Constructing positive reliable numerical solution for American call options: a new front-fixing approach

A new front-fixing transformation is applied to the Black?Scholes equation for the American call option pricing problem. The transformed non-linear problem involves homogeneous boundary conditions independent of the free boundary. The numerical solution by an explicit finite-difference method is positive and monotone. Stability and consistency of the scheme are studied. The explicit proposed method is compared with other competitive implicit ones from the points of view accuracy and computational cost

Numerical valuation of two-asset options under jump diffusion models using Gauss-Hermite quadrature

In this work a finite difference approach together with a bivariate Gauss-Hermite quadrature technique is developed for partial-integro differential equations related to option pricing problems on two underlying asset driven by jump-diffusion models. Firstly, the mixed derivative term is removed using a suitable transformation avoiding numerical drawbacks such as slow convergence and inaccuracy due to the appearance of spurious oscillations. Unlike the more traditional truncation approach we use 2D Gauss-Hermite quadrature with the additional advantage of saving computational cost. The explicit finite difference scheme becomes consistent, conditionally stable and positive. European and American option cases are treated. Numerical results are illustrated and analyzed with experiments and comparisons with other well recognized methods.This work has been partially supported by the European Union in the FP7-PEOPLE-2012-ITN program under Grant Agreement Number 304617 (FP7 Marie Curie Action, Project Multi-ITN STRIKE-Novel Methods in Computational Finance) and the Ministerio de Economía y Competitividad Spanish grant MTM2013-41765-P

Moving boundary transformation for American call options with transaction cost: Finite difference methods and computing

The pricing of American call option with transaction cost is a free boundary problem. Using a new transformation method the boundary is made to follow a certain known trajectory in time. The new transformed problem is solved by various finite difference methods, such as explicit and implicit schemes. Broyden’s and Schubert’s methods are applied as a modification to Newton’s method in the case of nonlinearity in the equation. An alternating direction explicit method with second-order accuracy in time is used as an example in this paper to demonstrate the technique. Numerical results demonstrate the efficiency and the rate of convergence of the methods

RECOMBINANT CYTOKINES IN THE TREATMENT OF PNEUMONIA. CLINICAL EXPERIENCE

Antimicrobial chemotherapy is a keystone of the treatment of pneumonia. Prescription of antibacterial drugs does not always ensure the success of treatment due to the secondary immune deficiency developing in the process of the disease and the rapid growthof acquired antibiotic resistance.The article presents experience and clinical and immunological effectiveness of the use of recombinant interleukin-2 (rIL-2) in the treatment and prevention of pneumonia in order to reduce the risk of pneumonia in cerebral strokes and severe exogenous poisoning.In our study, we analyzed two clinical cases with of pneumonia. In patients with severe forms of pneumonia using complex therapy with recombinant interleukin-2, the time to achieve clinical and laboratory remission is reduced, the manifestations of respiratory failure and intoxication syndrome are stopped.Thus, аccumulated clinical experience the administration of the recombinant drug interleukin-2 in combination with antimicrobial drugs in basic therapy showed positive effectiveness, validity and expediency, in order to improve the clinical course, normalize immunological parameters, as well as for the rapid and complete treatment of the inflammatory process in patients of different ages with severe pneumonia

Cytotoxic Activity of Salicylic Acid-Containing Drug Models with Ionic and Covalent Binding

Three different types of drug delivery platforms based on imidazolium ionic liquids (ILs) were synthesized in high preparative yields, namely, the models involving (i) ionic binding of drug and IL; (ii) covalent binding of drug and IL; and (iii) dual binding using both ionic and covalent approaches. Seven ionic liquids containing salicylic acid (SA-ILs) in the cation or/and in the anion were prepared, and their cytotoxicity toward the human cell lines CaCo-2 (colorectal adenocarcinoma) and 3215 LS (normal fibroblasts) was evaluated. Cytotoxicity of SA-ILs was significantly higher than that of conventional imidazolium-based ILs and was comparable to the pure salicylic acid. It is important to note that the obtained SA-ILs dissolved in water more readily than salicylic acid, suggesting benefits of possible usage of traditional nonsoluble active pharmaceutical ingredients in an ionic liquid form. © 2015 American Chemical Society

Cytotoxic Activity of Salicylic Acid-Containing Drug Models with Ionic and Covalent Binding

Three different types of drug delivery platforms based on imidazolium ionic liquids (ILs) were synthesized in high preparative yields, namely, the models involving (i) ionic binding of drug and IL; (ii) covalent binding of drug and IL; and (iii) dual binding using both ionic and covalent approaches. Seven ionic liquids containing salicylic acid (SA-ILs) in the cation or/and in the anion were prepared, and their cytotoxicity toward the human cell lines CaCo-2 (colorectal adenocarcinoma) and 3215 LS (normal fibroblasts) was evaluated. Cytotoxicity of SA-ILs was significantly higher than that of conventional imidazolium-based ILs and was comparable to the pure salicylic acid. It is important to note that the obtained SA-ILs dissolved in water more readily than salicylic acid, suggesting benefits of possible usage of traditional nonsoluble active pharmaceutical ingredients in an ionic liquid form. © 2015 American Chemical Society