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Tytuł:
A Note on Option Pricing with the Use of Discrete-Time Stochastic Volatility Processes
Autorzy:
Pajor, Anna
Powiązania:
https://bibliotekanauki.pl/articles/483255.pdf
Data publikacji:
2009
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
option pricing
SV model
Bayesian forecasting
Opis:
In this paper we show that in the lognormal discrete-time stochastic volatility model with predictable conditional expected returns, the conditional expected value of the discounted payoff of a European call option is infinite. Our empirical illustration shows that the characteristics of the predictive distributions of the discounted payoffs, obtained using Monte Carlo methods, do not indicate directly that the expected discounted payoffs are infinite.
Źródło:
Central European Journal of Economic Modelling and Econometrics; 2009, 1, 1; 71-81
2080-0886
2080-119X
Pojawia się w:
Central European Journal of Economic Modelling and Econometrics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Strategic option pricing
Autorzy:
Bieta, Volker
Broll, Udo
Siebe, Wilfried
Powiązania:
https://bibliotekanauki.pl/articles/1837957.pdf
Data publikacji:
2020-09-30
Wydawca:
Uniwersytet Ekonomiczny w Poznaniu
Tematy:
option pricing
game theory
Nash equilibrium
Opis:
In this paper an extension of the well-known binomial approach to option pricing is presented. The classical question is: What is the price of an option on the risky asset? The traditional answer is obtained with the help of a replicating portfolio by ruling out arbitrage. Instead a two-person game from the Nash equilibrium of which the option price can be derived is formulated. Consequently both the underlying asset’s price at expiration and the price of the option on this asset are endogenously determined. The option price derived this way turns out, however, to be identical to the classical no-arbitrage option price of the binomial model if the expiration-date prices of the underlying asset and the corresponding risk-neutral probability are properly adjusted according to the Nash equilibrium data of the game.
Źródło:
Economics and Business Review; 2020, 6, 3; 118-129
2392-1641
Pojawia się w:
Economics and Business Review
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Optimality of replication in the CRR model with transaction costs
Autorzy:
Rutkowski, Marek
Powiązania:
https://bibliotekanauki.pl/articles/1339057.pdf
Data publikacji:
1998
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
transaction costs
martingale measure
super-hedging
option pricing
Opis:
Recently, there has been a growing interest in optimization problems associated with the arbitrage pricing of derivative securities in imperfect markets (in particular, in models with transaction costs). In this paper, we examine the valuation and hedging of European claims in the multiplicative binomial model proposed by Cox, Ross and Rubinstein [5] (the CRR model), in the presence of proportional transaction costs. We focus on the optimality of replication; in particular, we provide sufficient conditions for the optimality of the replicating strategy in the case of long and short positions in European options. This work can be seen as a continuation of studies by Bensaid et al. [2] and Edirisinghe et al. [13]. We put, however, more emphasis on the martingale approach to the claims valuation in the presence of transaction costs, focusing on call and put options. The problem of optimality of replication in the CRR model under proportional transaction costs was recently solved in all generality by Stettner[30].
Źródło:
Applicationes Mathematicae; 1998-1999, 25, 1; 29-53
1233-7234
Pojawia się w:
Applicationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On option pricing in the multidimensional Cox-Ross-Rubinstein model
Autorzy:
Motoczyński, Michał
Stettner, Łukasz
Powiązania:
https://bibliotekanauki.pl/articles/1339064.pdf
Data publikacji:
1998
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
contingent claim
self-financing strategies
super-hedging
option pricing
Opis:
Option pricing in the multidimensional case, i.e. when the contingent claim paid at maturity depends on a number of risky assets, is considered. It is assumed that the prices of the risky assets are in discrete time subject to binomial disturbances. Two approaches to option pricing are studied: geometric and analytic. A numerical example is also given.
Źródło:
Applicationes Mathematicae; 1998-1999, 25, 1; 55-72
1233-7234
Pojawia się w:
Applicationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
OVERLAPPING MULTIGRID METHODS AS AN EFFICIENT APPROACH FOR SOLVING THE BLACK-SCHOLES EQUATION
Autorzy:
Bernardelli, Michał
Powiązania:
https://bibliotekanauki.pl/articles/453023.pdf
Data publikacji:
2015
Wydawca:
Szkoła Główna Gospodarstwa Wiejskiego w Warszawie. Katedra Ekonometrii i Statystyki
Tematy:
option pricing
Black-Scholes model
multigrid method
finite-difference scheme
Opis:
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.
Źródło:
Metody Ilościowe w Badaniach Ekonomicznych; 2015, 16, 1; 25-36
2082-792X
Pojawia się w:
Metody Ilościowe w Badaniach Ekonomicznych
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Lower Precision calculation for option pricing
Autorzy:
Ścibisz-Mordelska, K.
Nielek, R.
Powiązania:
https://bibliotekanauki.pl/articles/305297.pdf
Data publikacji:
2017
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
option pricing
lower precision
half-precision type
Monte Carlo
Black-Scholes formula
Opis:
The problem of options pricing is one of the most critical issues and fundamental building blocks in mathematical finance. The research includes deployment of lower precision type in two options pricing algorithms: Black-Scholes and Monte Carlo simulation. We make an assumption that the shorter the number used for calculations is (in bits), the more operations we are able to perform in the same time. The results are examined by a comparison to the outputs of single and double precision types. The major goal of the study is to indicate whether the lower precision types can be used in financial mathematics. The findings indicate that Black-Scholes provided more precise outputs than the basic implementation of Monte Carlo simulation. Modification of the Monte Carlo algorithm is also proposed. The research shows the limitations and opportunities of the lower precision type usage. In order to benefit from the application in terms of the time of calculation improved algorithms can be implemented on GPU or FPGA. We conclude that under particular restrictions the lower precision calculation can be used in mathematical finance.
Źródło:
Computer Science; 2017, 18 (4); 429-446
1508-2806
2300-7036
Pojawia się w:
Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Option pricing by Esscher transforms in the cases of normal inverse Gaussian and variance gamma processes
Autorzy:
Troush, N. N.
Kuzmina, A. V.
Powiązania:
https://bibliotekanauki.pl/articles/92926.pdf
Data publikacji:
2012
Wydawca:
Uniwersytet Przyrodniczo-Humanistyczny w Siedlcach
Tematy:
Esscher transforms
option pricing
generalized hyperbolic process
normal inverse Gaussian process
variance gamma process
Opis:
The class of Esscher transforms is an important tool for option pricing Gerber and Shiu (1994) showed that the Esscher transform is an efficient technique for valuing derivative securities if the log returns of the underlying securities are governed by certain stochastic processes with stationary and independent increments. Levy processes are the processes of such type. Special cases of the Levy processes such as the normal inverse Gaussian process and the variance gamma process are considered at this paper. Values of these processes parameters for the existence of Esscher transform are deduced. A new algorithm of a normal inverse Gaussian process and variance gamma process simulation is also presented in this paper. These algorithm is universal and simpler one compared with analogous algorithms.
Źródło:
Studia Informatica : systems and information technology; 2012, 1-2(16); 35-43
1731-2264
Pojawia się w:
Studia Informatica : systems and information technology
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Which Option Pricing Model Is the Best? HF Data for Nikkei 225 Index Options
Autorzy:
Kokoszczyński, Ryszard
Sakowski, Paweł
Ślepaczuk, Robert
Powiązania:
https://bibliotekanauki.pl/articles/1357377.pdf
Data publikacji:
2019-04-01
Wydawca:
Uniwersytet Warszawski. Wydział Nauk Ekonomicznych
Tematy:
Option pricing models
high-frequency data
realized volatility
implied volatility
stochastic volatility
emerging markets
Opis:
In this study, we analyse the performance of option pricing models using 5-minutes transactional data for the Japanese Nikkei 225 index options. We compare 6 different option pricing models: the Black (1976) model with different assumptions about the volatility process (realized volatility with and without smoothing, historical volatility and implied volatility), the stochastic volatility model of Heston (1993) and the GARCH(1,1) model. To assess the model performance, we use median absolute percentage error based on differences between theoretical and transactional options prices. We present our results with respect to 5 classes of option moneyness, 5 classes of option time to maturity and 2 option types (calls and puts). The Black model with implied volatility (BIV) comes as the best and the GARCH(1,1) as the worst one. For both call and put options, we observe the clear relation between average pricing errors and option moneyness: high error values for deep OTM options and the best fit for deep ITM options. Pricing errors also depend on time to maturity, although this relationship depend on option moneyness. For low value options (deep OTM and OTM), we obtained lower errors for longer maturities. On the other hand, for high value options (ITM and deep ITM) pricing errors are lower for short times to maturity. We obtained similar average pricing errors for call and put options. Moreover, we do not see any advantage of much complex and time-consuming models. Additionally, we describe liquidity of the Nikkei225 option pricing market and try to compare the results we obtain here with a detailed study for Polish emerging option market (Kokoszczyński et al. 2010b).
Źródło:
Central European Economic Journal; 2017, 4, 51; 18 - 39
2543-6821
Pojawia się w:
Central European Economic Journal
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
RESULTS OF MISTAKEN TIME PERIOD IN ANALYSIS IN THE CASE OF FRAMING EFFECT FOR SOME CAPITAL MARKETS’ MODELS
Autorzy:
Majewska, Agnieszka
Majewski, Sebastian
Powiązania:
https://bibliotekanauki.pl/articles/452764.pdf
Data publikacji:
2009
Wydawca:
Szkoła Główna Gospodarstwa Wiejskiego w Warszawie. Katedra Ekonometrii i Statystyki
Tematy:
behavioural finance
Black-Scholes Option Pricing Model
Tragic News Indicator
Sharpe’s model
framing effect
Opis:
Economic activity around the world should be supported by analysis determined by the different level of difficulty of applied quantitative methods. The article presents the importance selecting a proper time window for analysis for correct diagnosing of situations based on information taken from TNI, BSOPM, Markowitz’s, and Sharpe’s models. TNI shows the role of expansiveness of media relations regarding the SE. The correct specification of the time window causes the proper valuation of price and risk. Behavioural finance flaming effect is a field of discussion in his research.
Źródło:
Metody Ilościowe w Badaniach Ekonomicznych; 2009, 10, 1; 163-175
2082-792X
Pojawia się w:
Metody Ilościowe w Badaniach Ekonomicznych
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Wycena europejskiej opcji kupna – model ciągły
The European call option pricing – continuous model
Autorzy:
Kowgier, Henryk
Powiązania:
https://bibliotekanauki.pl/articles/449541.pdf
Data publikacji:
2013
Wydawca:
Zachodniopomorska Szkoła Biznesu w Szczecinie
Tematy:
miara martyngałowa
model ciągły
wycena europejskiej opcji kupna
martingale measure
continuous model
European call option pricing
Opis:
Celem tego artykułu jest ukazanie praktycznego wykorzystania metody martyngałowej dla procesów ciągłych do wyceny europejskiej opcji kupna wystawionej na akcję bez praw do dywidendy.
In the article a method of using practically the martingale representation theorem for the European call option pricing has been presented.
Źródło:
Zeszyty Naukowe ZPSB Firma i Rynek; 2013, 2(45); 17-26
2657-3245
Pojawia się w:
Zeszyty Naukowe ZPSB Firma i Rynek
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Lies, Damned Lies, and Statistics? Examples From Finance and Economics
Autorzy:
Abadir, Karim M.
Powiązania:
https://bibliotekanauki.pl/articles/483313.pdf
Data publikacji:
2013
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
flexible density specification
option pricing
term structure of interest rates
expectation hypothesis
nonlinear long-memory
macroeconomic dynamics
Opis:
Reliable data analysis is one of the hardest tasks in sciences and social sciences. Often misleading and sometimes puzzling results arise when the analysis is done without regard for the special features of the data. In this exposition, I will focus on designing new statistical tools to deal with some prominent questions in Finance and Economics. In particular, I will talk about the following. (1) How to characterize the randomness of variables, motivated by a problem in the pricing of financial options. (2) Uncovering the relation between interest rates on different maturities, now and in the future; the "term structure of interest rates". (3) Modelling the unconventional nonlinear long-memory dynamics that arise from a general-equilibrium economic model, and their implications for exchange rates, stock market indexes, and all macroeconomic variables; with recommendations for trading in financial markets, but also for the design of macroeconomic stabilization policies by governments.
Źródło:
Central European Journal of Economic Modelling and Econometrics; 2013, 5, 4; 231-248
2080-0886
2080-119X
Pojawia się w:
Central European Journal of Economic Modelling and Econometrics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
ANALIZA WYCENY OPCJI EUROPEJSKICH W MODELU HULLA – WHITE’A
ANALYSIS OF HULL – WHITE MODEL
Autorzy:
Orzechowski, Arkadiusz
Powiązania:
https://bibliotekanauki.pl/articles/452929.pdf
Data publikacji:
2016
Wydawca:
Szkoła Główna Gospodarstwa Wiejskiego w Warszawie. Katedra Ekonometrii i Statystyki
Tematy:
model J. Hulla i A. White’a
szereg Tayora
wycena opcji
Hull – White model
Taylor series
option pricing
Opis:
W niniejszym artykule analizowany jest model J. Hulla i A. White’a. W ramach podejmowanej problematyki przedstawiane są aspekty teoretyczne rozpatrywanego podejścia oraz wykorzystywane są dane empiryczne do sprawdzenia precyzji wyceny w relacji do cen rynkowych generowanych przez model F. Blacka i M. Scholesa. Ponadto, przeprowadzana jest analiza wrażliwości wyceny opcji. Otrzymane wyniki wskazują, iż model J. Hulla i A. White’a, w swojej podstawowej postaci, pozwala wycenić opcje równie dobrze jak model F. Blacka i M. Scholesa, bez konieczności jednak wprowadzania założenia upraszczającego opis funkcjonowania rynku kapitałowego, tj. stałości wariancji stóp zwrotu z aktywów bazowych.
In this article Hull – White model is analyzed. As a part of the subject matter theoretical aspects of the considered approach are presented. Then, empirical data is used to verify the accuracy of valuation with respect to the Black - Scholes model. In addition, the analysis of sensitivity of option pricing is performed. The results indicate that the Hull - White model allows to price options similarly to the Black – Scholes model but without imposing simplifying assumption which refers to description of the functioning of the capital market, i.e. constant variance of returns of the underlying assets.
Źródło:
Metody Ilościowe w Badaniach Ekonomicznych; 2016, 17, 3; 120-130
2082-792X
Pojawia się w:
Metody Ilościowe w Badaniach Ekonomicznych
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Application of the Trefftz method for option pricing
Autorzy:
Brzozowska-Rup, Katarzyna
Hożejowska, Sylwia
Hożejowski, Leszek
Powiązania:
https://bibliotekanauki.pl/articles/1918663.pdf
Data publikacji:
2020
Wydawca:
Politechnika Śląska. Wydawnictwo Politechniki Śląskiej
Tematy:
contract options
option pricing
Black-Scholes model
Trefftz method
opcje kontraktowe
wycena opcji
model Blacka-Scholesa
Metoda Trefftza
Opis:
Purpose: Option pricing is hardly a new topic, however, in many cases they lack an analytical solution. The article proposes a new approach to option pricing based on the semi-analytical Trefftz method. Design/methodology/approach: An appropriate transformation makes it possible to reduce the Black-Scholes equation to the heat equation. This admits the Trefftz method (which has shown its effectiveness in heat conduction problems) to be employed. The advantage of such an approach lies in its computational simplicity and in the fact that it delivers a solution satisfying the governing equation. Findings: The theoretical option pricing problem being considered in the paper has been solved by means of the Trefftz method, and the results achieved appear to comply with those taken from the Black-Scholes formula. Numerical simulations have been carried out and compared, which has confirmed the accuracy of the proposed approach. Originality/value: Although a number of solutions to the Black-Scholes model have appeared, the paper presents a thoroughly novel idea of implementation of the Trefftz method for solving this model. So far, the method has been applied to problems having nothing in common with finance. Therefore the present approach might be a starting point for software development, competitive to the existing methods of pricing options.
Źródło:
Zeszyty Naukowe. Organizacja i Zarządzanie / Politechnika Śląska; 2020, 146; 37-49
1641-3466
Pojawia się w:
Zeszyty Naukowe. Organizacja i Zarządzanie / Politechnika Śląska
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A fuzzy approach to option pricing in a Levy process setting
Autorzy:
Nowak, P.
Romaniuk, M.
Powiązania:
https://bibliotekanauki.pl/articles/330572.pdf
Data publikacji:
2013
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
option pricing
Lévy process
minimal entropy
martingale measure
fuzzy sets
Monte Carlo simulation
wycena opcji
entropia minimalna
zbiór rozmyty
symulacja Monte Carlo
Opis:
In this paper the problem of European option valuation in a Levy process setting is analysed. In our model the underlying asset follows a geometric Levy process. The jump part of the log-price process, which is a linear combination of Poisson processes, describes upward and downward jumps in price. The proposed pricing method is based on stochastic analysis and the theory of fuzzy sets.We assume that some parameters of the financial instrument cannot be precisely described and therefore they are introduced to the model as fuzzy numbers. Application of fuzzy arithmetic enables us to consider various sources of uncertainty, not only the stochastic one. To obtain the European call option pricing formula we use the minimal entropy martingale measure and Levy characteristics.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2013, 23, 3; 613-622
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Option pricing in CRR model with time dependent parameters for two periods of time - part I
Wycena opcji w modelu CRR z parametrami zależnymi od czasu dla dwóch jednostek czasu – cześć I
Autorzy:
Fraszka-Sobczyk, Emilia
Chojnowska-Michalik, Anna
Powiązania:
https://bibliotekanauki.pl/articles/1837608.pdf
Data publikacji:
2019
Wydawca:
Łódzkie Towarzystwo Naukowe
Tematy:
Cox-Ross-Rubinstein model (CRR model)
Black-Scholes formula
option pricing
model Coxa-Rossa-Rubinsteina
model CRR
wzór Blacka-Scholesa
wycena opcji
Opis:
In this paper we present some generalization of the Cox-Ross-Rubinstein (CRR) option pricing model. We assume that two parameters of the model (an interest rate of a bank account and a volatility of the logarithm of the stock price’s changes) are different in each of two analyzed periods of time.
W pracy przedstawiono pewien uogólniony model Coxa-Rossa-Rubinsteina na wycenę opcji. Założono, że dwa parametry modelu (stopa procentowa oraz współczynnik zmienności logarytmu cen akcji-volatility) zmieniają się w każdej z dwóch jednostek czasu.
Źródło:
Bulletin de la Société des Sciences et des Lettres de Łódź, Série: Recherches sur les déformations; 2019, 69, 1; 83-90
1895-7838
2450-9329
Pojawia się w:
Bulletin de la Société des Sciences et des Lettres de Łódź, Série: Recherches sur les déformations
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 26

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