Pricing Defaultable Bonds in a Markov Modulated Market

We address the problem of pricing defaultable bonds in a Markov modulated market. Using Merton's structural approach we show that various types of defaultable bonds are combination of European type contingent claims. Thus pricing a defaultable bond is tantamount to pricing a contingent claim in a Markov modulated market. Since the market is incomplete, we use the method of quadratic hedging and minimal martingale measure to derive locally risk minimizing derivative prices, hedging strategies and the corresponding residual risks. The price of defaultable bonds are obtained as solutions to a system of PDEs with weak coupling subject to appropriate terminal and boundary conditions. We solve the system of PDEs numerically and carry out a numerical investigation for the defaultable bond prices. We compare their credit spreads with some of the existing models. We observe higher spreads in the Markov modulated market. We show how business cycles can be easily incorporated in the proposed framework. We demonstrate the impact on spreads of the inclusion of rare states that attempt to capture a tight liquidity situation. These states are characterized by low risk-free interest rate, high payout rate and high volatility.

Facile C-O bond scission in alcohols on Zn surfaces

Interaction of methanol, ethanol, and 2-propanol with polycrystalline as well as (0001) surfaces of Zn has been investigated by photoelectron spectroscopy and vibrational energy loss spectroscopy. All the alcohols show evidence for the condensed species along with the chemisorbed species at 80 K. With increase in temperature to similar to 120 K, the condensed species desorbs, leaving the chemisorbed species which decomposes to give the alkoxy species. The alkoxy species is produced increasingly at lower temperatures as we go from methanol to 2-propanol, the 2-propoxy species occurring even at 80 K. The alkoxy species undergo C-O bond scission giving rise to a hydrocarbon species and oxygen. The C-O bond cleavage occurs at a relatively low temperature of similar to 150 K. The effect of preadsorbed oxygen is to stabilize the methoxy species and prevent C-O bond scission. On the other hand, coadsorption of oxygen with methanol favors the formation of the methoxy species and gives rise to hydrocarbon species arising from the C-O bond scission even at 80 K.

Modeling of a pressure modulated desalination system using bond graph methodology

A desalination system is a complex multi energy domain system comprising power/energy flow across several domains such as electrical, thermal, and hydraulic. The dynamic modeling of a desalination system that comprehensively addresses all these multi energy domains is not adequately addressed in the literature. This paper proposes to address the issue of modeling the various energy domains for the case of a single stage flash evaporation desalination system. This paper presents a detailed bond graph modeling of a desalination unit with seamless integration of the power flow across electrical, thermal, and hydraulic domains. The paper further proposes a performance index function that leads to the tracking of the optimal chamber pressure giving the optimal flow rate for a given unit of energy expended. The model has been validated in steady state conditions by simulation and experimentation.

Bond graph toolbox for handling complex variable

Bond graph is an apt modelling tool for any system working across multiple energy domains. Power electronics system modelling is usually the study of the interplay of energy in the domains of electrical, mechanical, magnetic and thermal. The usefulness of bond graph modelling in power electronic field has been realised by researchers. Consequently in the last couple of decades, there has been a steadily increasing effort in developing simulation tools for bond graph modelling that are specially suited for power electronic study. For modelling rotating magnetic fields in electromagnetic machine models, a support for vector variables is essential. Unfortunately, all bond graph simulation tools presently provide support only for scalar variables. We propose an approach to provide complex variable and vector support to bond graph such that it will enable modelling of polyphase electromagnetic and spatial vector systems. We also introduced a rotary gyrator element and use it along with the switched junction for developing the complex/vector variable's toolbox. This approach is implemented by developing a complex S-function tool box in Simulink inside a MATLAB environment This choice has been made so as to synthesise the speed of S-function, the user friendliness of Simulink and the popularity of MATLAB.

Chemical bond approach to determining conductivity band gaps in amorphous chalcogenides and pnictides

The minimum energy required for the formation of conjugate pair of charged defects is found to be approximately equal to the experimental activation energy for d.c. conductivity in a number of amorphous chalcoganides and pnictides. This observation implies that the defect pair formation energy represents an intrinsic gap for transport in amorphous chalcogenides.

Risk Minimizing Option Pricing in a Semi-Markov Modulated Market

We address risk minimizing option pricing in a semi-Markov modulated market where the floating interest rate depends on a finite state semi-Markov process. The growth rate and the volatility of the stock also depend on the semi-Markov process. Using the Föllmer–Schweizer decomposition we find the locally risk minimizing price for European options and the corresponding hedging strategy. We develop suitable numerical methods for computing option prices.

Portfolio Optimization in a Semi-Markov Modulated Market

We address a portfolio optimization problem in a semi-Markov modulated market. We study both the terminal expected utility optimization on finite time horizon and the risk-sensitive portfolio optimization on finite and infinite time horizon. We obtain optimal portfolios in relevant cases. A numerical procedure is also developed to compute the optimal expected terminal utility for finite horizon problem.

Theoretical investigations of the two-bond proton-carbon-13 coupling constants. Angular variations of the couplings involving carboxyl carbon

A formulation has been developed using perturbation theory to evaluate the π-contribution to the nuclear spin coupling constants involving nuclei at least one of which is an unsaturated center. This fromulation accounts for the π-contribution in terms of the core polarization and one-center exchange at the π-center. The formulation developed together with the Dirac vector model and Penney-Dirac bond-order formalisms was employed to calculate the geminal (two-bond) proton coupling constants of carboxyl carbons in α-disubstituted acetic acids. The calculated coupling constants were found to have an orientational dependence. The results of the calculation are in good agreement with the experimental values.

Valence bond analysis of the Kondo chain Hamiltonian

Accurate extrapolations for the ground state energy per site of the one - dimensional Kondo chain system is obtained from exact finite system calculations carried out employing a valence bond scheme. An analysis of the ground state wave function indicates that the localized spin is quenched for all nonzero values of the Kondo exchange constant in one dimension.

An investigation of bond formation in the weakly bound first excited 1Σ and lowest 3Σ states of HeH+

The role of the electronic kinetic energy and its Cartesian components is examined during the formation of the first excited 1�£ and the lowest 3�£ states of HeH+ employing wavefunctions of multi-configuration type with basis orbitals in elliptic coordinates. Results show that the bond formation in these states is preceded primarily by a charge transfer from H to He+ rather than by polarisation of the H-orbital by He+

Vibration spectra of ferroelectric alkali trihydrogen selenites and the nature of the hydrogen bond potential in these crystals

Raman spectra of the ferroelectric LiH3 (SeO3)2 and NaH3(SeO3)2 and the anti-ferroelectric KH3 (SeO3)2 have been recorded at room temperature using a He-Ne and also an Ar-ion laser source. The infrared absorption spectra of these crystals and their deuterated analogues have been recorded in the region 400–4000 cm−1 both below and above the Curie temperature. From an analysis of the spectrum in the region 400–900 cm−1 it is concluded that (i) in LiH3 (SeO3)2 the protons are ordered in an asymmetric double minimum potential with a low barrier and the spectrum can be interpreted in terms of HSeO3− and H2SeO3 vibrations, (ii) in NaH3 (SeO3)2 all three protons occupy a single minimum potential at room temperature and below the transition temperature the groups HSeO3− and H2SeO3 are present, (iii) the proton at the inversion centre in KH3(SeO3)2 is in a broad troughed potential well and the low temperature spectrum is more likely to be due to H3SeO3+ and SeO32− species. This deviation of the spectrum from that of the previous two crystals is attributed to the difference in H-bond scheme and hence the absence of any cooperative motion of protons in this crystal.

Systematic variation in bond lengths of peptides

The lengths of the carbonyl as well as of the adjacent C-N and C-C bonds in peptides are shown to vary systematically with the central C-N bond length. Results of ab initio calculations on N-methylacetamide and its Li+, Na+ and Mg2+ complexes are also discussed.

Conformations of Heterochiral and Homochiral Proline-Pseudoproline Segments in Peptides: Context Dependent Cis-Trans Peptide Bond Isomerization

The pseudoproline residue (Psi Pro, L-2,2-dimethyl-1,3-thiazolidine-4-carboxylic acid) has been introduced into heterochiral diproline segments that have been previously shown to facilitate the formation of beta-hairpins, containing central two and three residue turns. NMR studies of the octapeptide Boc-Leu-Phe-Val-(D)Pro-Psi Pro-Leu-Phe-Val-OMe (1), Boc-Leu-Val-Val-(D)Pro-Psi Pro-Leu-Val-Val-OMe (2), and the nonapeptide sequence Boc-Leu-Phe-Val-(D)Pro-Psi Pro-(D)Ala-Leu-Phe-Val-OMe (3) established well-registered beta-hairpin structures in chloroform solution, with the almost exclusive population of the trans conformation for the peptide bond preceding the Psi Pro residue. The beta-hairpin conformation of 1 is confirmed by single crystal X-ray diffraction. Truncation of the strand length in Boc-Val-(D)Pro-Psi Pro-Leu-OMe (4) results in air increase in the population of the cis conformer, with a cis/trans ratio of 3.65. Replacement of Psi Pro in 4 by (L)Pro in 5, results in almost exclusive population of the trans form, resulting in an incipient beta-hairpin conformation, stabilized by two intramolecular hydrogen bonds. Further truncation of the sequence gives an appreciable rise in the population of cis conformers in the tripeptide piv-(D)Pro-Psi Pro-Leu-OMe (6). In the homochiral segment Piv-Pro Psi Pro-Leu-OMe (7) only the cis form is observed with the NMR evidence strongly supporting a type VIa beta-turn conformation, stabilized by a 4 -> 1 hydrogen bond between the Piv (CO) and Leu (3) NH groups. The crystal structure of the analog peptide 7a (Piv-Pro-Psi(H,CH3)Pro-Leu-NHMe) confirms the cis peptide bond geometry for the Pro-Psi(H,CH3)pro peptide bond, resulting in a type VIa beta-turn conformation.

The hydrogen bond: a molecular beam microwave spectroscopist's view with a universal appeal

In this manuscript, we propose a criterion for a weakly bound complex formed in a supersonic beam to be characterized as a `hydrogen bonded complex'. For a `hydrogen bonded complex', the zero point energy along any large amplitude vibrational coordinate that destroys the orientational preference for the hydrogen bond should be significantly below the barrier along that coordinate so that there is at least one bound level. These are vibrational modes that do not lead to the breakdown of the complex as a whole. If the zero point level is higher than the barrier, the `hydrogen bond' would not be able to stabilize the orientation which favors it and it is no longer sensible to characterize a complex as hydrogen bonded. Four complexes, Ar-2-H2O, Ar-2-H2S, C2H4-H2O and C2H4-H2S, were chosen for investigations. Zero point energies and barriers for large amplitude motions were calculated at a reasonable level of calculation, MP2(full)/aug-cc-pVTZ, for all these complexes. Atoms in molecules (AIM) theoretical analyses of these complexes were carried out as well. All these complexes would be considered hydrogen bonded according to the AIM theoretical criteria suggested by Koch and Popelier for C-H center dot center dot center dot O hydrogen bonds (U. Koch and P. L. A. Popelier, J. Phys. Chem., 1995, 99, 9747), which has been widely and, at times, incorrectly used for all types of contacts involving H. It is shown that, according to the criterion proposed here, the Ar-2-H2O/H2S complexes are not hydrogen bonded even at zero kelvin and C2H4-H2O/H2S complexes are. This analysis can naturally be extended to all temperatures. It can explain the recent experimental observations on crystal structures of H2S at various conditions and the crossed beam scattering studies on rare gases with H2O and H2S.