Pricing options with discrete dividends by high order finite differences and grid stretching

Cornelis W. Oosterlee; Coenraad C.W. Leentvaart; Ariel Almendral Vázquez

Pricing options with discrete dividends by high order finite differences and grid stretching

Cornelis W. Oosterlee
, Coenraad C.W. Leentvaart
, Ariel Almendral Vázquez

extern
Delft University of Technology

Research output: Contribution to conference › Paper › Academic

Abstract

In this paper, we present an accurate numerical solution for the Black-Scholes equation with only a few grid points. Fourth order finite difference discretizations are employed, as well as a grid stretching in space by means of an analytic coordinate transformation. Next to standard European options, the method is also evaluated for digital options (discontinuous final condition) and for problems with discrete dividend modeled with a jump condition at the ex-dividend date. The method presented will be a basis for the numerical solution of high dimensional partial differential equations dealing with multi-asset options.

Original language	English
Publication status	Published - 2004
Externally published	Yes
Event	European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2004 - Jyvaskyla, Finland Duration: 24 Jul 2004 → 28 Jul 2004

Conference

Conference	European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2004
Country/Territory	Finland
City	Jyvaskyla
Period	24/07/04 → 28/07/04

Keywords

Black-Scholes
Discrete dividend
Fourth order finite differences
Stretched grid

Cite this

@conference{e2d5d426d7734503a2487418e80d9c07,

title = "Pricing options with discrete dividends by high order finite differences and grid stretching",

abstract = "In this paper, we present an accurate numerical solution for the Black-Scholes equation with only a few grid points. Fourth order finite difference discretizations are employed, as well as a grid stretching in space by means of an analytic coordinate transformation. Next to standard European options, the method is also evaluated for digital options (discontinuous final condition) and for problems with discrete dividend modeled with a jump condition at the ex-dividend date. The method presented will be a basis for the numerical solution of high dimensional partial differential equations dealing with multi-asset options.",

keywords = "Black-Scholes, Discrete dividend, Fourth order finite differences, Stretched grid",

author = "Oosterlee, \{Cornelis W.\} and Leentvaart, \{Coenraad C.W.\} and V{\'a}zquez, \{Ariel Almendral\}",

year = "2004",

language = "English",

note = "European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2004 ; Conference date: 24-07-2004 Through 28-07-2004",

}

Pricing options with discrete dividends by high order finite differences and grid stretching. / Oosterlee, Cornelis W.; Leentvaart, Coenraad C.W.; Vázquez, Ariel Almendral.
2004. Paper presented at European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2004, Jyvaskyla, Finland.

Research output: Contribution to conference › Paper › Academic

TY - CONF

T1 - Pricing options with discrete dividends by high order finite differences and grid stretching

AU - Oosterlee, Cornelis W.

AU - Leentvaart, Coenraad C.W.

AU - Vázquez, Ariel Almendral

PY - 2004

Y1 - 2004

N2 - In this paper, we present an accurate numerical solution for the Black-Scholes equation with only a few grid points. Fourth order finite difference discretizations are employed, as well as a grid stretching in space by means of an analytic coordinate transformation. Next to standard European options, the method is also evaluated for digital options (discontinuous final condition) and for problems with discrete dividend modeled with a jump condition at the ex-dividend date. The method presented will be a basis for the numerical solution of high dimensional partial differential equations dealing with multi-asset options.

AB - In this paper, we present an accurate numerical solution for the Black-Scholes equation with only a few grid points. Fourth order finite difference discretizations are employed, as well as a grid stretching in space by means of an analytic coordinate transformation. Next to standard European options, the method is also evaluated for digital options (discontinuous final condition) and for problems with discrete dividend modeled with a jump condition at the ex-dividend date. The method presented will be a basis for the numerical solution of high dimensional partial differential equations dealing with multi-asset options.

KW - Black-Scholes

KW - Discrete dividend

KW - Fourth order finite differences

KW - Stretched grid

UR - https://www.scopus.com/pages/publications/84893479241

M3 - Paper

AN - SCOPUS:84893479241

T2 - European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2004

Y2 - 24 July 2004 through 28 July 2004

ER -

Pricing options with discrete dividends by high order finite differences and grid stretching

Abstract

Conference

Keywords

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