Issue #1 (Volume 7 2018)

The problem of calibration of local volatility model of Dupire has been formalized. It uses genetic algorithm as alternative to regularization approach with further application of gradient descent algorithm. Components that solve Dupire’s partial differential equation that represents dynamics of underlying asset’s price within Dupire model have been built. This price depends in particular on values of volatility parameters. Local volatility is parametrized in two dimensions (by Dupire model): time to maturity of the option and strike price (execution price). On maturity axis linear interpolation is used while on strike axis we use B-Splines. Genetic operators of mutation and selection are then applied to parameters of B-Splines. Resulting parameters allow us to obtain the values of local volatility both in knot points and intermediate points using interpolation techniques. Then we solve Dupire equation and calculate model values of option prices. To calculate cost function we simulate market values of option prices using classic Black-Scholes model. An experimental research to compare simulated market volatility and volatility obtained by means of calibration of Dupire model has been conducted. The goal is to estimate the precision of the approach and its usability in practice. To estimate the precision of obtained results we use a measure based on average deviation of modeled local volatility from values used to simulate market prices of the options. The research has shown that the approach to calibration using genetic algorithm of optimization requires some additional manipulations to achieve convergence. In particular it requires non-uniform discretization of the space of model parameters as well as usage of de Boor interpolation. Value 0.07 turns out to be the most efficient mutation parameter. Using this parameter leads to quicker convergence. It has been proved that the algorithm allows precise calibration of local volatility surface from option prices.

The article is devoted to solving the actual problem of increasing the efficiency of assessing the credit risks of individual borrowers by finding the optimal combination of the results of calculations of specific scoring models. The principles of the formation of an ensemble of models are given and the existing approaches to the construction of ensemble structures are analyzed. In the process of experimental research has been applied one of the modifications of the boosting algorithm and implemented the author's algorithm for constructing an ensemble of models based on the specialization of experts. The radial-basis function neural networks were used as specific expert models. As a result of a comparative analysis of the efficiency of the used ensemble technologies it was confirmed that the algorithm for constructing an ensemble based on the specialization of experts proposed by the authors is the most adapted for the task of assessing credit risk.

The article highlights the results of a study of the dynamic evolutionary processes of trophic relations between populations of enterprises. A model based on differential equations is constructed, which describes the economic system and takes into account the dynamics of the specific income of competing populations of enterprises in relations of protocooperation, nonlinearity of growth and competition. This model can be used to analyze the dynamics of transient processes in various life cycle scenarios and predict the synergistic effect of mergers and acquisitions. A bifurcation analysis of possible scenarios of dynamic modes of merger and acquisition processes using the neural network system of pattern recognition was carried out. To this end, a Kohonen self-organizing map has been constructed, which recognizes phase portraits of bifurcation diagrams of enterprises life cycle into five separate classes in accordance with the scenarios of their development. As a result of the experimental study, characteristic modes of the evolution of economic systems were revealed, and also conclusions were made on the mechanisms of influence of the external environment and internal structure on the regime of evolution of populations of enterprises.

The article is devoted to the creation of a method for using of neural networks approach in solving problems of energy efficiency management at the industrial enterprise. The method allows to obtain an approximate expected value of the energy intensity of production, depending on the values of the main factors affecting it. The multilayer perceptron was chosen as the type of neural network, synthesis of which was carried out by using the genetic algorithm. When sampling for the synthesis of a neural network, we used the results that were obtained by means of a priori ranking, correlation and regression analysis based on the statistical data of industrial enterprises in machine-building profile. The recommendations of the use of the method and the application of its results in the practical implementation at the industrial enterprise are given. Calculations based on the aforementioned method ensured a high precision of prediction of energy intensity values for industrial enterprises that were included in the sample during the synthesis of the neural network, and an acceptable error while testing on industrial enterprises from a test sample.

The article proposes an approach to analyzing the reliability of commercial banks using multilayer neural networks and Kohonen self-organizing maps, and also conducted their approbation on the example of the Ukrainian banking system from 2014 to 2018 with breakdown into 3 periods. Based on the experiments, the best variants of the architecture of neural networks are revealed. It is found that solving the problem of assessing the reliability of commercial banks in the clustering formulation gives a better result than in the classification formulation. The conclusion that a rapid change in the conditions of functioning of a modern banking system makes inefficient the use of analytical models with rigidly prescribed coefficients is experimentally substantiated. The results of the research are of practical importance and can be used to identify potential partners in the banking sector of the economy.