Conservative and Finite Volume Methods for the Convection-Dominated Pricing Problem
作者机构：EON Global CommoditiesHolzstraße 640221 DusseldorfGermany Lehrstuhl fur Angewandte Mathematik und Numerische AnalysisFachbereich C-Mathematik und NaturwissenschaftenBergische Universitat WuppertalGaußstr.2042119WuppertalGermany
出 版 物：《Advances in Applied Mathematics and Mechanics》 (应用数学与力学进展（英文）)
年 卷 期：2013年第5卷第6期
页 面：759-790页
核心收录：
学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学]
主 题：Black-Scholes equation convection-dominated case exponential fitting methods fitted finite volume method Kurganov-Tadmor scheme minmod limiter
摘 要：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 thespatialvariable,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.
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