The Black-Scholes Equation Revisited: Asymptotic Expansions and Singular Perturbations

19 Pages Posted: 23 Mar 2005

See all articles by Martin Widdicks

Martin Widdicks

University of Manchester - Manchester Business School

Peter Duck

University of Manchester - Department of Mathematics

Ari Andricopoulos

University of Manchester - Department of Mathematics

David Newton

University of Bath - School of Management

Abstract

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.

Suggested Citation

Widdicks, Martin and Duck, Peter and Andricopoulos, Ari and Newton, David, The Black-Scholes Equation Revisited: Asymptotic Expansions and Singular Perturbations. Available at SSRN: https://ssrn.com/abstract=687247

Martin Widdicks (Contact Author)

University of Manchester - Manchester Business School ( email )

Oxford Road
Manchester M60 1QD, N/A M13 9PL
United Kingdom

Peter Duck

University of Manchester - Department of Mathematics ( email )

Oxford Road
Manchester M60 1QD, N/A M13 9PL
United Kingdom

Ari Andricopoulos

University of Manchester - Department of Mathematics ( email )

Oxford Road
Manchester M60 1QD, N/A M13 9PL
United Kingdom

David Newton

University of Bath - School of Management ( email )

Claverton Down
Bath, BA2 7AY
United Kingdom

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