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An Eulerian‐Lagrangian method for option pricing in finance
Author(s) -
Wang Zheng,
AlLawatia Mohamed,
Wang Hong
Publication year - 2007
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20176
Subject(s) - greeks , partial differential equation , valuation (finance) , partial derivative , eulerian path , mathematics , valuation of options , black–scholes model , lagrangian , mathematical optimization , mathematical economics , econometrics , economics , mathematical analysis , finance , volatility (finance) , financial economics
This article is devoted to the development and application of an Eulerian‐Lagrangian method (ELM) for the solution of the Black‐Scholes partial differential equation for the valuation of European option contracts. This method fully utilizes the transient behavior of the governing equations and generates very accurate option's fair values and their derivatives also known as option Greeks, even if coarse spatial grids and large time steps are used. Numerical experiments on two standard option contracts are presented which show that the ELM method (favorably) compares in terms of accuracy and efficiency to many other well‐perceived methods. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 23: 293–329, 2007