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Effective Asymptotics Analysis For Finance

Author

Listed:
  • 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)

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.

Suggested Citation

  • Cyril Grunspan & Joris Van Der Hoeven, 2020. "Effective Asymptotics Analysis For Finance," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 23(02), pages 1-23, March.
    • Handle: RePEc:wsi:ijtafx:v:23:y:2020:i:02:n:s0219024920500132
    DOI: 10.1142/S0219024920500132
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    References listed on IDEAS

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