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Journal articles on the topic 'Black Scholes'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Sugandha, Agus. "REVIEW PERSAMAAN BLACK-SCHOLES FRAKSIONAL DIMODIFIKASI." Perwira Journal of Science & Engineering 1, no. 2 (2022): 26–37. http://dx.doi.org/10.54199/pjse.v1i2.68.

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Paper ini akan dibahas solusi dari persamaan Black-Scholes fraksional yang merupakan bentuk umum dari persamaan Black-Scholes dan kebaruan penelitian tentang persamaan Black-Scholes yang dimodifikasi. Adapun metode-metode untuk mencari solusi dari persamaan Black Scholes Fraksional sudah banyak ditulis dalam banyak jurnal internasional. Solusi persamaan Black Scholes fraksional dalam hal ini ditinjau dengan pendekatan Kalkulus Fraksional. Dengan pendekatan Kalkulus Fraksional proses penyelesaian dalam mencari solusi persamaan Black Scholes Fraksional menjadi lebih efisien. Beberapa Metode yang

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2

Rusmaningtyas, Rahmanita Febrianti, Neva Satyahadewi, and Setyo Wira Rizki. "Perbandingan Harga Opsi Saham Tipe Eropa Menggunakan Model Black Scholes dan Black Scholes Fraksional." Jurnal EurekaMatika 9, no. 2 (2022): 177–84. http://dx.doi.org/10.17509/jem.v10i1.44454.

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One of the investment is stocks. Stocks have derivative instrument in the form of stock options. Stocks option is a contract between two parties in the form of the right to sell and buy a stocks at a certain price and time. The method used in this study is the fractional Black Scholes and Black Scholes method with time of maturity fractioned by the Hurst parameter. The purpose od this study is to compare the prices of call and put options using the Black Scholes and Fractional Back Scholes. The data using close price of Apple Inc shares within period between October 1st 2020 until September 30

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3

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

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4

Sugandha, Agus, Endang Rusyaman, Sukono, and Ema Carnia. "A New Solution to the Fractional Black–Scholes Equation Using the Daftardar-Gejji Method." Mathematics 11, no. 24 (2023): 4887. http://dx.doi.org/10.3390/math11244887.

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The main objective of this study is to determine the existence and uniqueness of solutions to the fractional Black–Scholes equation. The solution to the fractional Black–Scholes equation is expressed as an infinite series of converging Mittag-Leffler functions. The method used to discover the new solution to the fractional Black–Scholes equation was the Daftardar-Geiji method. Additionally, the Picard–Lindelöf theorem was utilized for the existence and uniqueness of its solution. The fractional derivative employed was the Caputo operator. The search for a solution to the fractional Black–Schol

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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 (2017): 489–502. http://dx.doi.org/10.1108/jes-05-2016-0107.

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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 th

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6

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.

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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 dem

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

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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.

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8

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 (2022): 7–15. http://dx.doi.org/10.14421/quadratic.2022.021-02.

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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

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9

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

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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: D

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10

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 (2018): 1850028. http://dx.doi.org/10.1142/s2424786318500287.

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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.

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11

Hendrawan, Riko, and Abdul Safar. "Comparing Black-Scholes and GARCH Models in Long Strangle Option Strategies for LQ45 Index." Research of Finance and Banking 1, no. 2 (2023): 85–92. http://dx.doi.org/10.58777/rfb.v1i2.137.

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This study compared the Black-Scholes and GARCH models in a long strangle strategy applied to the LQ45 index using closing price data from 1998 to 2021. It aimed to assess the benefits, calculate returns during crises and non-crisis periods, and evaluate performance through Average Mean Square Error (AMSE). The Black-Scholes model consistently outperformed GARCH in one- and three-month options. One-month options had an average return of 28.64%, and three-month options, 43.31%. In crises, Black-Scholes delivered average profits of 43.36% for one-month and 45.14% for three-month options. In non-

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12

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

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13

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.

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14

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.

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15

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.

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16

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

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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.

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17

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.

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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 va

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18

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 (2022): 667. http://dx.doi.org/10.3390/fractalfract6110667.

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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-dimens

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19

Taufik, Ahmad, Mochammad Idris, and Aprida Siska Lestia. "METODE BLACK-SCHOLES DALAM PENENTUAN HARGA OPSI." EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN (EPSILON: JOURNAL OF PURE AND APPLIED MATHEMATICS) 18, no. 1 (2024): 122. http://dx.doi.org/10.20527/epsilon.v18i1.12604.

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The Black-Scholes Method is one of the option pricing method that introduced by Fischer Black and Myron Scholes in 1973. This study aim to review the determination of the price of an option with stocks as the underlying assets and based on Black and Scholes assumptions. These assumptions lead to construct an equation named Black-Scholes differential equations, which is the equation that must be satisfied for option as the derivative instrument and non-dividend giving stocks as the underlying assets. After the Black-Scholes differential equations formed successfully, the next step is to find th

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20

Yavuz, M., and N. Özdemir. "A different approach to the European option pricing model with new fractional operator." Mathematical Modelling of Natural Phenomena 13, no. 1 (2018): 12. http://dx.doi.org/10.1051/mmnp/2018009.

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In this work, we have derived an approximate solution of the fractional Black-Scholes models using an iterative method. The fractional differentiation operator used in this paper is the well-known conformable derivative. Firstly, we redefine the fractional Black-Scholes equation, conformable fractional Adomian decomposition method (CFADM) and conformable fractional modified homotopy perturbation method (CFMHPM). Then, we have solved the fractional Black-Scholes (FBS) and generalized fractional Black-Scholes (GFBS) equations by using the proposed methods, which can analytically solve the fracti

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21

Li, Chenwei. "A Study of Option Pricing Models with Market Price Adjustments: Empirical Analysis Beyond the Black-Scholes Model." Advances in Economics, Management and Political Sciences 137, no. 1 (2024): 94–98. https://doi.org/10.54254/2754-1169/2024.18702.

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In 1973, Fischer Black and Myron Scholes unveiled the Black-Scholes option pricing model, a groundbreaking contribution that profoundly influenced the domain of option pricing theory. The introduction of the Black-Scholes pricing formula has garnered substantial acclaim across both academic and industrial spheres, leading to its widespread dissemination and application. This formula not only underscores its vital significance but also exemplifies its unique position as a cornerstone of financial theory, reshaping how options are valued and traded in markets worldwide. However, in the real fina

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

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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

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23

Rifki Chandra Utama, Afra Maulia Fitriana Hilnie, and Wiwit Angga Siswahyudi. "EUROPEAN PUT OPTION PRICING MODEL WITH GRAM-CHARLIER EXPANSION IN THIRD MOMENTS." Perwira Journal of Science & Engineering 2, no. 1 (2022): 41–49. http://dx.doi.org/10.54199/pjse.v2i1.118.

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The Black-Scholes model is one of the most popular and widely applied option pricing models in both academic and practical contexts developed by Black and Scholes (1973). The practical assumption in the Black-Scholes model is stock return following the normal distribution with constant volatility. However, many stock returns are not normally distributed, so should consider the skewness and kurtosis of the stock return. This developmental model adapts the Gram-Charlier expansion to adapt skewness and kurtosis to the Black-Scholes formula. Approximation method used is an alternative approach wit

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Arraut, Ivan, and Ka-I. Lei. "The Role of the Volatility in the Option Market." AppliedMath 3, no. 4 (2023): 882–908. http://dx.doi.org/10.3390/appliedmath3040047.

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We review some general aspects about the Black–Scholes equation, which is used for predicting the fair price of an option inside the stock market. Our analysis includes the symmetry properties of the equation and its solutions. We use the Hamiltonian formulation for this purpose. Taking into account that the volatility inside the Black–Scholes equation is a parameter, we then introduce the Merton–Garman equation, where the volatility is stochastic, and then it can be perceived as a field. We then show how the Black–Scholes equation and the Merton–Garman one are locally equivalent by imposing a

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Sinkala, Winter, and Tembinkosi F. Nkalashe. "Studying a Tumor Growth Partial Differential Equation via the Black–Scholes Equation." Computation 8, no. 2 (2020): 57. http://dx.doi.org/10.3390/computation8020057.

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Two equations are considered in this paper—the Black–Scholes equation and an equation that models the spatial dynamics of a brain tumor under some treatment regime. We shall call the latter equation the tumor equation. The Black–Scholes and tumor equations are partial differential equations that arise in very different contexts. The tumor equation is used to model propagation of brain tumor, while the Black–Scholes equation arises in financial mathematics as a model for the fair price of a European option and other related derivatives. We use Lie symmetry analysis to establish a mapping betwee

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Chauhan, Arun, and Ravi Gor. "COMPARISON OF THREE OPTION PRICING MODELS FOR INDIAN OPTIONS MARKET." International Journal of Engineering Science Technologies 5, no. 4 (2021): 54–64. http://dx.doi.org/10.29121/ijoest.v5.i4.2021.203.

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  Black-Scholes option pricing model is used to decide theoretical price of different Options contracts in many stock markets in the world. In can find many generalizations of BS model by modifying some assumptions of classical BS model. In this paper we compared two such modified Black-Scholes models with classical Black-Scholes model only for Indian option contracts. We have selected stock options form 5 different sectors of Indian stock market. Then we have found call and put option prices for 22 stocks listed on National Stock Exchange by all three option pricing models. Finall

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Hendrawan, Riko, Gede Teguh Laksana, and Wiwin Aminah. "Can The IDX Be Hegded ? : Comparison of Black Scholes Option Model And Garch Option Model Using Long Strangle Strategy." Jurnal Manajemen Indonesia 20, no. 3 (2020): 252. http://dx.doi.org/10.25124/jmi.v20i3.3521.

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The purpose of this research was to compare the accuracy of the Black Scholes option model and the GARCH option model on index options using IDX Composite (IHSG) data from 2009-2018 with the long strangle strategy. The Black Scholes volatility constructed by using historical volatility, while GARCH volatility constructed by using the ARIMA model and the best lag. The accuracy of options analyzed using the average percentage mean square error (AMSE) to find the best model. The results of this study showed that for the one month option, the GARCH model is more accurate for a call option with 0.2

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Megis, Febi Fortuna, and Arnellis Arnellis. "Analisis Metode Black-Scholes dan Monte Carlo Terhadap Penentuan Opsi Jual Eropa." Journal of Mathematics UNP 7, no. 4 (2022): 50. http://dx.doi.org/10.24036/unpjomath.v7i4.13850.

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Managing the risks that will occur when investing, things that can be done by trading options. Options are used as a means of hedge against the uncertainty of stock price movements. The calculation of the option price is done using two methods, namely the Black-Scholes method and the Monte Carlo method. This study aims to compare the results of determining the price of European put options using the Black-Scholes and Monte Carlo methods. This type of research is basic research The data used is the daily closing price of the pharmaceutical industry in Indonesia for the period August 2020 to Aug

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SHOKROLLAHI, FOAD. "THE VALUATION OF EUROPEAN OPTION UNDER SUBDIFFUSIVE FRACTIONAL BROWNIAN MOTION OF THE SHORT RATE." International Journal of Theoretical and Applied Finance 23, no. 04 (2020): 2050022. http://dx.doi.org/10.1142/s0219024920500223.

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In this paper, we propose an extension of the Merton model. We apply the subdiffusive mechanism to analyze European option in a fractional Black–Scholes environment, when the short rate follows the subdiffusive fractional Black–Scholes model. We derive a pricing formula for call and put options and discuss the corresponding fractional Black–Scholes equation. We present some features of our model pricing model for the cases of [Formula: see text] and [Formula: see text].

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Rani,, Dr Pushpa. "Analysis of Option Prices Using Black Scholes Model." INTERANTIONAL JOURNAL OF SCIENTIFIC RESEARCH IN ENGINEERING AND MANAGEMENT 08, no. 05 (2024): 1–5. http://dx.doi.org/10.55041/ijsrem34488.

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A mathematical formula used in finance to calculate the theoretical price of an option and ascertain its option premium is known as the Black Scholes option pricing model, which aids option traders in making informed decisions. This article estimates the option premium of various call and put options using the Black Scholes Model. The three distinct option chains chosen for this essay are all Mid-Cap companies that are listed on the Indian National Stock Exchange. The companies are Suzlon Energy, Kalyan jewellers India, and Exide Industries Ltd. The analysis demonstrates that the options are e

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Fatone, Lorella, Francesca Mariani, Maria Cristina Recchioni, and Francesco Zirilli. "The Use of Statistical Tests to Calibrate the Black-Scholes Asset Dynamics Model Applied to Pricing Options with Uncertain Volatility." Journal of Probability and Statistics 2012 (2012): 1–20. http://dx.doi.org/10.1155/2012/931609.

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A new method for calibrating the Black-Scholes asset price dynamics model is proposed. The data used to test the calibration problem included observations of asset prices over a finite set of (known) equispaced discrete time values. Statistical tests were used to estimate the statistical significance of the two parameters of the Black-Scholes model: the volatility and the drift. The effects of these estimates on the option pricing problem were investigated. In particular, the pricing of an option with uncertain volatility in the Black-Scholes framework was revisited, and a statistical signific

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RIGATOS, GERASIMOS G. "BOUNDARY CONTROL OF THE BLACK–SCHOLES PDE FOR OPTION DYNAMICS STABILIZATION." Annals of Financial Economics 11, no. 02 (2016): 1650009. http://dx.doi.org/10.1142/s2010495216500093.

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The objective of the paper is to develop a boundary control method for the Black–Scholes PDE which describes option dynamics. It is shown that the procedure for numerical solution of Black–Scholes PDE results into a set of nonlinear ordinary differential equations (ODEs) and an associated state equations model. For the local subsystems, into which a Black–Scholes PDE is decomposed, it becomes possible to apply boundary-based feedback control. The controller design proceeds by showing that the state-space model of the Black–Scholes PDE stands for a differentially flat system. Next, for each sub

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Sinkala, Winter, and Tembinkosi F. Nkalashe. "Lie Symmetry Analysis of a First-Order Feedback Model of Option Pricing." Advances in Mathematical Physics 2015 (2015): 1–9. http://dx.doi.org/10.1155/2015/361785.

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A first-order feedback model of option pricing consisting of a coupled system of two PDEs, a nonliner generalised Black-Scholes equation and the classical Black-Scholes equation, is studied using Lie symmetry analysis. This model arises as an extension of the classical Black-Scholes model when liquidity is incorporated into the market. We compute the admitted Lie point symmetries of the system and construct an optimal system of the associated one-dimensional subalgebras. We also construct some invariant solutions of the model.

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Ahmad, Manzoor, Rajshree Mishra, and Renu Jain. "Analytical solution of time fractional Black-Scholes equation with two assets through new Sumudu Transform iterative method." Gulf Journal of Mathematics 15, no. 1 (2023): 42–56. http://dx.doi.org/10.56947/gjom.v15i1.1060.

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There is a scopious rise in the study of financial derivatives over the past two or three decades. Mathematical model proposed by Black and Scholes expounds financial derivatives in a more momentous way. The Black-Scholes model on a single asset is a partial differential equation characterizing the behavior of European options. In this article, we introduce the new Sumudu transform iterative method (NSTIM) as a new technique to obtain the analytical solution of time fractional Black-Scholes model involving European options with two assets. The proposed model is the advanced version of the regu

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

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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 w

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Gustyana, Tieka Trikartika, and Andrieta Shintia Dewi. "ANALISIS PERBANDINGAN KEAKURATAN HARGA CALL OPTION DENGAN MENGGUNAKAN METODE MONTE CARLO SIMULATION DAN METODE BLACK SCHOLES PADA INDEKS HARGA SAHAM GABUNGAN (IHSG)." Jurnal Manajemen Indonesia 14, no. 3 (2017): 259. http://dx.doi.org/10.25124/jmi.v14i3.387.

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Opsi adalah salah satu instrument derivative. Option merupakan investasi yang cukup menarik untuk dilakukan apabila volatilitasnya tinggi. Risiko dapat digambarkan dengan volatilitas. Volatilitas menggambarkan probabilitas yang terjadi pada harga saham dari waktu ke waktu. IHSG merupakan Indeks Harga Saham Gabungan yang menggambarkan harga saham di Bursa Efek Indonesia (BEI), dimana IHSG juga merupakan indikator pergerakan harga seluruh saham di BEI.Metode penelitian yang digunakan dalam penelitian ini adalah metode deskriptif. Penentuan harga premi opsi call dengan menggunakan dua metoda yait

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DENI, PUTU AYU, KOMANG DHARMAWAN, and G. K. GANDHIADI. "PENENTUAN HARGA OPSI DAN NILAI HEDGE MENGGUNAKAN PERSAMAAN NON-LINEAR BLACK-SCHOLES." E-Jurnal Matematika 5, no. 1 (2016): 27. http://dx.doi.org/10.24843/mtk.2016.v05.i01.p117.

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Option are contracts that give the right to sell and buy the asset at a price and a certain period of time. In addition investors use option as a means of hedge against asset owned. Many methods are used to determine the price of option, one of them by using the Black-Scholes equation. But its use these in the assumption that the value for the constant volatility. On market assumption are not appropriates, so many researchers proposed using a volatility calculation option that is non-constant Black-Scholes equation modelled using the volatility is not constant in the range so as to produce a n

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Wu, Yawei. "Options Pricing Comparison between the Black-Scholes Model and the Binomial Tree Model: A Case Study of American Equity Option and European-style Index Option." BCP Business & Management 32 (November 22, 2022): 168–77. http://dx.doi.org/10.54691/bcpbm.v32i.2885.

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In recent years, quantitative researchers used a wide range of models to price options, from the Black-Scholes model to more complex models such as the Heston model. This paper aims to analyze the effectiveness of the Black-Scholes model and the Binomial Tree model by using them to price Berkshire Hathaway’s equity options and European-style S&P 100 index options. The method used in this paper is gathering the market data of the options first. Second, using the data gathered to price the options by applying the Black-Scholes and Binomial Tree models. Third, comparing the derived theoretica

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Hendrawan, Riko, and Tri Suci Indah Sari. "Testing Black Scholes and Garch Option Models on Pharmaceutical State-Owned Enterprises Holding." 14th GCBSS Proceeding 2022 14, no. 2 (2022): 1. http://dx.doi.org/10.35609/gcbssproceeding.2022.2(39).

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This study aims at testing the implementation of option contracts using Black Scholes and GARCH Option Models on the pharmaceutical State-Owned Enterprises (BUMN, Badan Usaha Milik Negara) holding using Long Straddle Strategy. The data were the closing stock price from 2002 to 2021 of two companies holding: INAF and KAEF. Results of this study were calculated by comparing percentage of average mean squared error of the Black Scholes and GARCH model with the implementation of Long Straddle Strategy, in which the smaller the percentage the better the model. The result showed that for one-month d

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Bhattacharya, Sukanto, and Kuldeep Kumar. "Computational Exploration of the Biological Basis of Black-Scholes Expected Utility Function." Journal of Applied Mathematics and Decision Sciences 2007 (February 11, 2007): 1–15. http://dx.doi.org/10.1155/2007/39460.

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It has often been argued that there exists an underlying biological basis of utility functions. Taking this line of argument a step further in this paper, we have aimed to computationally demonstrate the biological basis of the Black-Scholes functional form as applied to classical option pricing and hedging theory. The evolutionary optimality of the classical Black-Scholes function has been computationally established by means of a haploid genetic algorithm model. The objective was to minimize the dynamic hedging error for a portfolio of assets that is built to replicate the payoff from a Euro

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ZHAO, JINSHI, and JIAZHEN HUO. "COORDINATION MECHANISM COMBINING SUPPLY CHAIN OPTIMIZATION AND RULE IN EXCHANGE." Asia-Pacific Journal of Operational Research 30, no. 05 (2013): 1350015. http://dx.doi.org/10.1142/s0217595913500152.

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There are two kinds of option pricing. The option pricing in exchange follows the Black–Scholes rule but does not consider the optimizing of supply chain. The traditional supply chain option contract can optimize supply chain but does not meet the Black–Scholes rule. We integrate the assumption of above two kinds of option pricing, and design a model to combine the Black–Scholes rule and traditional option contract of optimizing in a supplier-led supply chain. Our combined model can guide the enterprises to write or buy option considering both option pricing rule in financial market and the op

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Lee, Jung-Kyung. "On a Free Boundary Problem for American Options Under the Generalized Black–Scholes Model." Mathematics 8, no. 9 (2020): 1563. http://dx.doi.org/10.3390/math8091563.

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We consider the problem of pricing American options using the generalized Black–Scholes model. The generalized Black–Scholes model is a modified form of the standard Black–Scholes model with the effect of interest and consumption rates. In general, because the American option problem does not have an exact closed-form solution, some type of approximation is required. A simple numerical method for pricing American put options under the generalized Black–Scholes model is presented. The proposed method corresponds to a free boundary (also called an optimal exercise boundary) problem for a partial

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Kermiche, Lamya. "Too Much Of A Good Thing? A Review Of Volatility Extensions In Black-Scholes." Journal of Applied Business Research (JABR) 30, no. 4 (2014): 1171. http://dx.doi.org/10.19030/jabr.v30i4.8662.

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Since the seminal Black and Scholes model was introduced in the 1970s, researchers and practitioners have been continuously developing new models to enhance the original. All these models aim to ease one or more of the Black and Scholes assumptions, but this often results in a set of equations that is difficult if not impossible to use in practice. Nevertheless, in the wake of the financial crisis, an understanding of the various pricing models is essential to calm investors nerves. This paper reviews the models developed since Black and Scholes, giving the advantages and disadvantages of each

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Kim, Sol. "The Best Option Pricing Model for KOSPI 200 Weekly Options." Korean Journal of Financial Studies 51, no. 5 (2022): 499–521. http://dx.doi.org/10.26845/kjfs.2022.10.51.5.499.

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This study finds the best option pricing model for KOSPI 200 weekly options. It examines the in-sample pricing, out-of-sample pricing and hedging performances of the short-term options with a maximum maturity of seven days or less, which have not been analyzed in previous studies. The Black and Scholes (1973) model, Ad Hoc Black-Scholes model, and stochastic volatility and jumps models are compared. As a result, one of the Ad Hoc BlackScholes models, the absolute smile model using the strike price as an independent variable shows the best performance. However, its performance is not significan

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Liao, Xuanting, and Jiawei Zhuang. "The Research on the Pricing of Double Barrier Option Based on the Black-Scholes Model." BCP Business & Management 37 (February 1, 2023): 320–25. http://dx.doi.org/10.54691/bcpbm.v37i.3582.

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The two barrier values in the double barrier option are the focus in the evaluation simulation and they affect the knock-in and knock-out of the option. This paper, simulates a double barrier option and calculates its option value based on the Black-Scholes Model, using Coca-Cola stock data from January 2022 to the end of July, and verifies the feasibility of the Black-Scholes model. This paper also analyzes the sensitivity of the influence of the two barrier values on the option value, outlining the option value changes under different barrier values. The main finding of this paper is that th

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Ghevariya, S. "SOLUTION OF BLACK-SCHOLES EQUATION FOR STANDARD POWER EUROPEAN OPTIONS WITH DISCRETE DIVIDEND PAYMENT." Eurasian Journal of Mathematical and Computer Applications 11, no. 4 (2023): 29–39. http://dx.doi.org/10.32523/2306-6172-2023-11-4-29-39.

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The Nobel Prize celebrated option pricing formulas derived by Fischer Black and Myron Scholes for plain vanilla payoffs known as Black-Scholes formulas. They developed these formulas for pricing European call and put options based on certain assumptions in order to minimize risk factor. The underlying asset pays a constant dividend payment during the life of option was one of the assumption to derive these formulas. S. P. Zhu and X. J. He tried and succeed to improve this assumption by taking discrete dividend payments for underlying asset at fixed dividend date. They derived approximate Black

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Blanco, Belen. "Capturing the volatility smile: parametric volatility models versus stochastic volatility models." Public and Municipal Finance 5, no. 4 (2016): 15–22. http://dx.doi.org/10.21511/pmf.05(4).2016.02.

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Black-Scholes option pricing model (1973) assumes that all option prices on the same underlying asset with the same expiration date, but different exercise prices should have the same implied volatility. However, instead of a flat implied volatility structure, implied volatility (inverting the Black-Scholes formula) shows a smile shape across strikes and time to maturity. This paper compares parametric volatility models with stochastic volatility models in capturing this volatility smile. Results show empirical evidence in favor of parametric volatility models. Keywords: smile volatility, para

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Bature, Sani Sufyan, and Ira Sumiati. "Application Of Natural Decomposition Method For Solution Of Fractional Black-Scholes Equation." International Journal of Global Operations Research 4, no. 1 (2023): 26–34. http://dx.doi.org/10.47194/ijgor.v4i1.201.

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The Black-Scholes equation is a partial differential equation that can model the European call option price problem. This equation can be of the order of natural numbers or fractional. The aim of this paper is to find a solution to the fractional order Black-Scholes partial differential equation. The method used to find solutions to these equations is the Natural decomposition method. Two numerical examples are presented in this paper. The results show that the Natural decomposition method is effective and easy to use to solve the fractional Black-Scholes equation.

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

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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,

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

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