Solving American Option Pricing Models by the Front Fixing Method: Numerical Analysis and Computing

被引：26

作者：

Company, R. ^{[1
]}

Egorova, V. N. ^{[1
]}

Jodar, L. ^{[1
]}

机构：

[1] Univ Politecn Valencia, Inst Matemat Multidisciplinar, Valencia 46022, Spain

来源：

ABSTRACT AND APPLIED ANALYSIS | 2014年

关键词：

BOUNDARY; EQUATION;

D O I：

10.1155/2014/146745

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper presents an explicit finite-difference method for nonlinear partial differential equation appearing as a transformed Black-Scholes equation for American put option under logarithmic front fixing transformation. Numerical analysis of the method is provided. The method preserves positivity and monotonicity of the numerical solution. Consistency and stability properties of the scheme are studied. Explicit calculations avoid iterative algorithms for solving nonlinear systems. Theoretical results are confirmed by numerical experiments. Comparison with other approaches shows that the proposed method is accurate and competitive.

引用

页数：9

共 35 条

[1] EFFICIENT ANALYTIC APPROXIMATION OF AMERICAN OPTION VALUES [J].

BARONEADESI, G ;

WHALEY, RE .

JOURNAL OF FINANCE, 1987, 42 (02) :301-320

[2]

Brennan M., 1978, J FINANCIAL QUANTITA, V13

[3] A consistent stable numerical scheme for a nonlinear option pricing model in illiquid markets [J].

Company, Rafael ;

Jodar, Lucas ;

Pintos, Jose-Ramon .

MATHEMATICS AND COMPUTERS IN SIMULATION, 2012, 82 (10) :1972-1985

[4]

Crank J., 1984, FREE MOVING BOUNDARY

[5]

Duffy D.J., 2006, Finite Difference Methods in Financial Engineering. A Partial Differential Equation Approach

[6] On the solution of complementarity problems arising in American options pricing [J].

Feng, Liming ;

Linetsky, Vadim ;

Morales, Jose Luis ;

Nocedal, Jorge .

OPTIMIZATION METHODS & SOFTWARE, 2011, 26 (4-5) :813-825

[7] Quadratic convergence for valuing American options using a penalty method [J].

Forsyth, PA ;

Vetzal, KR .

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2002, 23 (06) :2095-2122

[8] THE AMERICAN PUT OPTION VALUED ANALYTICALLY [J].

GESKE, R ;

JOHNSON, HE .

JOURNAL OF FINANCE, 1984, 39 (05) :1511-1524

[9] A fast numerical method for the Black-Scholes equation of American options [J].

Han, H ;

Wu, XN .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2003, 41 (06) :2081-2095

[10] VALUING DERIVATIVE SECURITIES USING THE EXPLICIT FINITE-DIFFERENCE METHOD [J].

HULL, J ;

WHITE, A .

JOURNAL OF FINANCIAL AND QUANTITATIVE ANALYSIS, 1990, 25 (01) :87-100

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