Standard Galerkin formulation with high order Lagrange finite elements for option markets pricing

Markolefas, S

dc.contributor.author	Markolefas, S	en
dc.date.accessioned	2014-03-01T01:29:13Z
dc.date.available	2014-03-01T01:29:13Z
dc.date.issued	2008	en
dc.identifier.issn	0096-3003	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/19169
dc.subject	Black-Scholes equation	en
dc.subject	Call options	en
dc.subject	High order finite elements	en
dc.subject	Option contracts pricing models	en
dc.subject	Put options	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.other	Discrete time control systems	en
dc.subject.other	Finite element method	en
dc.subject.other	Interpolation	en
dc.subject.other	Lagrange multipliers	en
dc.subject.other	Mathematical models	en
dc.subject.other	Partial differential equations	en
dc.subject.other	Polynomial approximation	en
dc.subject.other	Stochastic control systems	en
dc.subject.other	Black-Scholes equation	en
dc.subject.other	Crank-Nicolson methods	en
dc.subject.other	Galerkin formulations	en
dc.subject.other	Option contracts pricing models	en
dc.subject.other	Galerkin methods	en
dc.title	Standard Galerkin formulation with high order Lagrange finite elements for option markets pricing	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.amc.2007.05.017	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.amc.2007.05.017	en
heal.language	English	en
heal.publicationDate	2008	en
heal.abstract	A semi-discrete Galerkin formulation (combined with high order Lagrangian finite elements) is employed for the approximate solution of the parabolic partial differential equation (widely known as Black-Scholes equation), which governs the evolution of the non-arbitrage (equilibrium) value of an option contract written on a singe underlying security. The Crank-Nicolson method is employed for the discretization in the time domain. Extensive numerical experimentation with American call and put stock options (where the stock may pay discrete cash dividends) and comparison with existing analytical, as well as, with approximate solutions, confirms the efficiency and accuracy of the proposed formulation. Moreover, it is verified that the p-extension (increasing the order of the polynomial interpolants, on a relatively coarse finite element mesh) is much more efficient (in terms of both accuracy and CPU time) than the h-extension (reducing the element sizes, with fixed low polynomial order). The work may be extended to more complicated option pricing models (e.g., multiasset options or options on assets with stochastic volatilities). (c) 2007 Elsevier Inc. All rights reserved.	en
heal.publisher	ELSEVIER SCIENCE INC	en
heal.journalName	Applied Mathematics and Computation	en
dc.identifier.doi	10.1016/j.amc.2007.05.017	en
dc.identifier.isi	ISI:000253173800035	en
dc.identifier.volume	195	en
dc.identifier.issue	2	en
dc.identifier.spage	707	en
dc.identifier.epage	720	en