Using Localised Quadratic Functions on an Irregular Grid for Pricing High-Dimensional American Options

S.J. Berridge, J.M. Schumacher

Research output: Working paperDiscussion paperOther research output

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Abstract

We propose a method for pricing high-dimensional American options on an irregular grid; the method involves using quadratic functions to approximate the local effect of the Black-Scholes operator.Once such an approximation is known, one can solve the pricing problem by time stepping in an explicit or implicit manner.We study stability of the method in two dimensions, and find that the grid structure is important in providing a stable approximation to the operator.
Original languageEnglish
Place of PublicationTilburg
PublisherFinance
Number of pages22
Volume2004-20
Publication statusPublished - 2004

Publication series

NameCentER Discussion Paper
Volume2004-20

Fingerprint

Grid
American options
Pricing
Approximation
Operator
Black-Scholes

Keywords

  • option pricing
  • inequality
  • markov chains

Cite this

Berridge, S. J., & Schumacher, J. M. (2004). Using Localised Quadratic Functions on an Irregular Grid for Pricing High-Dimensional American Options. (CentER Discussion Paper; Vol. 2004-20). Tilburg: Finance.
Berridge, S.J. ; Schumacher, J.M. / Using Localised Quadratic Functions on an Irregular Grid for Pricing High-Dimensional American Options. Tilburg : Finance, 2004. (CentER Discussion Paper).
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abstract = "We propose a method for pricing high-dimensional American options on an irregular grid; the method involves using quadratic functions to approximate the local effect of the Black-Scholes operator.Once such an approximation is known, one can solve the pricing problem by time stepping in an explicit or implicit manner.We study stability of the method in two dimensions, and find that the grid structure is important in providing a stable approximation to the operator.",
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Berridge, SJ & Schumacher, JM 2004 'Using Localised Quadratic Functions on an Irregular Grid for Pricing High-Dimensional American Options' CentER Discussion Paper, vol. 2004-20, Finance, Tilburg.

Using Localised Quadratic Functions on an Irregular Grid for Pricing High-Dimensional American Options. / Berridge, S.J.; Schumacher, J.M.

Tilburg : Finance, 2004. (CentER Discussion Paper; Vol. 2004-20).

Research output: Working paperDiscussion paperOther research output

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AB - We propose a method for pricing high-dimensional American options on an irregular grid; the method involves using quadratic functions to approximate the local effect of the Black-Scholes operator.Once such an approximation is known, one can solve the pricing problem by time stepping in an explicit or implicit manner.We study stability of the method in two dimensions, and find that the grid structure is important in providing a stable approximation to the operator.

KW - option pricing

KW - inequality

KW - markov chains

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CY - Tilburg

ER -

Berridge SJ, Schumacher JM. Using Localised Quadratic Functions on an Irregular Grid for Pricing High-Dimensional American Options. Tilburg: Finance. 2004. (CentER Discussion Paper).