Higher-Order Finite Element Solutions of Option Prices

Research output: Working paperResearch

Abstract

Kinks and jumps in the payoff function of option contracts prevent an effectiveimplementation of higher-order numerical approximation methods. Moreover, thederivatives (the greeks) are not easily determined around such singularities, even withstandard lower-order methods. This paper suggests a transformation to turn the originalill-conditioned pricing problem into a well-behaved numerical problem. For astandard test case, both vanilla- and binary call price functions are approximated with(tensor) B-splines of up to 10'th order. Polynomial convergence rates of orders up toapproximately 10 are obtained for prices as well as for first and second order derivatives(delta and gamma). Unlike similar studies, numerical approximation errors aremeasured both as weighted averages and in the supnorm over a state space includingtime-to-maturities down to a split second.KEYWORDS: Numerical option pricing, Transformed state spaces, Higher-orderB-splines.
Original languageEnglish
Place of PublicationKøbenhavn
Number of pages43
Publication statusPublished - 2004

Cite this

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title = "Higher-Order Finite Element Solutions of Option Prices",
abstract = "Kinks and jumps in the payoff function of option contracts prevent an effectiveimplementation of higher-order numerical approximation methods. Moreover, thederivatives (the greeks) are not easily determined around such singularities, even withstandard lower-order methods. This paper suggests a transformation to turn the originalill-conditioned pricing problem into a well-behaved numerical problem. For astandard test case, both vanilla- and binary call price functions are approximated with(tensor) B-splines of up to 10'th order. Polynomial convergence rates of orders up toapproximately 10 are obtained for prices as well as for first and second order derivatives(delta and gamma). Unlike similar studies, numerical approximation errors aremeasured both as weighted averages and in the supnorm over a state space includingtime-to-maturities down to a split second.KEYWORDS: Numerical option pricing, Transformed state spaces, Higher-orderB-splines.",
keywords = "Derivater, Numeriske analyser, Optioner",
author = "Peter Raahauge",
year = "2004",
language = "English",
type = "WorkingPaper",

}

Higher-Order Finite Element Solutions of Option Prices. / Raahauge, Peter.

København, 2004.

Research output: Working paperResearch

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N2 - Kinks and jumps in the payoff function of option contracts prevent an effectiveimplementation of higher-order numerical approximation methods. Moreover, thederivatives (the greeks) are not easily determined around such singularities, even withstandard lower-order methods. This paper suggests a transformation to turn the originalill-conditioned pricing problem into a well-behaved numerical problem. For astandard test case, both vanilla- and binary call price functions are approximated with(tensor) B-splines of up to 10'th order. Polynomial convergence rates of orders up toapproximately 10 are obtained for prices as well as for first and second order derivatives(delta and gamma). Unlike similar studies, numerical approximation errors aremeasured both as weighted averages and in the supnorm over a state space includingtime-to-maturities down to a split second.KEYWORDS: Numerical option pricing, Transformed state spaces, Higher-orderB-splines.

AB - Kinks and jumps in the payoff function of option contracts prevent an effectiveimplementation of higher-order numerical approximation methods. Moreover, thederivatives (the greeks) are not easily determined around such singularities, even withstandard lower-order methods. This paper suggests a transformation to turn the originalill-conditioned pricing problem into a well-behaved numerical problem. For astandard test case, both vanilla- and binary call price functions are approximated with(tensor) B-splines of up to 10'th order. Polynomial convergence rates of orders up toapproximately 10 are obtained for prices as well as for first and second order derivatives(delta and gamma). Unlike similar studies, numerical approximation errors aremeasured both as weighted averages and in the supnorm over a state space includingtime-to-maturities down to a split second.KEYWORDS: Numerical option pricing, Transformed state spaces, Higher-orderB-splines.

KW - Derivater

KW - Numeriske analyser

KW - Optioner

M3 - Working paper

BT - Higher-Order Finite Element Solutions of Option Prices

CY - København

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