Effective asymptotic analysis for finance

Cyril Grunspan () and Joris van der Hoeven ()
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Cyril Grunspan: ESILV - École Supérieure d'Ingénierie Léonard de Vinci
Joris van der Hoeven: LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau] - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique

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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 functions.

Keywords: exp-log function; BlackScholes formula A.M.S. subject classification: 68W30; 41A60; 91G80; 16A12; Hardy field; pricing; algorithm; asymptotic expansion; Black-Scholes formula; Asymptotic expansion (search for similar items in EconPapers)
Date: 2020-03-01
New Economics Papers: this item is included in nep-cwa
Note: View the original document on HAL open archive server: https://hal.science/hal-01573621v3
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Published in International Journal of Theoretical and Applied Finance, 2020, 23 (2), ⟨10.1142/S0219024920500132⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-01573621

DOI: 10.1142/S0219024920500132

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