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A Review of the Recent Advances Made in the Black-Scholes Models and Respective Solutions Methods

Yasir Hamad Al Saedi, Gurudeo Anand Tularam
2018 Journal of Mathematics and Statistics  
The Black-Scholes model has been a major advance in finance over a period of time; this paper examines this model in some detail, in terms of the latest developments in both analytical and numerical solutions  ...  This analysis reveals that transaction costs, high volatility, illiquid markets and large investor preferences are the key issues of today's financial derivatives markets, especially after the Global Financial  ...  The corresponding author confirms that all of the other authors have read and approved the manuscript and there are no ethical issues involved.  ... 
doi:10.3844/jmssp.2018.29.39 fatcat:jbp6djfzkfg7pfgcep6kjgbdva

An efficient wavelet based approximation method to time fractional Black-Scholes European option pricing problem arising in financial market

G. Hariharan, S. Padma, P. Pirabaharan
2013 Applied Mathematical Sciences  
In this paper, a wavelet based hybrid method is employed to provide the quick and accurate solutions of fractional Black-Scholes equation with boundary condition for a European option pricing (EOP) problem  ...  The fractional Black-Scholes is used as a model for valuing European or American call and put options on a non-dividend paying stock.  ...  I am very grateful to the reviewers for their useful comments that led to improvement of my manuscript.  ... 
doi:10.12988/ams.2013.35261 fatcat:dzpg3nyexref3m5xrdk4rjbn7e

Introduction [chapter]

2021 Discrete-Time Approximations and Limit Theorems  
In this case we have the Black-Scholes formula as the result of limit transition, weak convergence holds in the Skorokhod topology, and we can immediately conclude that the convergence of option prices  ...  Therefore, the following questions immediately arise. How wrong are we if we replace discrete time with continuous? And what is the rate of convergence of asset and option prices in this case?  ...  Black-Scholes model.  ... 
doi:10.1515/9783110654240-201 fatcat:ucy6bhqml5awjjxkywxwtwhpgq

A comparative effectiveness of stochastic approximation method and pseudo inversion method for solution to PDE with financial application

Bright O. Osu, Okechukwu U.Solomon
2016 Zenodo  
This paper presents a comparative effectiveness of stochastic approximation method and pseudo inversion method for American option valuation under the Black-Scholes model.  ...  The stochastic approximation method proves to be faster in pricing an American options than the pseudo inversion method which needs the system to be stabilized for its accuracy.  ...  The Black-Scholes Model assumes a market consisting of a single risky asset (S) and a risky-free bank account (r).  ... 
doi:10.5281/zenodo.3977428 fatcat:5iadeldysrfjhjafr4dxarpxdq

Pricing Option with Stochastic Interest Rates and Transaction Costs in Fractional Brownian Markets

Lina Song, Kele Li
2018 Discrete Dynamics in Nature and Society  
This work deals with European option pricing problem in fractional Brownian markets. Two factors, stochastic interest rates and transaction costs, are taken into account.  ...  By the means of the hedging and replicating techniques, the new equations satisfied by zero-coupon bond and the nonlinear equation obeyed by European option are established in succession.  ...  Fractional Black-Scholes Model In a fractional Brownian market, the following assumptions are made in financial market with transaction costs and stochastic interest rates: (I) The price of the underlying  ... 
doi:10.1155/2018/7056734 fatcat:eulescr27zfrfbscc4cko3lnce

Pricing of American Carbon Emission Derivatives and Numerical Method under the Mixed Fractional Brownian Motion

Yuling Wang, Jing Wang, Lijun Pei
2021 Discrete Dynamics in Nature and Society  
characteristics of the option market.  ...  To capture the long memory properties such as self-similarity and long-range dependence in the price process, we proposed a model based on a fractional BlackScholes, which is more in line with the actual  ...  In this paper, we propose a fractional Black-Scholes model and its hedging strategy for fractional European option based on the fractional risk neutral measure.  ... 
doi:10.1155/2021/6612284 fatcat:3efu57sx5zdr7prlfufcpdbaym

Pricing Path-Independent Payoffs with Exotic Features in the Fractional Diffusion Model

Jean-Philippe Aguilar
2020 Fractal and Fractional  
We also discuss other aspects of option pricing such as volatility modeling, and provide comparisons of our results with other financial models.  ...  the context of the fractional diffusion model.  ...  Conflicts of Interest: The author declares no conflict of interest.  ... 
doi:10.3390/fractalfract4020016 doaj:7a07133f5c3a4b7985af2c892ba9cc23 fatcat:6p2el7bze5bpdgxldlvfgciqxq

Derivative pricing as a transport problem: MPDATA solutions to Black-Scholes-type equations [article]

Sylwester Arabas, Ahmad Farhat
2018 arXiv   pre-print
This is done in a convergence analysis comparing MPDATA numerical solutions with classic Black-Scholes analytical formulae for the valuation of European options.  ...  We depict second-order accuracy in time and space of the embraced numerical scheme.  ...  Background The Black-Scholes model in a nutshell A common ansatz in financial market modelling is that the price S of an asset follows a continuous-time lognormal diffusion process known as geomet-ric  ... 
arXiv:1607.01751v5 fatcat:lz2nny75kbhbdcnwjc5ypj6qxm

Cubic Hermite Finite Element Method for Nonlinear Black-Scholes Equation Governing European Options

Teófilo Domingos Chihaluca
2021 INTERMATHS Revista de Matemática Aplicada e Interdisciplinar  
A numerical algorithm for solving a generalized Black-Scholes partial differential equation, which arises in European option pricing considering transaction costs is developed.  ...  The efficiency and accuracy of the proposed method are tested numerically, and the results confirm the theoretical behaviour of the solutions, which is also found to be in good agreement with the exact  ...  The Black-Scholes model [9] is a well-known popular model which is used to calculate the price of European options.  ... 
doi:10.22481/intermaths.v2i2.9481 fatcat:bdxoldx5efezldyewuora5nhdm

A robust numerical solution to a time-fractional Black–Scholes equation

S. M. Nuugulu, F. Gideon, K. C. Patidar
2021 Advances in Difference Equations  
AbstractDividend paying European stock options are modeled using a time-fractional BlackScholes (tfBS) partial differential equation (PDE).  ...  The aim of this paper is two fold: firstly, to construct a time-fractional (tfBS) PDE for pricing European options on continuous dividend paying stocks, and, secondly, to propose an implicit finite difference  ...  Authors' contributions Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.  ... 
doi:10.1186/s13662-021-03259-2 fatcat:bkrtwcn2cranlgrd27z4jg53gy

A Comprehensive Literature Review on Pricing Equity Warrants Using Stochastic Approaches

Siti Zulaiha Ibrahim, Teh Raihana Nazirah Roslan, Ali F Jameel
2021 Universal Journal of Accounting and Finance  
Prior studies revealed that most researchers tend to employ the Black Scholes model to price equity warrants.  ...  However, the Black Scholes model was found deficient by contributing to large estimation errors and mispricing of equity warrants.  ...  Particularly, the Black Scholes model evaluates the variability of financial instruments over a period of time, and was originally used to estimate the price of European call option which can only be exercised  ... 
doi:10.13189/ujaf.2021.090314 fatcat:4spvbcpr5naklb24abvlnlepju

Solution of time fractional Black-Scholes European option pricing equation arising in financial market

A.S.V. Ravi Kanth, K. Aruna
2016 Nonlinear Engineering  
AbstractIn this paper, we present fractional differential transform method (FDTM) and modified fractional differential transform method (MFDTM) for the solution of time fractional Black-Scholes European  ...  option pricing equation.  ...  In [15] presented the fractional Black-Scholes equation with a time-fractional derivative to price European call option.  ... 
doi:10.1515/nleng-2016-0052 fatcat:bwo7sqogozg5nbguikvxt7unfi

Real options valuation

Barry R. Cobb, John M. Charnes
2007 2007 Winter Simulation Conference  
Just as a financial option derives much of its value from the potential price movements of the underlying financial asset, a real option derives much of its value from the potential fluctuations of the  ...  The ability of their managers to make smart decisions in the face of volatile market and technological conditions is essential for firms in any competitive industry.  ...  When used to price a European option, this model provides a discrete-time approximation to the continuous-time Black-Scholes-Merton result.  ... 
doi:10.1109/wsc.2007.4419599 dblp:conf/wsc/CobbC07 fatcat:knw5ja6i6na6tiap4p2xx4hnaq

Model Risk and Uncertainty—Illustrated with Examples from Mathematical Finance [chapter]

Karl F. Bannör, Matthias Scherer
2014 Risk - A Multidisciplinary Introduction  
However, there are numerous models available to model particular phenomena of financial markets and calculated option prices, hedging strategies, portfolio allocations, etc. depend on the chosen model.  ...  Keywords Financial market models · Parameter risk · Model risk · Risk-capturing functionals · Convex risk measure Mathematics Subject Classification (2010) 62C12 · 91G20 The Facts • In natural sciences  ...  European put and call options) cannot be calculated with simple formulae any more as in the Black-Scholes model, instead one has to rely on numerical algorithms as, e.g., techniques from Fourier analysis  ... 
doi:10.1007/978-3-319-04486-6_10 fatcat:skva6vjs7fcjrjkgxbvz74sf2i

A numerical study of the European option by the MLPG method with moving kriging interpolation

P. Phaochoo, A. Luadsong, N. Aschariyaphotha
2016 SpringerPlus  
The Black-Scholes equation, which is proposed by Black and Scholes (1973) , is a financial model that is concerned with options. An option is a contract between the seller and the buyer.  ...  The Black-Scholes equation provides an option pricing formula for European option. The analytic solution is used in general cases with basic assumptions but it is not satisfied in some conditions.  ...  The authors would like to thank their advisor for providing advice and taking care of this research and Rajamangala University of Technology Krungthep, for providing a scholarship.  ... 
doi:10.1186/s40064-016-1947-5 pmid:27064892 pmcid:PMC4783319 fatcat:5idarku2kzajxcps3nlheg7ah4
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