Pricing credit derivatives

The financial crisis set off by the default of Lehman Brothers in 2008 leading to disastrous consequences for the global economy has focused attention on regulation and pricing issues related to credit derivatives. Credit risk refers to the potential losses that can arise due to the changes in the credit quality of financial instruments. These changes could be due to changes in the ratings, market price (spread) or default on contractual obligations. Credit derivatives are financial instruments designed to mitigate the adverse impact that may arise due to credit risks. However, they also allow the investors to take up purely speculative positions. In this article we provide a succinct introduction to the notions of credit risk, the credit derivatives market and describe some of the important credit derivative products. There are two approaches to pricing credit derivatives, namely the structural and the reduced form or intensity-based models. A crucial aspect of the modelling that we touch upon briefly in this article is the problem of calibration of these models. We hope to convey through this article the challenges that are inherent in credit risk modelling, the elegant mathematics and concepts that underlie some of the models and the importance of understanding the limitations of the models.

On isentropic lines and isentropic exponents

The three indicators of isentropic lines, namely, the isentropic index, the ratio of pressure and density p/rho and the derivative (partial derivative p/partial derivative rho)s are investigated for all of the fluids in the RefProp 9.0 program. The behaviour of these three entities is evaluated along the saturated vapour line as well as in the superheated vapour region. There is a distinct demarcation of fluids whose isentropic indices can be less than 1 and others for which this behaviour is absent. The critical molar volume is found to be the characterizing feature. Several other interesting features of those three thermodynamic properties are also highlighted. It is observed that most practical engineering compression and expansion processes occur along the decreasing direction of the sound speed.

Model Pseudoconvex Domains and Bumping

The Levi geometry at weakly pseudoconvex boundary points of domains in C-n, n >= 3, is sufficiently complicated that there are no universal model domains with which to compare a general domain. Good models may be constructed by bumping outward a pseudoconvex, finite- type Omega subset of C-3 in such a way that: (i) pseudoconvexity is preserved, (ii) the (locally) larger domain has a simpler defining function, and (iii) the lowest possible orders of contact of the bumped domain with partial derivative Omega, at the site of the bumping, are realized. When Omega subset of C-n, n >= 3, it is, in general, hard to meet the last two requirements. Such well-controlled bumping is possible when Omega is h-extendible/semiregular. We examine a family of domains in C-3 that is strictly larger than the family of h-extendible/semiregular domains and construct explicit models for these domains by bumping.

Path-integral formulation for Levy flights: Evaluation of the propagator for free, linear, and harmonic potentials in the over- and underdamped limits

Levy flights can be described using a Fokker-Planck equation, which involves a fractional derivative operator in the position coordinate. Such an operator has its natural expression in the Fourier domain. Starting with this, we show that the solution of the equation can be written as a Hamiltonian path integral. Though this has been realized in the literature, the method has not found applications as the path integral appears difficult to evaluate. We show that a method in which one integrates over the position coordinates first, after which integration is performed over the momentum coordinates, can be used to evaluate several path integrals that are of interest. Using this, we evaluate the propagators for (a) free particle, (b) particle subjected to a linear potential, and (c) harmonic potential. In all the three cases, we have obtained results for both overdamped and underdamped cases. DOI: 10.1103/PhysRevE.86.061105

Synthesis and supramolecular assembly of the bifunctional borinic acid 1,2-fcB(OH)](2)

Treatment of the chloro-substituted diboradiferrocene derivative 1 with Me3SiOMe and subsequent hydrolysis resulted in formation of the novel organometallic bis(borinic acid) derivative 3. The assembly of 3 into supramolecular structures via hydrogen bonding and reversible covalent boron-oxygen bond formation was explored. Upon crystallization from acetone or THF one-dimensional chains form in which molecules of 3 alternately serve as hydrogen bond donors and acceptors. The additional OH hydrogens that are not involved in hydrogen bonding within the polymeric chains undergo hydrogen bonding to the solvent molecules. Removal of the solvent was achieved at moderate temperature under high vacuum. While the polymeric chains remain intact, in the absence of the solvent as a hydrogen bond acceptor, short contacts to the Cp rings of neighboring polymer strands lead to a network-like structure. At higher temperatures, further dehydration occurs with formation of B-O-B linkages as confirmed by MALDI-TOF mass spectrometry. Oligomers with up to 15 repeating units (30 ferrocenes) were detected.

The Structural Characterization of Folded Peptides Containing the Conformationally Constrained beta-Amino Acid Residue beta(2,2)Ac(6)c

Backbone alkylation has been shown to result in a dramatic reduction in the conformational space that is sterically accessible to a-amino acid residues in peptides. By extension, the presence of geminal dialkyl substituents at backbone atoms also restricts available conformational space for beta and ? residues. Five peptides containing the achiral beta 2,2-disubstituted beta-amino acid residue, 1-(aminomethyl)cyclohexanecarboxylic acid (beta 2,2Ac6c), have been structurally characterized in crystals by X-ray diffraction. The tripeptide Boc-Aib-beta 2,2Ac6c-Aib-OMe (1) adopts a novel fold stabilized by two intramolecular H-bonds (C11 and C9) of opposite directionality. The tetrapeptide Boc-Aib-beta 2,2Ac6c]2-OMe (2) and pentapeptide Boc-Aib-beta 2,2Ac6c]2-Aib-OMe (3) form short stretches of a hybrid a beta C11 helix stabilized by two and three intramolecular H-bonds, respectively. The structure of the dipeptide Boc-Aib-beta 2,2Ac6c-OMe (5) does not reveal any intramolecular H-bond. The aggregation pattern in the crystal provides an example of an extended conformation of the beta 2,2Ac6c residue, forming a polar sheet like H-bond. The protected derivative Ac-beta 2,2Ac6c-NHMe (4) adopts a locally folded gauche conformation about the C beta?Ca bonds (?=-55.7 degrees). Of the seven examples of beta 2,2Ac6c residues reported here, six adopt gauche conformations, a feature which promotes local folding when incorporated into peptides. A comparison between the conformational properties of beta 2,2Ac6c and beta 3,3Ac6c residues, in peptides, is presented. Backbone torsional parameters of H-bonded a beta/beta a turns are derived from the structures presented in this study and earlier reports.

Formulation development and evaluation of lamivudine controlled release tablets using cross-linked sago starch

Objectives: Modified starches based polymeric substances find utmost applicability in pharmaceutical formulation development. Cross-linked starches showed very promising results in drug delivery application. The present investigation concerns with the development of controlled release tablets of lamivudine using cross-linked sago starch. Methods: The cross-linked derivative was synthesized with phosphorous oxychloride and native sago starch in basic pH medium. The cross-linked sago starch was tested for acute toxicity and drug-excipient compatibility study. The formulated tablets were evaluated for various physical characteristics, in vitro dissolution release study and in vivo pharmacokinetic study in rabbit model. Results: In vitro release study showed that the optimized formulation exhibited highest correlation (R) in case of zero order kinetic model and the release mechanism followed a combination of diffusion and erosion process. There was a significant difference in the pharmacokinetic parameters (T-max, C-max, AUC, V-d, T-1/2, and MDT) of the optimized formulation as compared to the marketed conventional tablet Lamivir (R). Conclusion: The cross-linked starch showed promising results in terms of controlling the release behavior of the active drug from the matrix. The hydrophilic matrix synthesized by cross-linking could be used with a variety of active pharmaceutical ingredients for making their controlled/sustained release formulations.

A Savitzky-Golay Filtering Perspective of Dynamic Feature Computation

We address the classical problem of delta feature computation, and interpret the operation involved in terms of Savitzky- Golay (SG) filtering. Features such as themel-frequency cepstral coefficients (MFCCs), obtained based on short-time spectra of the speech signal, are commonly used in speech recognition tasks. In order to incorporate the dynamics of speech, auxiliary delta and delta-delta features, which are computed as temporal derivatives of the original features, are used. Typically, the delta features are computed in a smooth fashion using local least-squares (LS) polynomial fitting on each feature vector component trajectory. In the light of the original work of Savitzky and Golay, and a recent article by Schafer in IEEE Signal Processing Magazine, we interpret the dynamic feature vector computation for arbitrary derivative orders as SG filtering with a fixed impulse response. This filtering equivalence brings in significantly lower latency with no loss in accuracy, as validated by results on a TIMIT phoneme recognition task. The SG filters involved in dynamic parameter computation can be viewed as modulation filters, proposed by Hermansky.

Hypernuclear matter in strong magnetic field

Compact stars with strong magnetic fields (magnetars) have been observationally determined to have surface magnetic fields of order of 10(14)-10(15) G, the implied internal field strength being several orders larger. We study the equation of state and composition of dense hypernuclear matter in strong magnetic fields in a range expected in the interiors of magnetars. Within the non-linear Boguta-Bodmer-Walecka model we find that the magnetic field has sizable influence on the properties of matter for central magnetic field B >= 10(17) G, in particular the matter properties become anisotropic. Moreover, for the central fields B >= 10(18) G, the magnetized hypernuclear matter shows instability, which is signalled by the negative sign of the derivative of the pressure parallel to the field with respect to the density, and leads to vanishing parallel pressure at the critical value B-cr congruent to 10(19) G. This limits the range of admissible homogeneously distributed fields in magnetars to fields below the critical value B-cr. (c) 2012 Elsevier B.V. All rights reserved.

Investigation of phase separation in bulk heterojunction solar cells via supramolecular chemistry

In this work, we have prepared two donor-acceptor-donor (D-A-D) pi-conjugated oligomers to investigate the effect of phase separation on the performance of bulk heterojunction (BHJ) solar cells. These charge transfer low band gap pi-conjugated oligomers (TTB and NMeTTB) were synthesized by Knoevenagel condensation of terthiophenecarbaldehyde and barbiturate appended pyran derivative. The thin film morphology of both the oligomers and along with electron acceptor 6,6]-phenyl-C60-butyric acid methyl ester (PC61BM) was investigated by atomic force microscopy (AFM) and transmission electron microscopy (TEM). The blend of NMeTTB and PC61BM thin film yield highly ordered thin film, whereas there was clear phase separation between TTB and PC61BM in thin film. The BHJ solar cell was fabricated using a blend of NMeTTB and TTB with PC61BM acceptor in 1:1 ratio as active layer, and a power conversion efficiency of 1.8% was obtained. This device characteristic was compared with device having TTB:PC61BM as active layer, and large difference is observed in photocurrents. This poor performance of TTB in BHJ devices was attributed to the difference in the nanoscale morphology of the corresponding derivatives. We rationalize our findings based on the low charge carrier mobility in organic field-effect transistors and miscibility/phase separation parameter of binary components (oligomers and PC61BM) in the active layer of bulk heterojunction solar cells.

A novel filtering framework through Girsanov correction for the identification of nonlinear dynamical systems

Using a Girsanov change of measures, we propose novel variations within a particle-filtering algorithm, as applied to the inverse problem of state and parameter estimations of nonlinear dynamical systems of engineering interest, toward weakly correcting for the linearization or integration errors that almost invariably occur whilst numerically propagating the process dynamics, typically governed by nonlinear stochastic differential equations (SDEs). Specifically, the correction for linearization, provided by the likelihood or the Radon-Nikodym derivative, is incorporated within the evolving flow in two steps. Once the likelihood, an exponential martingale, is split into a product of two factors, correction owing to the first factor is implemented via rejection sampling in the first step. The second factor, which is directly computable, is accounted for via two different schemes, one employing resampling and the other using a gain-weighted innovation term added to the drift field of the process dynamics thereby overcoming the problem of sample dispersion posed by resampling. The proposed strategies, employed as add-ons to existing particle filters, the bootstrap and auxiliary SIR filters in this work, are found to non-trivially improve the convergence and accuracy of the estimates and also yield reduced mean square errors of such estimates vis-a-vis those obtained through the parent-filtering schemes.

Effect of temperature and strain rate on the deformation behavior and microstructure of a homogenized AZ31 magnesium alloy

The plastic deformation behavior and dynamic recrystallization (DRX) in homogenized AZ31 Mg alloy was investigated in uniaxial compression in the temperature range between 150 and 400 degrees C with strain rates ranging from 10(-3) to 10(2) s(-1). Twinning was found to contribute significantly during the early stages of deformation. The onset of twinning was examined in detail by recourse to the examination of the appearance of first local maxima before peak strain in the stress-strain responses and the second derivative of stress with strain. High strain hardening rate was observed immediately after the onset of twinning and was found to increase with the Zener-Hollomon parameter. DRX was observed at temperatures above 250 degrees C whereas deformation at lower temperatures (< 250 degrees C) leads to extensive twinning at all the strain rates. At intermediate temperatures of 250-300 degrees C, plastic strains tend to localize near grain/twin boundaries, confining DRX only to these regions. Increase in the temperature promotes non-basal slip, which, in turn, leads to uniform deformation; DRX too becomes uniform. Deformation behavior in three different regimes of temperature is discussed. The dependence of critical stress for the onset of DRX and peak flow stress on temperature and strain rate are also described. (C) 2013 Elsevier B.V. All rights reserved.

Resolution of Singularities for a Class of Hilbert Modules

Let M be the completion of the polynomial ring C(z) under bar] with respect to some inner product, and for any ideal I subset of C (z) under bar], let I] be the closure of I in M. For a homogeneous ideal I, the joint kernel of the submodule I] subset of M is shown, after imposing some mild conditions on M, to be the linear span of the set of vectors {p(i)(partial derivative/partial derivative(w) over bar (1),...,partial derivative/partial derivative(w) over bar (m)) K-I] (., w)vertical bar(w=0), 1 <= i <= t}, where K-I] is the reproducing kernel for the submodule 2] and p(1),..., p(t) is some minimal ``canonical set of generators'' for the ideal I. The proof includes an algorithm for constructing this canonical set of generators, which is determined uniquely modulo linear relations, for homogeneous ideals. A short proof of the ``Rigidity Theorem'' using the sheaf model for Hilbert modules over polynomial rings is given. We describe, via the monoidal transformation, the construction of a Hermitian holomorphic line bundle for a large class of Hilbert modules of the form I]. We show that the curvature, or even its restriction to the exceptional set, of this line bundle is an invariant for the unitary equivalence class of I]. Several examples are given to illustrate the explicit computation of these invariants.

An approximately H-1-optimal Petrov-Galerkin meshfree method: application to computation of scattered light for optical tomography

Nearly pollution-free solutions of the Helmholtz equation for k-values corresponding to visible light are demonstrated and verified through experimentally measured forward scattered intensity from an optical fiber. Numerically accurate solutions are, in particular, obtained through a novel reformulation of the H-1 optimal Petrov-Galerkin weak form of the Helmholtz equation. Specifically, within a globally smooth polynomial reproducing framework, the compact and smooth test functions are so designed that their normal derivatives are zero everywhere on the local boundaries of their compact supports. This circumvents the need for a priori knowledge of the true solution on the support boundary and relieves the weak form of any jump boundary terms. For numerical demonstration of the above formulation, we used a multimode optical fiber in an index matching liquid as the object. The scattered intensity and its normal derivative are computed from the scattered field obtained by solving the Helmholtz equation, using the new formulation and the conventional finite element method. By comparing the results with the experimentally measured scattered intensity, the stability of the solution through the new formulation is demonstrated and its closeness to the experimental measurements verified.

On k-stellated and k-stacked spheres

We introduce the class Sigma(k)(d) of k-stellated (combinatorial) spheres of dimension d (0 <= k <= d + 1) and compare and contrast it with the class S-k(d) (0 <= k <= d) of k-stacked homology d-spheres. We have E-1(d) = S-1(d), and Sigma(k)(d) subset of S-k(d) ford >= 2k-1. However, for each k >= 2 there are k-stacked spheres which are not k-stellated. For d <= 2k - 2, the existence of k-stellated spheres which are not k-stacked remains an open question. We also consider the class W-k(d) (and K-k(d)) of simplicial complexes all whose vertex-links belong to Sigma(k)(d - 1) (respectively, S-k(d - 1)). Thus, W-k(d) subset of K-k(d) for d >= 2k, while W-1(d) = K-1(d). Let (K) over bar (k)(d) denote the class of d-dimensional complexes all whose vertex-links are k-stacked balls. We show that for d >= 2k + 2, there is a natural bijection M -> (M) over bar from K-k(d) onto (K) over bar (k)(d + 1) which is the inverse to the boundary map partial derivative: (K) over bar (k)(d + 1) -> (K) over bar (k)(d). Finally, we complement the tightness results of our recent paper, Bagchi and Datta (2013) 5], by showing that, for any field F, an F-orientable (k + 1)-neighbourly member of W-k(2k + 1) is F-tight if and only if it is k-stacked.