A note on Black–Scholes implied volatility

Jesús Chargoy-Corona and Carlos Ibarra-Valdez

Physica A: Statistical Mechanics and its Applications, 2006, vol. 370, issue 2, 681-688

Abstract: An approximate formula for the Black–Scholes implied volatility is given by means of an asymptotic representation of the Black–Scholes formula. This representation is based on a variable change that reduces the number of meaningful variables from five to three. It is stated clearly which is the family of functions we are going to work, specially the inverse of the normal accumulative function. Estimates for the error in the resulting approximate formulas for both the option value and the volatility are obtained as well.

Keywords: Black–Scholes formula; Implied volatility; Asymptotic and approximate formulae (search for similar items in EconPapers)
Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:370:y:2006:i:2:p:681-688

DOI: 10.1016/j.physa.2006.03.019

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