Method of Reducing Dimension of Space Variables in Multi-dimensional Black-Scholes Equations

MATEMATIKA

Ning Wan¹  Hyong chol O¹  Yong-hwa Ro¹ 

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关键词: Black-Scholes equations;    Multi-dimensional;    Reducing dimension;    Options;    Foreign currency strike price;    Basket option;    Foreign currency option;    Zero coupon bond derivative.;   

DOI  :  10.11113/matematika.v30.n.706

学科分类：社会科学、人文和艺术（综合）

来源: Universiti Teknologi Malaysia * Fakulti Sains

【 摘 要 】

We study a method of reducing space dimension in multi-dimensionalBlack-Scholes partial differential equations as well as in multi-dimensional parabolic equations. We prove that a multiplicative transformation of space variables in theBlack-Scholes partial differential equation reserves the form of Black-Scholes partialdifferential equation and reduces the space dimension. We show that this transformation can reduce the number of sources of risks by two or more in some cases by givingremarks and several examples of financial pricing problems. We also present that theinvariance of the form of Black-Scholes equations is based on the invariance of theform of parabolic equation under a change of variables with the linear combination ofvariables.

【 授权许可】

Unknown