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THE BLACK‐SCHOLES EQUATION REVISITED: ASYMPTOTIC EXPANSIONS AND SINGULAR PERTURBATIONS
Author(s) -
Widdicks Martin,
Duck Peter W.,
Andricopoulos Ari D.,
Newton David P.
Publication year - 2005
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/j.0960-1627.2005.00224.x
Subject(s) - singular perturbation , valuation (finance) , calculator , valuation of options , black–scholes model , mathematics , barrier option , mathematical economics , mathematical optimization , economics , econometrics , computer science , mathematical analysis , finance , volatility (finance) , operating system
In this paper, novel singular perturbation techniques are applied to price European, American, and barrier options. Employment of these methods leads to a significant simplification of the problem in all cases, by reducing the number of parameters. For American options, the valuation problem is reduced to a procedure that may be performed on a rudimentary handheld calculator. The method also sheds light on the evolution of option prices for all of the cases considered, the results being particularly illuminating for American and barrier options.