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1

The normality of financial data after an extraction of jumps in the jump-diffusion model

100%
Gardoń A.
Mathematical Economics
|
2011
|
issue 7 (14)
93-106
EN
When modelling financial data the jump-diffusion processes, driven by Wiener (W) and Poisson (N) processes, gain increasing importance. On the one hand, they explain better than the Itô diffusion the heavy tails of distributions of percentage changes of stock prices; on the other hand, unlike for example α-stable processes, they are based on the well developed mathematical tools for the Wiener and Poisson processes. After the identification of the jump times, e.g. by means of one of the so-called threshold methods, which are not linked with the continuous part of the model, the parameters from the continuous terms may be estimated similarly as for the Itô diffusion. But it is not obvious if the financial data after an extraction of jumps are already normally distributed. Therefore results of several normality tests will be presented here for chosen data from the Polish stock exchange market.
2
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On Some Risk-Reducing Derivative

100%
Milian A.
Optimum. Studia Ekonomiczne
|
2014
|
vol. 5(71)
EN
In this paper, we propose some derivative designed for small stock investors. Using the Black-Scholes model we derive an explicit formula for the price of the derivative, computing its discounted expected payoff. The payoff is modelled on the payoff of the catastrophe bonds, random occurrence of a natural disaster is replaced by a random stock price falling. Different variants of the proposed derivative are obtained by introducing a parameter to the payoff of the derivative. By Monte Carlo method, to reduce the risk of large losses associated with the investment, indicated the variant of this instrument, appropriate to selected typical values of volatility of considered stock.
3
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REAL OPTIONS COMPARED TO TRADITIONAL COMPANY VALUATION METHODS: POSSIBILITIES AND CONSTRAINTS IN THEIR USE

100%
Dzyuma U.
Finansowy Kwartalnik Internetowy e-Finanse
|
2012
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vol. 8
|
issue 2
51-68
EN
The subject of the article is the presentation of an unconventional method of establishing the value of the company together with investment ventures – basing on the concept of real options (Real Option Valuation – ROV). The option calculation can be applied in many areas, such as: evaluation of investment effectiveness, valuation of the company and its separate parts, estimating the value of company assets and liabilities, credit risk assessment. The concept of real options is very popular all over the world. However, in Poland we rarely use option methods in the above areas, although the method is currently considered a revolutionary solution to the problem of underassessment of huge risk projects.
4
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OVERLAPPING MULTIGRID METHODS AS AN EFFICIENT APPROACH FOR SOLVING THE BLACK-SCHOLES EQUATION

100%
Bernardelli M.
Metody Ilościowe w Badaniach Ekonomicznych
|
2015
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vol. 16
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issue 1
25-36
EN
In this paper the modification of a two-level multigrid method by allowing an overlap between adjacent subdomains and its application to a one-dimensional Black-Scholes equation is described. The method is based on the finite-difference schema known as implicit Euler. Numerical experiments confirm the superiority of the proposed method in relation to the classic multigrid method in form of shortening computation time, memory savings and ease of parallelization. The comparison shows the advantages of overlapping grids vs method without them, mainly due to improved accuracy of the solution.
5

Opcje – jak wyceniać, aby zyskać?

75%
Duczkowski N.
Studia Ekonomiczne (Economic Studies)
|
2009
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issue 1-2(60-61)
93-116
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.
6
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WYCENA ASYMETRYCZNYCH OPCJI LOGARYTMICZNYCH ZA POMOCĄ TRANSFORMATY FOURIERA

75%
Orzechowski A.
Metody Ilościowe w Badaniach Ekonomicznych
|
2018
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vol. 19
|
issue 3
238-250
PL
Celem artykułu jest wycena europejskich opcji logarytmicznych o asymetrycznym profilu wypłaty. W ramach podejmo­wanej problematyki zaproponowane zostały trzy podejścia pozwalające określić wartość modelową analizowanych instrumentów pochodnych przy utrzymaniu założeń właściwych modelowi F. Blacka i M. Scholesa, tj. podejście martyngałowe, F. Blacka i M. Scholesa oraz bazujące na transformacie Fouriera. Ponadto, dokonano analizy szybkości i dokładności obliczeniowej uwzględnionych podejść do wyceny analizowanych derywatów.
EN
"The aim of the article is to price European logarithmic options via Fourier transform. As a part of the subject metter, three approaches were proposed to determine theoretical value of the analyzed derivatives in the F. Black and M. Scholes setting, i.e. the martingale approach, F. Black and M. Scholes approach and the approach based on the Fourier transform. In addition, an analysis of the computational speed and accuracy of the valuations was carried out."
7
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Wpływ niepewności oszacowania zmienności na cenę instrumentów pochodnych

75%
Czernik T.
Studia Ekonomiczne
|
2013
|
vol. 124
131-142
EN
Valuation of derivatives is one of the most discussed topics of scientific treatises. In this paper we assess the likely impact of uncertainty on the price volatility of derivative. Results are presented on the example of the European digital option. It has been shown non-trivial dependence of the span of the confidence interval of the model parameters
8

How Firms Can Hedge Against Market Risk

75%
Echaust K.
Studies in Logic, Grammar and Rhetoric
|
2014
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vol. 37
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issue 1
39-49
EN
The article presents a problem of proper hedging strategy in expected utility model when forward contracts and options strategies are available. We consider a case of hedging when an investor formulates his own expectation on future price of underlying asset. In this paper we propose the way to measure effectiveness of hedging strategy, based on optimal forward hedge ratio. All results are derived assuming a constant absolute risk aversion utility function and a Black-Scholes framework.
9
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Options Pricing by Monte Carlo Simulation, Binomial Tree and BMS Model: a comparative study of Nifty50 options index

75%
Bendob A., Bentouir N.
Journal of Banking and Financial Economics
|
2019
|
issue 1(11)
79-95
EN
Investment behaviour, techniques and choices have evolved in the options markets since the launch of options trading in 1973. Today, we are entering the field of Big Data and the explosion of information, which has become the main feature of science, impacts investors' decisions and their trading position, particularly in the financial markets. Our paper aims to testing the effectiveness of the most popular options pricing models , which are the Monte Carlo simulation method, the Binomial model, and the benchmark model; the Black-Scholes model, when we ignore/take on account the Moneyness categories and different time to maturities; five months, one year, and two years, in addition to comparing these models, we will then test the effect of each model on the prediction of the current options prices, using the regression analysis, and the Nifty50 option index during the period of 25/07/2014 to 30/06/2016. The result shows that all models are overpriced in all Moneyness categories with a high level of volatility in In-the money category, other finding concludes that the Monte Carlo Simulation method is outperforming when the volatility is lower, while the Black-Sholes model and the Binomial model are outperforming in the entire sample with ignoring the Moneyness.
10
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Wartość zagrożona opcji europejskich szacowana przedziałowo. Symulacje

63%
Iskra D.
Studia Ekonomiczne
|
2013
|
vol. 124
183-192
EN
This paper presents a procedure for determining the value at risk ranges covering European options with a given level of confidence. Interval forecast VaR takes into account the uncertainty associated with the estimation error of the model parameters used. Option pricing model adapted Black-Sholes, and studies based on simulations.
11
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Zastosowanie wykładnika Hursta oraz funkcji Höldera w modelu Blacka-Scholesa

63%
Mastalerz-Kodzis A.
Studia Ekonomiczne
|
2017
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vol. 335
16-26
PL
W artykule zaprezentowano modyfikację klasycznego modelu Blacka- -Scholesa. Uwzględniono istnienie efektu pamięci w finansowych szeregach czasowych i wprowadzono do modelu wyceny instrumentów finansowych wykładnik Hursta oraz funkcję Höldera. Niniejszy artykuł składa się z części teoretycznej, w której przybliżono założenia i postać teoretyczną klasycznego modelu Blacka-Scholesa oraz omówiono jego wybrane modyfikacje, a także z części aplikacyjnej, w której ukazano efektywność uzyskanych rozwiązań.
EN
In the article we have presented the modification of a classic Black-Scholes model. We have considered the existence of memory effect in financial time series and introduced valuations of financial instruments, Hurst exponent and Hölder function into the model. The article consists of the theoretical part, in which we have presented the assumptions and the theoretical form of a classic Black-Scholes model and discussed its selected modifications, as well as the application part, which illustrates the effectiveness of the obtained solutions.
12
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Wpływ wartości ekstremalnych na zmienność stochastyczną

63%
Majewska J.
Studia Ekonomiczne
|
2013
|
vol. 162
131-143
EN
This article takes up validity of the use (on the Polish capital market) of stochastic models which take into account extreme observations. In the comparative analysis aside from the SV been considered models whose structure can better describe the appearance of extreme observations.
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