EFFECTIVE ASYMPTOTICS ANALYSIS FOR FINANCE

Cyril Grunspan and Joris van der Hoeven ()
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Cyril Grunspan: Léonard de Vinci, Pôle Universitaire, Research Center, Paris La Défense Cedex, 92916 France
Joris van der Hoeven: CNRS, LIX, École polytechnique, Palaiseau Cedex, 91128 France

International Journal of Theoretical and Applied Finance (IJTAF), 2020, vol. 23, issue 02, 1-23

Abstract: It is known that an adaptation of Newton’s method allows for the computation of functional inverses of formal power series. We show that it is possible to successfully use a similar algorithm in a fairly general analytical framework. This is well suited for functions that are highly tangent to identity and that can be expanded with respect to asymptotic scales of “exp-log functions”. We next apply our algorithm to various well-known functions coming from the world of quantitative finance. In particular, we deduce asymptotic expansions for the inverses of the Gaussian and the Black–Scholes pricing functions.

Keywords: Asymptotic expansion; algorithm; pricing; Hardy fields; exp-log function (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1142/S0219024920500132

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