Ekonomická revue. 2018, roč. 21

Permanent URI for this collectionhttp://hdl.handle.net/10084/133453

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Now showing 1 - 12 out of 12 results

Numerical Pricing of American-Style Options within the Black and Scholes Framework
(Vysoká škola báňská - Technická univerzita Ostrava, 2018) Hozman, Jiří; Kresta, Aleš; Tichý, Tomáš
Option pricing is one of the classical problems in financial engineering. Since exact solutions in analytical form are available for simple option contracts in particular, a numerical approach is desirable due to the fact that relaxed standard assumptions do not allow the construction of such solutions. In this paper, we consider the problem of pricing American-style options in the classical Black–Scholes framework; that is, we admit the early exercise feature. This constraint can be viewed as an additional non-linear source term in the option-pricing partial differential equation. The contribution of the paper lies in the proposal of a numerical scheme to solve this pricing equation and in the relationship of the presented technique with the existing pricing approaches. The numerical approach is based on the modification of the discontinuous Galerkin method incorporating a penalty term that handles the early exercise constraint. The capabilities of the scheme derived are documented using reference experiments and compared with the standard finite difference method.
Portfolio Credit Risk Based on Copulas
(Vysoká škola báňská - Technická univerzita Ostrava, 2018) Tian, Yuan
This paper is devoted to portfolio credit risk based on copulas. The goal of the paper is to combine the portfolio credit risk model and the copula functions to allow better estimation of credit risk by comparing the VaRs at different confidence levels. We will describe the general framework of the portfolio credit risk model, namely threshold models, and Monte Carlo simulation first, then we will provide a basic description of copula functions. In the paper, the CreditMetrics™ model is applied to two well-diversified portfolios consisting of ten bonds traded on the Frank furt Stock Exchange (FSE) from 9 October 2017 to 8 October 2018 to estimate their VaRs at different significance levels. One portfolio is of high quality with ten good-rating bonds, while the other is a credit-risky portfolio with ten risky bonds. After that, CreditMetrics™ with the copula functions is used to recalculate the correlation matrix and the real distribution of the portfolio value. By comparing the VaRs of two different portfolios using both the original CreditMetrics™ model and the CreditMetrics™ model based on the copula functions, we find that the original VaRs of both portfolios are lower than the VaRs calculated based on the copula functions at different con fidence levels, which illustrates that the credit risk is underestimated in the original CreditMetrics™ model for both portfolios. Moreover, the difference between the original VaR and the VaR based on the copula functions is more obvious for the credit-risky portfolio, especially when the confidence level is 95%.
Banking Crises and Diffusion of Information and Communication Technologies
(Vysoká škola báňská - Technická univerzita Ostrava, 2018) Koyuncu, Cuneyt; Yilmaz, Rasim
In this study, the relationship between Information and Communication Technologies (ICT) penetration and banking crises is investigated using a panel logit model of the incidence of banking crises. The period under investigation is between 1990 and 2011, and the largest sample of the study consists of 182 countries. For robustness, four ICT indicators and bivariate models, as well as multivariate models, are used. Our empirical investigation suggests that the diffusion of ICT technologies increases the possibility of banking crises, controlling for other factors that may cause banking crises. Among ICT indicators used in the study, the number of fixed broadband subscriptions per 100 people has the largest effect on the probability of a banking crisis. This paper contributes to the literature on banking crises by presenting the first empirical evidence on the relationship between ICT penetration and banking crises.
A Robust-optimization Approach to Uncertainty in Static Games
(Vysoká škola báňská - Technická univerzita Ostrava, 2018) Radi, Davide
This paper focuses on the robust games proposed by Aghassi and Bertsimas (2006). They represent a distribution free modelling framework for incomplete-information games, in which players are uncertain about the values of the parameters that define their own payoff functions. Each player is uncertainty averse in the sense that he/she max imizes his/her worst-case payoff. Such a player is named a robust player, and a solution to this game is called a robust-optimization equilibrium. By focusing on non-cooperative, simultaneous-move, one-shot, finite games, we consider a general setting that includes both matrix and non-matrix games. Sufficient conditions for the existence of a robust-optimization equilibrium are provided. The result of existence proposed here is based on the Kakutani Fixed-Point Theorem. A few examples are provided that also include a robust duopoly game.
On the Efficiency of Steel Sectors in EU Member Countries
(Vysoká škola báňská - Technická univerzita Ostrava, 2018) Zapletal, František; Herrera-Viedma, Enrique
Steel is one of the most multifunctional and most adaptable materials, and the iron and steel sector is a strategically important part of European industry. Steel products are vital for other industries including the construction to automotive sectors. Currently, the steel-producing companies in the EU face strong competition from non-EU (mainly Asian) countries, which exerts pressure on their efficiency. In this paper, we explore the efficiency of the steel sectors of EU members using the PROMETHEE method, which provides a clear graphical representation of the results. The aim is to compare the efficiency of the EU steel industries. We identify the input and output factors whose values differ by countries (e.g. price of input materials imported from outside the EU or the final product sale prices significantly influence the steel sectors, but their values are more or less identical for all EU countries). In our study, we involved three inputs (labour costs in the sector, number of employees and energy consumption) and three outputs (value of production, costs of emissions trading and net export). The results show that only 3 of 19 explored sectors are technically efficient (Bulgaria, Slovakia and Belgium). In line with Is
Misspecified Demand and Oligopolistic Competition: An Evolutionary Analysis
(Vysoká škola báňská - Technická univerzita Ostrava, 2018) Lamantia, Fabio D.
This paper proposes a simple oligopoly model in which firms can use the real demand function or a misspecified version of it to maximize their profits. While in cases of demand underestimation it is always more convenient for the firms not to distort this estimate, in cases of demand overestimation the possible configurations of equilibria can include any type of outcome based on the level of distortion to the demand. This result is made more robust by considering an evolutionary version of the game, in which the previous static game is played over time by firms randomly drawn from a population of companies. The last part of the paper provides some important considerations in terms of welfare, which underline the effect of demand distortion from the consumers’ point of view
Parametric families for the Lorenz curve: an analysis of income distribution in European countries
(Vysoká škola báňská - Technická univerzita Ostrava, 2018) Lando, Tommaso; Staníčková, Michaela; Franek, Jiří
The European Union Survey on Income and Living Conditions (EU-SILC) is the main source of information about living standards and poverty in the EU member states. We compare different parametric models for the Lorenz curve (LC) with an empirical analysis of the income distributions of 26 European countries in the year 2017. The objective of our empirical study is to verify whether simple mono-parametric models for the LCs can represent similarities or differences between European income distributions in sufficient detail, or whether an alternative, more sophisticated multi-parametric model should be used instead. In particular, we consider the power LC, the Pareto LC, the Lamè LC, a generalised bi-parametric version of the Lamè LC, a bi-parametric mixture of power LCs and the recently introduced arctan family of LCs. Whilst the first three families are ordered, in that different parametric values correspond to a situation of Lorenz ordering, the latter three may also identify the ambiguous situation of intersecting LCs. Therefore, besides focusing on the goodness-of-fit of the models considered and their mathematical simplicity, we evaluate the effectiveness of multi-parametric models in identifying the non-dominated cases.
Comparison of credit risk measurement in Central European banking
(Vysoká škola báňská - Technická univerzita Ostrava, 2018) Feng, Xiaoshan
This paper focuses on credit risk measurements in the financial institutions of Central Europe. The objective is to compare IRB approaches and a standardised approach to measuring credit risk in the Czech Republic, Germany and Poland. We compare these risk measurement process and the risk-weighted distribution of the banking industry in the three countries via two approaches. Analysis is based on valid data for the three countries’ banking industries from 2013 to 2017. We find that the banking industry using the IRB model as the main method represents the majority, but a rather big difference exists in the risk weights of using the standard model. Germany applies the highest risk weights in central governments under SA, while the Czech Republic and Poland apply the highest risk weights in retail claims. Under the A-IRB Approach, retail secured by real estate non-SME has the greatest level of risk exposure for the Czech Republic, while the most common exposure classes of Poland are corporate claims.
Sales prediction in the ice category applying fuzzy sets theory
(Vysoká škola báňská - Technická univerzita Ostrava, 2018) Dvořáčková, Hana; Kresta, Aleš; Tichý, Tomáš
With growing pressure on performance and data regarding customer behaviour and supply chain process widely available, stock keeping units aim to optimise the level of inventories. It is natural that good estimates of future sales can substantially increase the efficiency of the overall company. We can distinguish two basic perspectives: one assumes sales to be an independent process; the other explores its dependency on exogenous variables. In this paper we focus on the forecasting of sales in the Ice category when dependency on quarterly average temperatures in the form of exponential function is assumed. We concentrate especially on LFL-Forecaster, a method combining fuzzy transform and fuzzy natural logic of fuzzy sets theory, as a tool for average temperature forecasting. The results are compared with simple linear extrapolation and truly observed temperatures. The utilisation of LFL-Forecaster is found to be superior to simplifying linear regression.
Review of modern numerical methods for a simple vanilla option pricing problem
(Vysoká škola báňská - Technická univerzita Ostrava, 2018) Hozman, Jiří; Černá, Dana; Holčapek, Michal; Tichý, Tomáš; Valášek, Radek
Option pricing is a very attractive issue of financial engineering and optimization. The problem of determining the fair price of an option arises from the assumptions made under a given financial market model. The increasing complexity of these market assumptions contributes to the popularity of the numerical treatment of option valuation. Therefore, the pricing and hedging of plain vanilla options under the Black–Scholes model usually serve as a bench-mark for the development of new numerical pricing approaches and methods designed for advanced option pricing models. The objective of the paper is to present and compare the methodological concepts for the valuation of simple vanilla options using the relatively modern numerical techniques in this issue which arise from the discontinuous Galerkin method, the wavelet approach and the fuzzy transform technique. A theoretical comparison is accompanied by an empirical study based on the numerical verification of simple vanilla option prices. The resulting numerical schemes represent a particularly effective option pricing tool that enables some features of options that are depend-ent on the discretization of the computational domain as well as the order of the polynomial approximation to be captured better.
Setting the optimal limit value of motor insurance coverage by stochastic optimization
(Vysoká škola báňská - Technická univerzita Ostrava, 2018) Hanelová, Lucie; Valecký, Jiří
In this paper, we provide an alternative to a passive approach to the selection of insurance products or policy con-ditions. Specifically, we propose a method to make a decision about the optimal limit value for motor insurance coverage. Respecting the stochastic nature of individual loss, we formulate a problem of stochastic programming in which the total potential financial loss of the policyholder is minimized. Actually, we present a general optimization problem in which various relevant probability distributions of individual loss may be considered. In addition, we extend the work of Valecký (2017) and derive an insurance rate that describes better the dependence between the pure premium and the given limit value under the assumption that the individual potential loss follows a gamma distribution. Because of the absence of a closed-form solution, sample average approximation is applied to the objective function and the optimal solution to this approximated (SAA) problem is determined. Finally, the quality of the obtained solution is assessed by approximation to the optimality gap representing the difference between our candidate and the true solution.
Ageing of farmers in the Czech republic and the support from the EU funds
(Vysoká škola báňská - Technická univerzita Ostrava, 2018) Šimpachová Pechrová, Marie; Šimpach, Ondřej
The age structure of managers of agricultural holdings is not favourable in the Czech Republic and follows the general trend of population ageing. The lack of young farmers represents a threat to generation renewal and the competitiveness of the sector, as younger farmers tend to be more open to innovation and more often learn new approaches to farming and business. Therefore, the European Union supports generation renewal through Common Agricultural Policy instruments – direct payments and investment subsidies from the Rural Development Pro-gramme. The aim of the paper is to assess the ageing of the farm manager population and to evaluate whether the support from the EU is well targeted on the regional level based on correlation analysis. Using statistical and ad-ministrative data, we find that the subsidies from the Rural Development Programme in the year 2016 were granted in line with the seriousness of the ageing problem. When there was a larger share of older farmers in a region, the share of young farmers supported was larger. Vice versa, the correlation coefficient between the share of supported farmers and the share of young farmers in the region is negative, meaning that the greater was the share of young farmers, the smaller was the share of supported farmers.

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