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The Black-Scholes equation revisited: asymptotic expansions and singular perturbations. (English) Zbl 1124.91342
Summary: 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.

##### MSC:
 91G20 Derivative securities (option pricing, hedging, etc.) 35K55 Nonlinear parabolic equations 35B25 Singular perturbations in context of PDEs 35C20 Asymptotic expansions of solutions to PDEs
##### Keywords:
option valuation; numerical technique; look-up tables
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##### References:
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