American Options in the Heston Model with Stochastic Interest Rate and Its Generalizations

Abstract

We consider the Heston model with the stochastic interest rate of Cox–Ingersoll–Ross (CIR) type and more general models with stochastic volatility and interest rates depending on two CIR-factors; the price, volatility and interest rate may correlate. Time-derivative and infinitesimal generator of the process for factors that determine the dynamics of the interest rate and/or volatility are discretized. The result is a sequence of embedded perpetual options arising in the time discretization of a Markov-modulated Lévy model. Options in this sequence are solved using an iteration method based on the Wiener–Hopf factorization. Typical shapes of the early exercise boundary are shown, and good agreement of option prices with prices calculated with the Longstaff–Schwartz method and Medvedev–Scaillet asymptotic method is demonstrated.     

Kinetic study of the reaction of nucleophilic cyclopropanation of C60 fullerene with halogenated maleopimarimide

The kinetics of nucleophilic fullerene cyclopropanation by halomethyl ketones with a diterpene fragment has been studied by the Bingel method, and the influence of the biologically active cyclopropanating agent on the process has been estimated. It has been revealed that favorable conditions for carrying out the reaction result in maximum monofunctionalized methanofullerenes formation with the maximum yield.     

Effect of non-covalent interactions in 2,5-di-Me-pyrazine-di-N-oxide - methanol – Carbon nanotube electrocatalytic system

Catalytic oxidation of methanol (MeOH) in the absence of noble metals and noble metal oxides as catalysts, and the use of metal-free materials are inexpensive and attractive process for practical use in electrocatalysis, sensors, and in direct methanol fuel cells. In previous works, it was found that the use of single-walled (SWCNT) or multi-walled (MWCNT) carbon nanotube paper electrodes instead of GC increases the catalytic efficiency of organic compounds oxidation in the presence of aromatic di-N-oxides by several times. In this work, the effect of non-covalent interactions on the catalytic efficiency of MeOH oxidation in the presence of 2,5-di-Me-pyrazine-di-N-oxide (Pyr₁) in 0.1 M Bu₄NClO₄ solution in acetonitrile at SWCNT and MWСNT paper electrodes was studied by the methods of quantum chemical modeling, Raman spectroscopy, and using electrochemical data. New factors determined the features of mechanism of MeOH oxidation on CNT electrodes and lead to an increase in the catalytic efficiency of the electrode process in comparison with the GC electrode were established.     

Can We Merge the Weak and Strong Tetrel Bonds? Electronic Features of Tetrahedral Molecules Interacted with Halide Anions

Using the orbital-free quantum crystallography approach, we have disclosed the quantitative trends in electronic features for bonds of different strengths formed by tetrel (Tt) atoms in stable molecular complexes consisting of electrically neutral tetrahedral molecules and halide anions. We have revealed the role of the electrostatic and exchange-correlation components of the total one-electron static potential that are determined by the equilibrium atomic structure and by kinetic Pauli potential, which reflects the spin-dependent electron motion features of the weak and strong bonds. The gap between the extreme positions in the electrostatic and total static potentials along the line linking the Tt atom and halide anion is wide for weak bonds and narrow for strong ones. It is in very good agreement with the number of minima in the Pauli potential between the bounded atoms. This gap exponentially correlates with the exchange-correlation potential in various series with a fixed nucleophilic fragment. A criterion for categorizing the noncovalent tetrel bonds (TtB) based on the potential features is suggested.     

Straightforward Approach for Preparing Durable Antibacterial ZnO Nanoparticle Coatings on Flexible Substrates

Flexible antibacterial materials have gained utmost importance in protection from the distribution of bacteria and viruses due to the exceptional variety of applications. Herein, we demonstrate a readily scalable and rapid single-step approach for producing durable ZnO nanoparticle antibacterial coating on flexible polymer substrates at room temperature. Substrates used are polystyrene, poly(ethylene-co-vinyl acetate) copolymer, poly(methyl methacrylate), polypropylene, high density polyethylene and a commercial acrylate type adhesive tape. The deposition was achieved by a spin-coating process using a slurry of ZnO nanoparticles in toluene. A stable modification layer was obtained when toluene was a solvent for the polymer substrates, namely polystyrene and poly(ethylene-co-vinyl acetate). These coatings show high antibacterial efficiency causing >5 log decrease in the viable counts of Gram-negative bacteria Escherichia. coli and Gram-positive bacteria Staphylococcus aureus in 120 min. Even after tapping these coated surfaces 500 times, the antibacterial properties remained unchanged, showing that the coating obtained by the presented method is very robust. In contrast to the above findings, the coatings are unstable when toluene is not a solvent for the substrate.     

Pseudoisocyanine J-aggregate to optical waveguiding crystallite transition: microscopic and microspectroscopic exploration

Using fluorescent microscopy and microspectroscopy, optical properties and morphology transformations in individual pseudoisocyanine (PIC) J-aggregates in aqueous electrolyte solutions have been explored. A stringlike structure of J-aggregates with a string diameter much less than 1 microm has been observed. Photodestruction of the strings under short-wavelength excitation has been revealed. Rodlike PIC crystallites, about 1 microm in diameter, have been observed with time. The fluorescence spectrum of rodlike crystallites has been found to differ from that of stringlike J-aggregate and from PIC crystal powder spectra. The crystallites are very stable, and their photodestruction has not been observed under any excitation conditions. It has been found that rodlike crystallites in contrast to stringlike J-aggregates possess optical waveguide properties. The luminescence of crystallites can be observed only at the excitation spot and at butt ends located up to hundreds of micrometers from the excitation spot.     

Microwave-assisted three-component synthesis of 7-aryl-2-alkylthio-4,7-dihydro-1,2,4-triazolo[1,5-a]-pyrimidine-6-carboxamides and their selective reduction

Multicomponent reactions (MCRs) and microwave-assisted organic synthesis (MAOS) have been used as key methods for the synthesis of fused dihydropyrimidine derivatives. The three-component condensation of 3-amino-5-alkylthio-1,2,4-triazoles with aromatic aldehydes and acetoacetamides under microwave irradiation was developed as a rapid and efficient solution-phase method for the high-yielding preparation of 7-aryl-2-alkylthio-4,7-dihydro-1,2,4-triazolo[1,5-a]pyrimidine-6-carboxamide libraries. In addition, the selective reduction of the formed dihydrotriazolopyrimidines to trans-trans-2-alkylthio-7-aryl-4,5,6,7-tetrahydro-1,2,4-triazolo[1,5-a]pyrimidine-6-carboxamides was established. The described synthetic protocols provide rapid access to novel and diversely substituted dihydroazolopyrimidine libraries.     

2-Halopyridines in the triple reaction in the Pn/KOH/DMSO system to form tri(2-pyridyl)phosphine: Experimental and quantum-chemical dissimilarities

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Interfacial shear rheology

This review summarises the interfacial shear rheology in the context of problems occurring during the measuring process. The main areas covered are surfactants, proteins, macromolecules, monolayers, particles or mixed systems at the gas/liquid and liquid/liquid interface. New developments in measuring techniques, in data analysis, modelling and theory will be discussed, while micro-rheological techniques using optical or magnetic tweezers are not in the scope of this contribution.