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EN
In modeling two valued phenomena a binomial or negative binomial model is applied. In the paper minimum variance unbiased estimators of a probability of success obtained in two models are compared.
PL
Do modelowania zjawisk dychotomicznych wykorzystuje się model dwumianowy lub model ujemny dwumianowy. W pracy porównano estymatory nieobciążone o minimalnej wariancji prawdopodobieństwa sukcesu w tych dwóch modelach.
EN
Although there are many opinions critical of options, especially after the 2008 scandal, they are becoming increasingly popular in Poland again. Therefore, issues connected with options are not only the subject of interest in academic circles again but also arouse interest of economic entities, allowing enterprises to assess a variety of action strategies. Those instruments enable planning safeguards to protect against various negative future scenarios. Hence, it comes as no surprise that there has been an increase in the number and variety of enterprises that have accepted options as a way to plan for their future. The article provides a brief presentation of options. It also describes one of their pricing methods. Light of the foregoing has been hypothesized that 'valuation of options using mathematical calculators using the binomial model is an effective tool for supporting management positions in futures instruments’.
PL
Celem artykułu jest analiza czynników determinujących prawdopodobieństwo reelekcji wśród prezydentów polskich miast. Szacowane są parametry modelu dwumianowego w celu identyfikacji czynników wpływających na prawdopodobieństwo ponownego wyboru. Okazuje się, że mieszkańcy wysoko cenią wydatki dokonywane przez władze miasta w roku wyborczym, w tym przede wszystkim wydatki na gospodarkę mieszkaniową. Dużą szansę na reelekcję mają prezydenci miast dobrze pozyskujących środki z Unii Europejskiej, w których sytuacja na rynku pracy jest stabilna, a zamożność mieszkańców i firm (w porównaniu z początkiem kadencji) nie uległa pogorszeniu. Skuteczność ubiegania się o reelekcję jest wyższa w grupie miast wojewódzkich, a także należących w przeszłości do zaboru austriackiego, lub położonych na tzw. Ziemiach Odzyskanych. Zmienne z zakresu socjologii polityki okazały się mieć również istotny wpływ na analizowane prawdopodobieństwo.
EN
The aim of the paper is to analyze the factors determining the likelihood of reelection of Polish mayors. In order to identify the factors impacting the likelihood of reelection, the author estimates the parameters of the binomial model. The results show that spending in the election year, especially on housing, is greatly appreciated by the inhabitants of cities. The mayors who are very likely to be reelected are leaders of cities that are successful in acquiring EU funds, where the labour market is stable, and the material situation of inhabitants and businesses does not deteriorate during their term. Cities that are capitals of voivodeships offer a greater likelihood of reelection, as do those formerly in the Austrian partition or on the so-called Reclaimed Lands of Western Poland. Variables belonging to the domain of sociology of politics have an equally significant impact on the analyzed likelihood.
EN
The purpose of this publication is to analyze different methods of option valuation on the example of options listed on the Warsaw Stock Exchange. Models used for comparison are: Black-Scholes, binomial, Shelton, and the Monte Carlo method in two variants. An important part of the analysis is also a comparison of methods of estimating the basic instruments historical volatility, which have been compiled with the implied volatility. An important feature of this study is the verification of assumptions, which have been made by the winners of the Nobel Prize in 1997, Myron Scholes and Robert Merton, to build their model of option pricing. The calculation uses closing prices of options and basic instruments, which were taken from the www.gpwinfostrefa.pl. To option pricing risk-free rate and dividend rate for the WIG20 index were also needed. They have been calculated on the basis of data published by the National Bank of Poland on the www.nbp.pl, stooq.pl. The study provided interesting results concerning the selection of the best model to value options traded on the Warsaw Stock Exchange, and allowed to observe the universal relationship between the natural logarithm of measurement error, and correlation coefficient between the share price and its variation. The study also confirmed some well-known relationship between valuation errors and the types of options and provides relevant information to characterize the specificity of the Polish stock market options.
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