Theoretical Framework

All bond instruments are characterized by the promise to pay a stream of future cash flows. The term structure of interest rates and associated discount function is crucial to the valuation of any debt security and underpins any valuation framework. Armed with the term structure, we can value any bond, assuming it is liquid and default-free, by breaking it down into a set of cash flows and valuing each cash flow with the appropriate discount factor. Further characteristics of any bond, such as an element of default risk or embedded option, are valued incrementally over its discounted cash flow valuation. 

Valuation Under Known Interest-Rate Environment 

Forward rates can be calculated using the no-arbitrage argument. We use this basic premise to introduce the concept of OAS. Consider Table 12.1, which shows the spot interest rates for two interest periods. We can determine that the one-period interest rate starting one period from now is 7.009 percent. This is the implied one-period forward rate. 

We may use the spot rate term structure to value a default-free zero-coupon bond, so for example, a two-period bond would be priced at 89. Using the forward rate, we obtain the same valuation, which is exactly what we expect.  

This framework can be used to value other types of bonds. Let us say we wish to calculate the price of a two-period bond that has the following cash flow stream  

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In a number of classic papers Hohenberg, Kohn and Sham established a theoretical framework for justifying the replacement of die many-body wavefiinction by one-electron orbitals [15, 20, 21]. In particular, they proposed that die charge density plays a central role in describing the electronic stnicture of matter. A key aspect of their work was the local density approximation (LDA). Within this approximation, one can express the exchange energy as... 

A principal aim of the discussion thus far has been to set out a theoretical framework within which it is possible to rationalise the effects of surface roughness on adhesion. It may be useful to summarise this framework before examining practical examples taken from the literature. 

The use of quantum mechanics, or more specifically, orbitals and electronic configurations in teaching general chemistry is now such a widespread trend that it would be utterly futile to try to reverse it. Moreover, orbitals and configurations have been extremely useful in providing a theoretical framework for the unification of a multitude of chemical facts. 

Adar, L. (1969). A theoretical framework for the study of motivation in education. Jerusalem The Hebrew University School of Education. 

The two previous sections outline the main formal and applicative results obtained in our search for a theoretical framework where the number of variables which are explicitly taken into account would be as small as the observables allow. This framework should permit the use of different levels of approximation for the Hamiltonian operator and its orbital representation. That is, the size of the basis set and the kind of approximation used for the integrals should not be predetermined by the formalism. 

The observations on which thermodynamics is based refer to macroscopic properties only, and only those features of a system that appear to be temporally independent are therefore recorded. This limitation restricts a thermodynamic analysis to the static states of macrosystems. To facilitate the construction of a theoretical framework for thermodynamics [113] it is sufficient to consider only systems that are macroscopically homogeneous, isotropic, uncharged, and large enough so that surface effects can be neglected, and that are not acted on by electric, magnetic or gravitational fields. The only mechanical parameter to be retained is the volume V. For a mixed system the chemical composition is specified in terms of the mole numbers Ni, or the mole fractions [Ak — 1,2,..., r] of the chemically pure components of the system. The quantity V/(Y j=iNj) is called the molar... 

Campbell 2003 Rezaei-Moghaddam et al. 2005 Karami and Mansoorabadi 2008). Karami and Mansoorabadi (2008) developed a theoretical framework to explain the relationship between sustainable agricultural attitudes and behaviors. A schematic representation of the theoretical framework of this study is shown in Fig. 2.1. Briefly, according to this theoretical framework, farmers action is guided by two kinds of considerations ... 

Such dependence is naturally not acceptable if one wants to put similarity between quantum systems in a theoretical framework. As will be shown below, the so-called theory of molecular quantum similarity (MQS) does offer a solid basis. The aim of the present chapter is to introduce the basic aspects of the theory and to allow the reader to follow the literature. For applications and a more in-depth presentation of the mathematical aspects, the reader is referred to the review by Bultinck et al. [4],... 

A theoretical framework based on the one-point, one-time joint probability density function (PDF) is developed. It is shown that all commonly employed models for turbulent reacting flows can be formulated in terms of the joint PDF of the chemical species and enthalpy. Models based on direct closures for the chemical source term as well as transported PDF methods, are covered in detail. An introduction to the theory of turbulence and turbulent scalar transport is provided for completeness. 

The challenge within our programme is to follow up the consequences of the tube model for the non-linear rheology of branched polymers - would such a theoretical framework lead to any understanding of the special behaviour of, for example, LDPE in complex flows We build up our tools as before in the context of linear polymers. 

As it is shown in the following, among all the uncertain reasoning methods, the Dempster-Shafer theory offers a theoretical framework particularly suited to tackle the objectives of the state manager (modularity, uncertainty management, robustness). In addition, its application is independent of the method used to determine the fault signals. 

Criss et al. (1987) and Gregory et al. (1989) developed a theoretical framework that describes the kinetics of oxygen isotope exchange between minerals and coexisting fluids. Figure 2.17 shows characteristic patterns in 8-5 plots for some hy-drothermally altered granitic and gabbroic rocks. The arrays displayed on... 

A theoretical framework for considering how the behavior of dynamical systems change as some parameter of the system is altered. Poincare first apphed the term bifurcation for the splitting of asymptotic states of a dynamical system. A bifurcation is a period-doubling, -quadrupling, etc., that precede the onset of chaos and represent the sudden appearance of a qualitatively different behavior as some parameter is varied. Bifurcations come in four basic varieties flip bifurcations, fold bifurcations, pitchfork bifurcations, and transcritical bifurcations. In principle, bifurcation theory allows one to understand qualitative changes of a system change to, or from, an equilibrium, periodic, or chaotic state. 

Whereas a theoretical framework for understanding potential emission of secondary electrons is well established, a similar quantitative framework for kinetic ejection must await future theoretical development. Nevertheless, kinetic ejection... 

If there were a flag that represented the science of chemistry, it would be the periodic table. The periodic table is a concise organizational chart of the elements. The periodic table not only summarizes important facts about the elements, but it also incorporates a theoretical framework for understanding the relationships between elements. The modern periodic table attests to human s search for order and patterns in nature. As such, the periodic table is a dynamic blueprint for the basic building blocks of our universe. This chapter examines the development of the modern periodic table and presents information on how the modem periodic table is organized. 

Molecular mechanics lies conceptually between quantum mechanics and classical mechanics, in that data obtained from quantum mechanical calculations are incorporated into a theoretical framework established by the classical equations of motion. The Bom-Oppenheimer approximation, used in quantum mechanics, states that Schrddinger s equation can be separated into a part that describes the motion of electrons and a part that describes the motion of nuclei, and that these can be treated independently. Quantum mechanics is concerned with the properties of electrons molecular mechanics is concerned with the nuclei, while electrons are treated in a classical electrostatic manner. 

Any scientific hypothesis is simply an attempt to provide a theoretical framework that allows people to understand the processes that interest them and also enables... 

In Fig. 27 experimental 1/e values are represented as a function of the temperature for samples with different compositions. As shown, the experimental values qualitatively follow Eq. 7 although 1/e achieves a non-zero value at the critical temperature. The intrinsic composite structure of semicrystalline polymers has been invoked to understand this effect [8, 6]. The order of magnitude of the constant A has been reported to be around 103 °C [11] which is consistent with the relatively high polarizability of these materials. At this point it is important to emphasize that the knowledge of morphological aspects of these copolymers might help, in future, to develop a theoretical framework capable of accounting for the experimental observations. 

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