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Communications in Theoretical Physics 2021年第5期73卷 10-17页

作者： Rami Ahmad EI-Nabulsi Alireza Khalili Golmankhaneh Biomedical Device Innovation Center Shenzhen Technology University3002 Lantian RoadPingshan DistrictShenzhen518118China Research Center for Quantum Technology Faculty of ScienceChiang Mai UniversityChiang Mai50200Thailand Athens Institute for Education and Research Mathematics and Physics Divisions8 Valaoritou StreetKolonaki10671AthensGreece Department of Physics Urmia BranchIslamic Azad UniversityUrmiaIran

In this study,we prove that modified diffusion equations,including the generalized Burgers'equation with variable coefficients,can be derived from the black-scholes equation with a time-dependent parameter based on the propagator method known in quantum and statistical *** extension for the case of a local fractal derivative is also addressed and analyzed.

关键词： black-scholes equation heat kernels modified diffusion equations generalized Burger's equation fractal calculus

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The Operator Splitting Method for black-scholes equation

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Applied Mathematics 2011年第6期2卷 771-778页

作者： Yassir Daoud Turgut Ozis Faculty of Technology of Mathematical Sciences&Statistic El-Neelain UniversityKhartoumSudan Department of Mathematics Faculty of ScienceEge UniversityBornovaTurkey

The Operator Splitting method is applied to differential equations occurring as mathematical models in financial models. This paper provides various operator splitting methods to obtain an effective and accurate solution to the black-scholes equation with appropriate boundary conditions for a European option pricing problem. Finally brief comparisons of option prices are given by different models.

关键词： Operator Splitting Method black-scholes equation European Option Pricing

AN APPROXIMATION SCHEME FOR black-scholes equationS WITH DELAYS

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Journal of Systems Science & Complexity 2010年第3期23卷 438-455页

作者： Mou-Hsiung CHANG Tao PANG Moustapha PEMY Mathematics Division US Army Research Office P. O. Box 12211 RTP NC 27709 USA Department of Mathematics North Carolina State University Raleigh NC 27695 USA Department of Mathematics Towson University Towson MD 21252 USA

This paper addresses a finite difference approximation for an infinite dimensional black-scholesequation obtained by Chang and Youree (2007).The equation arises from a consideration ofan European option pricing problem in a market in which stock prices and the riskless asset prices havehereditary *** a general condition on the payoff function of the option,it is shown thatthe pricing function is the unique viscosity solution of the infinite dimensional black-scholes *** addition,a finite difference approximation of the viscosity solution is provided and the convergenceresults are proved.

关键词： black-scholes equation finite difference stochastic functional differential equations viscosity solutions.

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Symmetry Breaking for black-scholes equations

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Communications in Theoretical Physics 2007年第6期47卷 995-1000页

作者： YANG Xuan-Liu ZHANG Shun-Li QU Chang-Zheng School of Economics and Management Tsinghua University Beijing 100084 China Center for Nonlinear Studies Northwest University Xi＇an 710069 China Department of Mathematics Northwest University Xi＇an 710069 China

black-scholes equation is used to model stock option pricing. In this paper, optimal systems with one to four parameters of Lie point symmetries for black-scholes equation and its extension are obtained. Their symmetry breaking interaction associated with the optimal systems is also studied. As a. result, symmetry reductions and corresponding solutions for the resulting equations are obtained.

关键词： black-scholes equation symmetry optimal system symmetry breaking solution

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广义black-scholes方程的Adomian级数解及其数值计算

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高等学校计算数学学报 2016年第1期38卷 1-17页

作者：傅强朱哲殷涛重庆大学经济与工商管理学院重庆大学数学与统计学院

In this paper we present a numerical method for a generalized blackscholes partial differential equation for option *** first derive its series solution whose coefficients are determined by recursion formulas involving integrals by means of the Adomian *** we present a numerical scheme based on the trapezoidal rule instead of direct integral method for the Adomain series *** results show the effectiveness of the present method.

关键词： Option pricing black-scholes equation Adomian decomposition Trapezoidal rule

Efficient Numerical Valuation of Continuous Installment Options

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Advances in Applied Mathematics and Mechanics 2011年第2期3卷 141-164页

作者： Anton Mezentsev Anton Pomelnikov Matthias Ehrhardt IDE Halmstad UniversityBox 82330118HalmstadSweden Lehrstuhl fur Angewandte Mathematik und Numerische Analysis Fachbereich C-Mathematik und NaturwissenschaftenBergische Universitat WuppertalGaußstr.2042119 WuppertalGermany

In this work we investigate the novel Kryzhnyi method for the numerical inverse Laplace transformation and apply it to the pricing problem of continuous installment *** compare the results with the one obtained using other classical methods for the inverse Laplace transformation,like the Euler summation method or the Gaver-Stehfest method.

关键词： Installment options black-scholes equation numerical inverse Laplace transform Gaver-Stehfest method Euler summation method optimal stopping problem non-monotonic stopping boundary

Modelling and Numerical Valuation of Power Derivatives in Energy Markets

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Advances in Applied Mathematics and Mechanics 2012年第3期4卷 259-293页

作者： Mai Huong Nguyen Matthias Ehrhardt Institut fur Mathematik Technische Universitat BerlinStrasse des 17.Juni 13610623 BerlinGermany Lehrstuhl fur Angewandte Mathematik und Numerische Analysis Fachbereich C-Mathematik und NaturwissenschaftenBergische Universitat WuppertalGaußstr.2042119 WuppertalGermany

In this work we investigate the pricing of swing options in a model where the underlying asset follows a jump diffusion *** focus on the derivation of the partial integro-differential equation(PIDE)which will be applied to swing contracts and construct a novel pay-off function from a tree-based pay-off matrix that can be used as initial condition in the PIDE *** valuing swing type derivatives we develop a theta implicit-explicit finite difference scheme to discretize the PIDE using a Gaussian quadrature method for the integral *** on known results for the classical theta-method the existence and uniqueness of solution to the new implicit-explicit finite difference method is *** numerical examples illustrate the usability of the proposed method and allow us to analyse the sensitivity of swing options with respect to model *** particular the effects of number of exercise rights,jump intensities and dividend yields will be investigated in depth.

关键词： Swing options jump-diffusion process mean-reverting black-scholes equation energy market partial integro-differential equation theta-method Implicit-Explicit-Scheme

Conservative and Finite Volume Methods for the Convection-Dominated Pricing Problem

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Advances in Applied Mathematics and Mechanics 2013年第6期5卷 759-790页

作者： German I.Ramırez-Espinoza Matthias Ehrhardt EON Global Commodities Holzstraße 640221 DusseldorfGermany Lehrstuhl fur Angewandte Mathematik und Numerische Analysis Fachbereich C-Mathematik und NaturwissenschaftenBergische Universitat WuppertalGaußstr.2042119WuppertalGermany

This work presents a comparison study of different numerical methods to solve black-scholes-type partial differential equations(PDE)in the convectiondominated case,i.e.,for European options,if the ratio of the risk-free interest rate and the squared volatility-known in fluid dynamics as P´eclet number-is *** Asian options,additional similar problems arise when the"spatial"variable,the stock price,is close to *** we focus on three methods:the exponentially fitted scheme,a modification of Wang’s finite volume method specially designed for the black-scholes equation,and the Kurganov-Tadmor scheme for a general convection-diffusion equation,that is applied for the first time to option pricing *** emphasis is put in the Kurganov-Tadmor because its flexibility allows the simulation of a great variety of types of options and it exhibits quadratic *** the reduction technique proposed by Wilmott,a put-call parity is presented based on the similarity reduction and the put-call parity expression for Asian ***,we present experiments and comparisons with different(non)linear black-scholes PDEs.

关键词： black-scholes equation convection-dominated case exponential fitting methods fitted finite volume method Kurganov-Tadmor scheme minmod limiter

Modified Differential Transform Method for Solving black-scholes Pricing Model of European Option Valuation Paying Continuous Dividends

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Journal of Partial Differential equations 2023年第4期36卷 381-393页

作者： AHMAD Manzoor MISHRA Rajshree JAIN Renu School of Mathematics and Allied Sciences jiwaji UniversityGwalior-474011India Govt.Model Science College Gwalior-474011India

.Option pricing is a major problem in quantitative *** black-scholes model proves to be an effective model for the pricing of *** this paper a com-putational method known as the modified differential transform method has been em-ployed to obtain the series solution of black-scholes equation with boundary condi-tions for European call and put options paying continuous *** proposed method does not need discretization to find out the solution and thus the computa-tional work is reduced *** results are plotted graphically to establish the accuracy and efficacy of the proposed method.

关键词： European option pricing black-scholes equation call option put option modified differential transform method