An Explicit Implied Volatility Formula

24 Pages Posted: 1 Feb 2017 Last revised: 25 Jul 2018

See all articles by Dan Stefanica

Dan Stefanica

Baruch College, City University of New York

Rados Radoicic

CUNY Baruch College

Date Written: January 30, 2017

Abstract

We show that an explicit approximate implied volatility formula can be obtained from a Black–Scholes formula approximation that is 2% accurate. The relative error of the approximate implied volatility is uniformly bounded for options with any moneyness and with arbitrary large or small option maturities and volatilities, including for long dated options and options on highly volatile underlying assets. For options within a large trading range, such as options with maturity less than five years and implied volatility less than 150%, the error of the approximate implied volatility relative to the Black–Scholes implied volatility is less than ten percentage points.

Keywords: Implied Volatility, Black-Scholes Model, Approximation Formula, Uniform Bounds

JEL Classification: C60, C63

Suggested Citation

Stefanica, Dan and Radoicic, Rados, An Explicit Implied Volatility Formula (January 30, 2017). International Journal of Theoretical and Applied Finance, Vol. 20, no. 7, 2017. Available at SSRN: https://ssrn.com/abstract=2908494 or http://dx.doi.org/10.2139/ssrn.2908494

Dan Stefanica (Contact Author)

Baruch College, City University of New York ( email )

One Bernard Baruch Way
New York, NY 10010
United States

HOME PAGE: http://mfe.baruch.cuny.edu/dan-stefanica

Rados Radoicic

CUNY Baruch College ( email )

One Bernard Baruch Way
New York, NY 10010
United States

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