Relevant bibliographies by topics / Black Scholes / Journal articles

Journal articles on the topic 'Black Scholes'

To see the other types of publications on this topic, follow the link: Black Scholes.
Author: Grafiati
Published: 4 June 2021
Last updated: 11 September 2023

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the top 50 journal articles for your research on the topic 'Black Scholes.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Browse journal articles on a wide variety of disciplines and organise your bibliography correctly.

1

Schmitt, Markus. "Black-Scholes-Formel." Controlling 13, no. 6 (2001): 315–18. http://dx.doi.org/10.15358/0935-0381-2001-6-315.

Full text
APA, Harvard, Vancouver, ISO, and other styles
2

Wang, Lujian, Minqing Zhang, and Zhao Liu. "The Progress of Black-Scholes Model and Black-Scholes-Merton Model." BCP Business & Management 38 (March 2, 2023): 3405–10. http://dx.doi.org/10.54691/bcpbm.v38i.4314.

Full text
Abstract:
Black-Scholes (BS) model was first proposed in 1973, which has been modified by Robert Merton as the Black-Scholes-Merton (BSM) model subsequently. Contemporarily, these two models have been widely used and praised by financial scholars as well as employees. Plenty of scholars have tried to verify the accuracy of the and expressed their views on the existing defects in above models. Based on the existing literature, this article first introduces and derives the two models step by step and discusses the basic assumptions for these models. Subsequently, the applications of the two models are demonstrated separately. Specifically, the project valuation based on BS model is presented detaily while the applications of BSM model are introduced from four aspects (pricing of intangible assets, risk avoidance, default prediction and employee stock option’s pricing). Afterwards, the limitations and gaps of the models (e.g., volatility smile) ascribed to the ideal assumptions are discussed. In order to tackle the issue, improvement and suggestions are proposed including extending the models with different forms. These results offer a guideline for the option pricing, which can be widely applied in investment strategy.
APA, Harvard, Vancouver, ISO, and other styles
3

O'Brien, Thomas, and Risk/Finex. "From Black-Scholes to Black Holes." Journal of Finance 48, no. 4 (September 1993): 1560. http://dx.doi.org/10.2307/2329055.

Full text
APA, Harvard, Vancouver, ISO, and other styles
4

Omey, Edward, and Gulck van. "Markovian black and scholes." Publications de l'Institut Mathematique 79, no. 93 (2006): 65–72. http://dx.doi.org/10.2298/pim0693065o.

Full text
APA, Harvard, Vancouver, ISO, and other styles
5

Hahnenstein, Lutz, Sascha Wilkens, and Klaus Röder. "Die Black-Scholes-Optionspreisformel." WiSt - Wirtschaftswissenschaftliches Studium 30, no. 7 (2001): 355–61. http://dx.doi.org/10.15358/0340-1650-2001-7-355.

Full text
APA, Harvard, Vancouver, ISO, and other styles
6

Kruschwitz, Lutz, and Maria Stefanova. "Die Black-Scholes-Differentialgleichung." WiSt - Wirtschaftswissenschaftliches Studium 36, no. 2 (2007): 82–87. http://dx.doi.org/10.15358/0340-1650-2007-2-82.

Full text
APA, Harvard, Vancouver, ISO, and other styles
7

Aghili, A. "Fractional Black–Scholes equation." International Journal of Financial Engineering 04, no. 01 (March 2017): 1750004. http://dx.doi.org/10.1142/s2424786317500049.

Full text
Abstract:
In this paper, it has been shown that the combined use of exponential operators and special functions provides a powerful tool to solve certain class of generalized space fractional Laguerre heat equation. It is shown that exponential operators are powerful and effective method for solving certain singular integral equations and space fractional Black–Scholes equation.
APA, Harvard, Vancouver, ISO, and other styles
8

Munn, Luke. "From the Black Atlantic to Black-Scholes." Cultural Politics 16, no. 1 (March 1, 2020): 92–110. http://dx.doi.org/10.1215/17432197-8017284.

Full text
Abstract:
Rather than being unprecedented, contemporary technologies are the most sophisticated instances of a long-standing dream: if space could be more comprehensively captured and coded, it could be more intensively capitalized. Two moments within this lineage are explored: maritime insurance of slave ships in the eighteenth century, and the Black-Scholes model of option pricing from the twentieth century. Maritime insurance rendered the unknown space of the ocean knowable and therefore profitable. By collecting information at Lloyds, merchants developed a map of threat within the Atlantic, and by writing a 10 percent buffer into slave-ship contracts they internalized contingency. This codification of risk pressured captains and established a logic for the violence enacted on the ship’s human “cargo.” The Black-Scholes formula of option pricing sought to codify the ocean of risk represented by the financial market. The formula mapped stock movements into a knowable stochastic equation. Traders could quantify and hedge against the unpredictable, rendering the stock market a space of riskless profit. However, the 2008 financial crash demonstrated the limits of spatial calculation. Taken together, these two moments demonstrate the historical continuity of a core imperative to exhaustively capitalize space. This historicization also foregrounds the racialized inequalities coded within these informatic logics. Against the bright innovation narratives of technology, this article stresses a longer and darker lineage based on inequality and dispossession.
APA, Harvard, Vancouver, ISO, and other styles
9

Fink, Holger, and Stefan Mittnik. "Quanto Pricing beyond Black–Scholes." Journal of Risk and Financial Management 14, no. 3 (March 23, 2021): 136. http://dx.doi.org/10.3390/jrfm14030136.

Full text
Abstract:
Since their introduction, quanto options have steadily gained popularity. Matching Black–Scholes-type pricing models and, more recently, a fat-tailed, normal tempered stable variant have been established. The objective here is to empirically assess the adequacy of quanto-option pricing models. The validation of quanto-pricing models has been a challenge so far, due to the lack of comprehensive data records of exchange-traded quanto transactions. To overcome this, we make use of exchange-traded structured products. After deriving prices for composite options in the existing modeling framework, we propose a new calibration procedure, carry out extensive analyses of parameter stability and assess the goodness of fit for plain vanilla and exotic double-barrier options.
APA, Harvard, Vancouver, ISO, and other styles
10

Stanislavsky, A. A. "Black–Scholes model under subordination." Physica A: Statistical Mechanics and its Applications 318, no. 3-4 (February 2003): 469–74. http://dx.doi.org/10.1016/s0378-4371(02)01372-9.

Full text
APA, Harvard, Vancouver, ISO, and other styles
11

Ahmed, E., and H. A. Abdusalam. "On modified Black–Scholes equation." Chaos, Solitons & Fractals 22, no. 3 (November 2004): 583–87. http://dx.doi.org/10.1016/j.chaos.2004.02.018.

Full text
APA, Harvard, Vancouver, ISO, and other styles
12

Trzetrzelewski, Maciej. "The relativistic Black-Scholes model." EPL (Europhysics Letters) 117, no. 3 (February 1, 2017): 38004. http://dx.doi.org/10.1209/0295-5075/117/38004.

Full text
APA, Harvard, Vancouver, ISO, and other styles
13

Agliardi, R., P. Popivanov, and A. Slavova. "On nonlinear Black-Scholes equations." Nonlinear Analysis and Differential Equations 1 (2013): 75–81. http://dx.doi.org/10.12988/nade.2013.13009.

Full text
APA, Harvard, Vancouver, ISO, and other styles
14

Nygaard, Hans Kristian. "Incentivordninger og Black Scholes-formelen." Praktisk økonomi & finans 38, no. 4 (December 8, 2022): 356–65. http://dx.doi.org/10.18261/pof.38.4.6.

Full text
APA, Harvard, Vancouver, ISO, and other styles
15

Schnabel, Jacques A. "Restructuring the black-scholes isomorphism." Atlantic Economic Journal 16, no. 2 (June 1988): 85. http://dx.doi.org/10.1007/bf02306331.

Full text
APA, Harvard, Vancouver, ISO, and other styles
16

Ayache, Elie. "Time and Black-Scholes-Merton." Wilmott 2017, no. 88 (March 2017): 24–33. http://dx.doi.org/10.1002/wilm.10578.

Full text
APA, Harvard, Vancouver, ISO, and other styles
17

Mehrdoust, Farshid, Amir Hosein Refahi Sheikhani, Mohammad Mashoof, and Sabahat Hasanzadeh. "Block-pulse operational matrix method for solving fractional Black-Scholes equation." Journal of Economic Studies 44, no. 3 (August 14, 2017): 489–502. http://dx.doi.org/10.1108/jes-05-2016-0107.

Full text
Abstract:
Purpose The purpose of this paper is to evaluate a European option using the fractional version of the Black-Scholes model. Design/methodology/approach In this paper, the authors employ the block-pulse operational matrix algorithm to approximate the solution of the fractional Black-Scholes equation with the initial condition for a European option pricing problem. Findings The fractional derivative will be described in the Caputo sense in this paper. The authors show the accuracy and computational efficiency of the proposed algorithm through some numerical examples. Originality/value This is the first paper that considers an alternative algorithm for pricing a European option using the fractional Black-Scholes model.
APA, Harvard, Vancouver, ISO, and other styles
18

Janowicz, Maciej, and Andrzej Zembrzuski. "Symmetry Properties of Modified Black-Scholes Equation." Metody Ilościowe w Badaniach Ekonomicznych 22, no. 2 (May 17, 2022): 77–86. http://dx.doi.org/10.22630/mibe.2021.22.2.7.

Full text
Abstract:
This paper concerns the classical and conditional symmetries of the Black-Scholes equation. Modifications of the Black-Scholes equation have also been considered and their maximal algebras of invariance have been found. Examples of creation operators for the Black-Scholes eigenvalue problem have been provided.
APA, Harvard, Vancouver, ISO, and other styles
19

Bayram, Mustafa, Buyukoz Orucova, and Tugcem Partal. "Parameter estimation in a Black Scholes." Thermal Science 22, Suppl. 1 (2018): 117–22. http://dx.doi.org/10.2298/tsci170915277b.

Full text
Abstract:
In this paper we discuss parameter estimation in black scholes model. A non-parametric estimation method and well known maximum likelihood estimator are considered. Our aim is to estimate the unknown parameters for stochastic differential equation with discrete time observation data. In simulation study we compare the non-parametric method with maximum likelihood method using stochastic numerical scheme named with Euler Maruyama.
APA, Harvard, Vancouver, ISO, and other styles
20

Masebe, Tshidiso. "New Symmetries of Black-Scholes Equation." WSEAS TRANSACTIONS ON SYSTEMS 20 (April 19, 2021): 76–87. http://dx.doi.org/10.37394/23202.2021.20.10.

Full text
Abstract:
Lie Point symmetries and Euler’s formula for solving second order ordinary linear differential equations are used to determine symmetries for the one-dimensional Black- Scholes equation. One symmetry is utilized to determine an invariant solutions
APA, Harvard, Vancouver, ISO, and other styles
21

Kutner, George W. "BLACK-SCHOLES REVISITED: SOME IMPORTANT DETAILS." Financial Review 23, no. 1 (February 1988): 95–104. http://dx.doi.org/10.1111/j.1540-6288.1988.tb00777.x.

Full text
APA, Harvard, Vancouver, ISO, and other styles
22

Beck, Thomas M. "Black-Scholes Revisited: Some Important Details." Financial Review 28, no. 1 (February 1993): 77–90. http://dx.doi.org/10.1111/j.1540-6288.1993.tb01338.x.

Full text
APA, Harvard, Vancouver, ISO, and other styles
23

Higham, D. J. "Black-Scholes for scientific computing students." Computing in Science and Engineering 6, no. 6 (November 2004): 72–79. http://dx.doi.org/10.1109/mcse.2004.62.

Full text
APA, Harvard, Vancouver, ISO, and other styles
24

Hamza, Kais, and Fima C. Klebaner. "On the implicit Black–Scholes formula." Stochastics 80, no. 1 (February 2008): 97–102. http://dx.doi.org/10.1080/17442500701607706.

Full text
APA, Harvard, Vancouver, ISO, and other styles
25

Arriojas, Mercedes, Yaozhong Hu, Salah-Eldin Mohammed, and Gyula Pap. "A Delayed Black and Scholes Formula." Stochastic Analysis and Applications 25, no. 2 (February 27, 2007): 471–92. http://dx.doi.org/10.1080/07362990601139669.

Full text
APA, Harvard, Vancouver, ISO, and other styles
26

Vecer, Jan. "BLACK-SCHOLES REPRESENTATION FOR ASIAN OPTIONS." Mathematical Finance 24, no. 3 (November 2, 2012): 598–626. http://dx.doi.org/10.1111/mafi.12012.

Full text
APA, Harvard, Vancouver, ISO, and other styles
27

Liu, Wei, Xudong Huang, and Weian Zheng. "Black–Scholes’ model and Bollinger bands." Physica A: Statistical Mechanics and its Applications 371, no. 2 (November 2006): 565–71. http://dx.doi.org/10.1016/j.physa.2006.03.033.

Full text
APA, Harvard, Vancouver, ISO, and other styles
28

David, Claire. "Control of the Black–Scholes equation." Computers & Mathematics with Applications 73, no. 7 (April 2017): 1566–75. http://dx.doi.org/10.1016/j.camwa.2017.02.007.

Full text
APA, Harvard, Vancouver, ISO, and other styles
29

Magdziarz, Marcin. "Black-Scholes Formula in Subdiffusive Regime." Journal of Statistical Physics 136, no. 3 (July 24, 2009): 553–64. http://dx.doi.org/10.1007/s10955-009-9791-4.

Full text
APA, Harvard, Vancouver, ISO, and other styles
30

Lee, Eun-Kyung, and Yoon-Dong Lee. "Understanding Black-Scholes Option Pricing Model." Communications for Statistical Applications and Methods 14, no. 2 (August 31, 2007): 459–79. http://dx.doi.org/10.5351/ckss.2007.14.2.459.

Full text
APA, Harvard, Vancouver, ISO, and other styles
31

Gonzalez Granada, Jose Rodrigo, Luis Fernado Plaza Galvez, and Olena Vasyunkina. "From Black-Scholes to Hamilton-Jacobi." Contemporary Engineering Sciences 11, no. 90 (2018): 4455–63. http://dx.doi.org/10.12988/ces.2018.89495.

Full text
APA, Harvard, Vancouver, ISO, and other styles
32

Qiu, Yan, and Jens Lorenz. "A non-linear Black-Scholes equation." International Journal of Business Performance and Supply Chain Modelling 1, no. 1 (2009): 33. http://dx.doi.org/10.1504/ijbpscm.2009.026264.

Full text
APA, Harvard, Vancouver, ISO, and other styles
33

Lescot, Paul. "Symmetries of the Black-Scholes equation." Methods and Applications of Analysis 19, no. 2 (2012): 147–60. http://dx.doi.org/10.4310/maa.2012.v19.n2.a3.

Full text
APA, Harvard, Vancouver, ISO, and other styles
34

Xuan-Liu, Yang, Zhang Shun-Li, and Qu Chang-Zheng. "Symmetry Breaking for Black–Scholes Equations." Communications in Theoretical Physics 47, no. 6 (June 2007): 995–1000. http://dx.doi.org/10.1088/0253-6102/47/6/006.

Full text
APA, Harvard, Vancouver, ISO, and other styles
35

Dixit, Alok, and Shivam Singh. "Ad-Hoc Black–Scholes vis-à-vis TSRV-based Black–Scholes: Evidence from Indian Options Market." Journal of Quantitative Economics 16, no. 1 (February 15, 2017): 57–88. http://dx.doi.org/10.1007/s40953-017-0078-3.

Full text
APA, Harvard, Vancouver, ISO, and other styles
36

SABRINA, FITRI, DODI DEVIANTO, and FERRA YANUAR. "PENENTUAN HARGA OPSI TIPE EROPA DENGAN MENGGUNAKAN MODEL BLACK SCHOLES FRAKSIONAL." Jurnal Matematika UNAND 9, no. 2 (June 29, 2020): 154. http://dx.doi.org/10.25077/jmu.9.2.154-161.2020.

Full text
Abstract:
Harga opsi tipe Eropa dapat ditentukan dengan model Black Scholes fraksional dengan waktu jatuh tempo dapat difraksional menggunakan parameter Hurst. Gerak Brown fraksional ini dapat diformulasikan ke dalam persamaan diferensial stokastik untuk menentukan model Black Scholes fraksional. Data harga saham Microsoft Corporation (MC) dari tanggal 1 Oktober 2018 sampai 30 September 2019 dapat dibentuk ke dalam model Black Scholes fraksional. Pada saat harga pelaksanaan saham MC meningkat, harga opsi call tipe Eropa semakin menurun dan untuk harga opsi put tipe Eropa semakin meningkat. Kata Kunci: Diferensial stokastik, opsi tipe Eropa, model Black Scholes fraksional
APA, Harvard, Vancouver, ISO, and other styles
37

Yong, Benny. "Perbandingan Efek Dilusi pada Nilai Waran dengan Menggunakan Metode Black-Scholes, Dilusi Black-Scholes, dan Pengamatan Variabel." JURNAL SILOGISME : Kajian Ilmu Matematika dan Pembelajarannya 1, no. 1 (November 29, 2016): 23. http://dx.doi.org/10.24269/js.v1i1.244.

Full text
APA, Harvard, Vancouver, ISO, and other styles
38

Muhamad Rashif Hilmi, Devi Nurtiyasari, and Angga Syahputra. "Pemanfaatan Skewness dan Kurtosis dalam Menentukan Harga Opsi Beli Asia." Quadratic: Journal of Innovation and Technology in Mathematics and Mathematics Education 2, no. 1 (May 30, 2022): 7–15. http://dx.doi.org/10.14421/quadratic.2022.021-02.

Full text
Abstract:
Opsi Asia adalah opsi dimana besar perhitungan keuntungannya menggunakan rata-rata harga aset selama periode kontrak. Penentuan harga Opsi Asia yang umum digunakan adalah dengan metode Black-Scholes. Metode Black-Scholes mempunyai beberapa syarat yang harus terpenuhi, salah satunya adalah logaritma dari rata-rata harga aset berdistribusi normal atau nilai skewness dan kurtosis tidak normal. Dalam aplikasinya, sangat sedikit kasus dimana syarat ini terpenuhi . Salah satu solusi dari permasalahan ini adalah memasukkan nilai skewness dan kurtosis kedalam model. Model ini menggunakan ekspansi Gram-Charlier untuk menambahkan nilai skewness dan kurtosis kepada rumus Black-Scholes. Harga Opsi Asia yang diperoleh adalah harga opsi Asia metode Black-Scholes ditambah dengan persamaan yang berhubungan dengan skewness dan kurtosis yang tidak normal. Dalam studi kasus dilakukan perbandingan harga Opsi Asia metode Black-Scholes dengan ekspansi Gram-Charlier dimana data yang digunakan adalah data simulasi dan diperoleh kesimpulan nilai skewness dan kurtosis dapat mempengaruhi harga Opsi beli Asia dengan Metode Black-Scholes.
APA, Harvard, Vancouver, ISO, and other styles
39

Eshaghi, Shiva, Alireza Ansari, Reza Ghaziani, and Mohammadreza Darani. "Fractional Black-Scholes model with regularized Prabhakar derivative." Publications de l'Institut Math?matique (Belgrade) 102, no. 116 (2017): 121–32. http://dx.doi.org/10.2298/pim1716121e.

Full text
Abstract:
We introduce a fractional type Black-Scholes model in European options including the regularized Prabhakar derivative. We apply the reconstruction of variational iteration method to get the approximate analytical solutions for some models of generalized fractional Black-Scholes equations in terms of the generalized Mittag-Leffler functions.
APA, Harvard, Vancouver, ISO, and other styles
40

Purwandari, Diana. "PENGARUH PEMBAGIAN DIVIDEN MELALUI MODEL BLACK-SCHOLES." Jurnal Lebesgue : Jurnal Ilmiah Pendidikan Matematika, Matematika dan Statistika 2, no. 3 (December 30, 2021): 351–54. http://dx.doi.org/10.46306/lb.v2i3.111.

Full text
Abstract:
Stock trading has a risk that can be said to be quite large due to fluctuations in stock prices. In stock trading, one alternative to reduce the amount of risk is options. The focus of this research is on European options which are financial contracts by giving the holder the right, not the obligation, to sell or buy the principal asset from the writer when it expires at a predetermined price. The Black-Scholes model is an option pricing model commonly used in the financial sector. This study aims to determine the effect of dividend distribution through the Black-Scholes model on stock prices. The effect of dividend distribution through the Black-Scholes model on stock prices results in the stock price immediately after the dividend distribution being lower than the stock price shortly before the dividend distribution
APA, Harvard, Vancouver, ISO, and other styles
41

Özer, H. Ünsal, and Ahmet Duran. "The source of error behavior for the solution of Black–Scholes PDE by finite difference and finite element methods." International Journal of Financial Engineering 05, no. 03 (September 2018): 1850028. http://dx.doi.org/10.1142/s2424786318500287.

Full text
Abstract:
Black–Scholes partial differential equation (PDE) is one of the most famous equations in mathematical finance and financial industry. In this study, numerical solution analysis is done for Black–Scholes PDE using finite element method with linear approach and finite difference methods. The numerical solutions are compared with Black–Scholes formula for option pricing. The numerical errors are determined for the finite element and finite difference applications to Black–Scholes PDE. We examine the error behavior and find the source of the corresponding errors under various market situations.
APA, Harvard, Vancouver, ISO, and other styles
42

Sun, Yesen, Wenxiu Gong, Hongliang Dai, and Long Yuan. "Numerical Method for American Option Pricing under the Time-Fractional Black–Scholes Model." Mathematical Problems in Engineering 2023 (February 20, 2023): 1–17. http://dx.doi.org/10.1155/2023/4669161.

Full text
Abstract:
The fractional Black–Scholes model has had limited applications in financial markets. Instead, the time-fractional Black–Scholes equation has attracted much research interest. However, it is difficult to obtain the analytic expression for American option pricing under the time-fractional Black–Scholes model. This paper will present an operator-splitting method to price the American options under the time-fractional Black–Scholes model. The fractional partial differential complementarity problem (FPDCP) that the American option price satisfied is split into two subproblems: a linear boundary value problem and an algebraic system. A high-order compact (HOC) scheme and a grid stretching (GS) method are considered for the linear boundary problem. Furthermore, numerical results show that the HOC scheme with a GS method gives an accurate numerical solution for American options under the time-fractional Black–Scholes model.
APA, Harvard, Vancouver, ISO, and other styles
43

Susanti, Desi, and Dodi Devianto. "PENURUNAN MODEL BLACK SCHOLES DENGAN PERSAMAAN DIFERENSIAL STOKASTIK UNTUK OPSI TIPE EROPA." Jurnal Matematika UNAND 3, no. 1 (March 1, 2014): 17. http://dx.doi.org/10.25077/jmu.3.1.17-26.2014.

Full text
Abstract:
Opsi tipe Eropa adalah kontrak yang memberikan hak kepada pemilik ataupemegangnya untuk membeli atau menjual sejumlah aset (saham) suatu perusahaan tertentu dengan harga tertentu (harga pelaksanaan), yang dilaksanakan saat jatuh temposaja. Harga opsi saham dapat ditentukan dengan model Black Scholes yang dirumuskanoleh Fisher Black dan Mayor Scholes pada tahun 1973. Model ini mengasumsikan bahwaharga saham tidak membayarkan dividen, tidak ada pembayaran pajak, suku bunga bebas resiko, dan opsi yang digunakan bertipe Eropa. Perubahan harga saham yang terjadidi pasar bergerak secara acak menurut waktu. Perubahan tersebut dapat diasumsikanmengikuti proses Wiener yang merupakan suatu gerak Brown. Perubahan harga sahamyang mengikuti gerak Brown dapat diformulasikan kedalam suatu persamaan diferensial stokastik, dimana solusinya dapat menentukan model Black Scholes. Perhitunganharga opsi saham Sony Corporation periode 31 Desember 2012 sampai 31 Desember2013 deng-an Black Scholes menunjukkan bahwa pada semua harga pelaksanaan yangdipakai sebaiknya opsi call dibeli karena harga opsi di pasar lebih rendah dibandingkanyang dihitung dengan Black Scholes, sedangkan untuk opsi put pada harga pelaksanaan19.00 dolar sebaiknya opsi dijual.
APA, Harvard, Vancouver, ISO, and other styles
44

Ampun, Sivaporn, Panumart Sawangtong, and Wannika Sawangtong. "An Analysis of the Fractional-Order Option Pricing Problem for Two Assets by the Generalized Laplace Variational Iteration Approach." Fractal and Fractional 6, no. 11 (November 11, 2022): 667. http://dx.doi.org/10.3390/fractalfract6110667.

Full text
Abstract:
An option is the right to buy or sell a good at a predetermined price in the future. For customers or financial companies, knowing an option’s pricing is crucial. It is well recognized that the Black–Scholes model is an effective tool for estimating the cost of an option. The Black–Scholes equation has an explicit analytical solution known as the Black–Scholes formula. In some cases, such as the fractional-order Black–Scholes equation, there is no closed form expression for the modified Black–Scholes equation. This article shows how to find the approximate analytic solutions for the two-dimensional fractional-order Black–Scholes equation based on the generalized Riemann–Liouville fractional derivative. The generalized Laplace variational iteration method, which incorporates the generalized Laplace transform with the variational iteration method, is the methodology used to discover the approximate analytic solutions to such an equation. The expression of the two-parameter Mittag–Leffler function represents the problem’s approximate analytical solution. Numerical investigations demonstrate that the proposed scheme is accurate and extremely effective for the two-dimensional fractional-order Black–Scholes Equation in the perspective of the generalized Riemann–Liouville fractional derivative. This guarantees that the generalized Laplace variational iteration method is one of the effective approaches for discovering approximate analytic solutions to fractional-order differential equations.
APA, Harvard, Vancouver, ISO, and other styles
45

Ayache, Elie. "A Truthful Generalization of Black‐Scholes‐Merton." Wilmott 2021, no. 111 (January 2021): 32–43. http://dx.doi.org/10.1002/wilm.10903.

Full text
APA, Harvard, Vancouver, ISO, and other styles
46

Pereira, Alfredo M., and M. Sean Tarter. "An Unhedgeable Black–Scholes–Merton Implicit Option?" Risks 10, no. 7 (June 29, 2022): 134. http://dx.doi.org/10.3390/risks10070134.

Full text
Abstract:
In this paper, we focus on an implicit assumption in the BSM framework that limits the scope of market network connections to seeking gains in the currency basis, i.e., on trading strategies between the numeraire and the stock and between the numeraire and the option, separately. We relax this assumption and derive the equivalent of the standard BSM approach under a more general market network framework in order to assess its implications. In doing so, we find that it is not possible to hedge on an implicit option that allows one to directly trade the option and stock. This represents a potential challenge to the BSM framework, since the missing market network connection provides a potentially useful mechanism for risk-bearing portfolio managers to alter their portfolios.
APA, Harvard, Vancouver, ISO, and other styles
47

Abdelkawy, M. A., and António M. Lopes. "Spectral Solutions for Fractional Black–Scholes Equations." Mathematical Problems in Engineering 2022 (July 20, 2022): 1–9. http://dx.doi.org/10.1155/2022/9365292.

Full text
Abstract:
This paper presents a numerical method to solve accurately the fractional Black–Scholes model of pricing evolution. A fully spectral collocation technique for the two independent variables is derived. The shifted fractional Jacobi–Gauss–Radau and shifted fractional Jacobi–Gauss–Lobatto collocation techniques are utilized. Firstly, the independent variables are interpolated at the shifted fractional Jacobi nodes, and the solution of the model is approximated by means of a sequence of shifted fractional Jacobi orthogonal functions. Then, the residuals at the shifted fractional Jacobi quadrature locations are estimated. As a result, an algebraic system of equations is obtained that can be solved using any appropriate approach. The accuracy of the proposed method is demonstrated using two numerical examples. It is observed that the new technique is more accurate, efficient, and feasible than other approaches reported in the literature. Indeed, the results show the exponential convergence of the method, both for smooth and nonsmooth solutions.
APA, Harvard, Vancouver, ISO, and other styles
48

Kiptum, Purity Jebotibin, Joseph E. Esekon, and Owino Maurice Oduor. "Greek Parameters of Nonlinear Black-Scholes Equation." International Journal of Mathematics and Soft Computing 5, no. 2 (July 10, 2015): 69. http://dx.doi.org/10.26708/ijmsc.2015.2.5.09.

Full text
APA, Harvard, Vancouver, ISO, and other styles
49

Ahmad Dar, Amir, and N. Anuradha. "Comparison: Binomial model and Black Scholes model." Quantitative Finance and Economics 2, no. 1 (2018): 230–45. http://dx.doi.org/10.3934/qfe.2018.1.230.

Full text
APA, Harvard, Vancouver, ISO, and other styles
50

Ahmad Dar, Amir, and N. Anuradha. "Comparison: Binomial model and Black Scholes model." Quantitative Finance and Economics 2, no. 1 (2018): 715–30. http://dx.doi.org/10.3934/qfe.2018.1.715.

Full text
APA, Harvard, Vancouver, ISO, and other styles
You might also be interested in the bibliographies on the topic 'Black Scholes' for other source types:
Dissertations / Theses Books
We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!

To the bibliography