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Tytuł:
Option pricing formulas under a change of numeraire
Autorzy:
Attalienti, Antonio
Bufalo, Michele
Powiązania:
https://bibliotekanauki.pl/articles/254885.pdf
Data publikacji:
2020
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
Black-Scholes formula
binomial model
martingale measures
numeraire
Opis:
We present some formulations of the Cox-Ross-Rubinstein and Black-Scholes formulas for European options obtained through a suitable change of measure, which corresponds to a change of numeraire for the underlying price process. Among other consequences, a closed formula for the price of an European call option at each node of the multi-period binomial tree is achieved, too. Some of the results contained herein, though comparable with analogous ones appearing elsewhere in the financial literature, provide however a supplementary widening and deepening in view of useful applications in the more challenging framework of incomplete markets. This last issue, having the present paper as a preparatory material, will be treated extensively in a forthcoming paper.
Źródło:
Opuscula Mathematica; 2020, 40, 4; 451-473
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Asymmetric square root options – can we price them via the fourier transform?
Autorzy:
Ulmer, Adam
Powiązania:
https://bibliotekanauki.pl/articles/2147436.pdf
Data publikacji:
2019-06-03
Wydawca:
Szkoła Główna Gospodarstwa Wiejskiego w Warszawie. Katedra Ekonometrii i Statystyki
Tematy:
asymmetric square root options
Fourier transform
Black-Scholes model
Źródło:
Metody Ilościowe w Badaniach Ekonomicznych; 2019, 20, 1; 62-71
2082-792X
Pojawia się w:
Metody Ilościowe w Badaniach Ekonomicznych
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Efficiency and Convergence of Bisection, Secant, and Newton Raphson Methods in Estimating Implied Volatility
Autorzy:
Mahrudinda, Mahrudinda
Munandar, Devi
Purwani, Sri
Powiązania:
https://bibliotekanauki.pl/articles/1193324.pdf
Data publikacji:
2021
Wydawca:
Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
Tematy:
Black-Scholes model
Newton Raphson
bisection
secant
volatility
volatility implied
Opis:
This study aims to estimate volatility prices based on the black-Scholes model (BSM) function with research data taken during the COVID-19 pandemic. The estimates of the volatility values are obtained by using three numerical methods, namely the bisection, secant, and Newton Raphson methods. The numerical processes that produce some iteration results in the three methods are then analyzed and the best convergence is sought. As a result, Newton Raphson method produces the smallest number of iterations, which stops at the 3rd iteration and gets a volatility value of 0.500451 with an absolute error value of 0.000388. However, the method requires an initial approximation which lies only in two intervals on the axis σ which are close to the true root. Meanwhile, for the other two methods, namely Bisection and Secant, this limitation does not apply, as long as there is an interval that guarantees the existence of roots. In this case, bisection method requires11 iterations to converge with volatility value of 0.500342 and error value of 0.000878. Whereas secant method requires 4 iterations to converge with a volatility value of 0.500449 and error value of 1.68938E-05. This suggests, that in some cases the use of Newton method, should be initialized with the use of bisection or secant method, to ensure successful iteration and accelerate the rate of convergence.
Źródło:
World Scientific News; 2021, 153, 2; 157-168
2392-2192
Pojawia się w:
World Scientific News
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
REAL OPTIONS COMPARED TO TRADITIONAL COMPANY VALUATION METHODS: POSSIBILITIES AND CONSTRAINTS IN THEIR USE
Autorzy:
Dzyuma, Ulyana
Powiązania:
https://bibliotekanauki.pl/articles/599684.pdf
Data publikacji:
2012
Wydawca:
Wyższa Szkoła Informatyki i Zarządzania z siedzibą w Rzeszowie
Tematy:
real options
company valuation methods binomial model
Black-Scholes model
Opis:
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.
Źródło:
Finansowy Kwartalnik Internetowy e-Finanse; 2012, 8, 2; 51-68
1734-039X
Pojawia się w:
Finansowy Kwartalnik Internetowy e-Finanse
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:
HISTORICAL AND IMPLIED VOLATILITIES: A REVIEW OF METHODOLOGY
Autorzy:
Krawiec, Monika
Powiązania:
https://bibliotekanauki.pl/articles/453267.pdf
Data publikacji:
2013
Wydawca:
Szkoła Główna Gospodarstwa Wiejskiego w Warszawie. Katedra Ekonometrii i Statystyki
Tematy:
historical volatility
Black-Scholes implied volatility
model-free implied volatility
Opis:
Volatility is a subject of numerous studies. Many of them focus on predictive power of different sources of volatility. Most often, the Black-Scholes implied volatility is believed to outperform historical volatility, although some research demonstrates that implied volatility is a biased forecast of future volatility. Taken into account different opinions, the paper aims at presenting alternative methods for estimating volatility.
Źródło:
Metody Ilościowe w Badaniach Ekonomicznych; 2013, 14, 1; 304-316
2082-792X
Pojawia się w:
Metody Ilościowe w Badaniach Ekonomicznych
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On Some Risk-Reducing Derivative
Autorzy:
Milian, Anna
Powiązania:
https://bibliotekanauki.pl/articles/429889.pdf
Data publikacji:
2014
Wydawca:
Uniwersytet w Białymstoku. Wydawnictwo Uniwersytetu w Białymstoku
Tematy:
Black-Scholes model
risk-reducing derivatives
Monte Carlo method
risk transfer
Opis:
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.
Źródło:
Optimum. Economic Studies; 2014, 5(71)
1506-7637
Pojawia się w:
Optimum. Economic Studies
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Mellin transform in higher dimensions for the valuation of the European basket put option with multi-dividend paying stocks
Autorzy:
Sunday, Emmanuel Fadugba
Powiązania:
https://bibliotekanauki.pl/articles/1156232.pdf
Data publikacji:
2018
Wydawca:
Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
Tematy:
Dividend paying stock
European basket option
Generalized Black-Scholes equation
Mellin transform
Opis:
Numerical approximations and analytical techniques have been proposed for the pricing of basket put option but there is no known integral equation for the valuation of European basket put option with multi-dividend yields. Mellin transform is useful when dealing with the unstable mathematical system. This paper presents the integral equation for the price of the European basket put option which pays multi-dividend yields by means of the Mellin transform in higher dimensions that enables option equations to be solved directly in terms of market prices rather than log-prices, providing a more natural setting to the problem of pricing. The expression for the integral equation for the valuation of the European basket put option was obtained by solving the multi-dimensional partial differential equation for the price of the option via the multi-dimensional Mellin transform. The analytical solution to the derived integral equation for the case of two-dividend paying stocks was obtained. Also the effect of the correlation coefficients on the price of the European basket put option was considered. A comparative study of the Mellin transform, Monte Carlo method and implied binomial model for the valuation of the option in the case of was considered. The numerical results showed that negatively correlated assets are more sensitive to correlation changes than positively correlated assets as shown in Tables 1 and 2. Also the numerical evaluation of our expression is more efficient and produces a comparable result than the other methods. Hence the Mellin transform is a good approach for the valuation of European basket put option with multi-dividend yields.
Źródło:
World Scientific News; 2018, 94, 2; 72-98
2392-2192
Pojawia się w:
World Scientific News
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:
Controllabilty and stability analysis on a group associated with Black-Scholes equation
Autorzy:
Tiwari, Archana
Bhattacharyya, Debanjana
Pati, K. C.
Powiązania:
https://bibliotekanauki.pl/articles/229513.pdf
Data publikacji:
2020
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
Black-Scholes equation
Schrödinger equation
Lie group
optimal control
stability
numerical integration
Opis:
In this paper we have studied the driftless control system on a Lie group which arises due to the invariance of Black-Scholes equation by conformal transformations. These type of studies are possible as Black-Scholes equation can be mapped to one dimensional free Schrödinger equation. In particular we have studied the controllability, optimal control of the resulting dynamics as well as stability aspects of this system. We have also found out the trajectories of the states of the system through two unconventional integrators along with conventional Runge-Kutta integrator.
Źródło:
Archives of Control Sciences; 2020, 30, 3; 553-573
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-10 z 33

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