Calibration to American options: numerical investigation of the de-Americanization method.

American options are the reference instruments for the model calibration of a large and important class of single stocks. For this task, a fast and accurate pricing algorithm is indispensable. The literature mainly discusses pricing methods for American options that are based on Monte Carlo, tree and partial differential equation methods. We present an alternative approach that has become popular under the name de-Americanization in the financial industry. The method is easy to implement and enjoys fast run-times (compared to a direct calibration to American options). Since it is based on ad hoc simplifications, however, theoretical results guaranteeing reliability are not available. To quantify the resulting methodological risk, we empirically test the performance of the de-Americanization method for calibration. We classify the scenarios in which de-Americanization performs very well. However, we also identify the cases where de-Americanization oversimplifies and can result in large errors

A Model of Import Demand for Grain in the Soviet Union

In the agricultural sector, it is important to identify the main directions of investment in order to ensure the food supply for the country's population. One of the most important cases in this sector is ensuring the secure supply of meat and meat products. The state has to choose the most effective tools for supporting the development of indigenous producers and the industry in this sector. The security of the country's food supply is influenced by a large amount of quantitative and qualitative factors. Interaction of these factors and the necessary state support instruments in the meat sector is unevenly treated in the researches of the scientists and varies depending on the specifics of the development of the food sector in a country. The problem of the research is to find out and evaluate the main financial demands and investment directions of the state’s support programs for the support of Ukrainian meat’s sector, which could help secure the state’s demand for the food supply. The purpose of the research is to find out effective mechanisms for the state support and financing of the long-term projects aimed to ensuring the food security in the country. The methodology of research: analysis of research results of Ukrainian and foreign scientists and statistical information (2006–2018 m.). The information is grouped and structured to determine the forecast of meat consumption in Ukraine for 2020, the expected number of population and the determination of the missing quantities of this product in the country. The study provides a model for identifying the volume of long-term investments to ensure the food the security of the country’s supply of meat, identifying the main directions of these investments. The research was based on economic analysis and synthesis models, correlation-regression analysis, mathematic modeling method, etc. The results of research demonstrate the indicators of the food security in the country and determine the adequacy of the food consumption; also the estimation of the investment need for meat production by 2020 is carried out

A reduced basis method for parametrized variational inequalities applied to contact mechanics

International audienceWe investigate new developments of the Reduced-Basis (RB) method for parametrized optimization problems with nonlinear constraints. We propose a reduced-basis scheme in a saddle-point form combined with the Empirical Interpolation Method to deal with the nonlinear constraint. In this setting, a primal reduced-basis is needed for the primal solution and a dual one is needed for the Lagrange multipliers. We suggest to construct the latter using a cone-projected greedy algorithm that conserves the non-negativity of the dual basis vectors. The reduction strategy is applied to elastic frictionless contact problems including the possibility of using non-matching meshes. The numerical examples confirm the efficiency of the reduction strategy

A Feynman–Kac-type formula for Lévy processes with discontinuous killing rates

The roots of the present paper go back to the author’s dissertation [17], which was financially supported by the DFG through project EB66/11-1