Can There Be an Explicit Formula for Implied Volatility?

6 Pages Posted: 24 Nov 2012

See all articles by Stefan Gerhold

Stefan Gerhold

Vienna University of Technology

Date Written: November 21, 2012

Abstract

It is "well known" that there is no explicit expression for the Black-Scholes implied volatility. We prove that, as a function of underlying, strike, and call price, implied volatility does not belong to the class of D-finite functions. This does not rule out all explicit expressions, but shows that implied volatility does not belong to a certain large class, which contains many elementary functions and classical special functions.

Keywords: Call option, Black-Scholes formula, implied volatility, D-finite function, asymptotics

JEL Classification: G13

Suggested Citation

Gerhold, Stefan, Can There Be an Explicit Formula for Implied Volatility? (November 21, 2012). Available at SSRN: https://ssrn.com/abstract=2179924 or http://dx.doi.org/10.2139/ssrn.2179924

Stefan Gerhold (Contact Author)

Vienna University of Technology ( email )

Karlsplatz 13
Vienna
Austria

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