Tighter Bounds for Implied Volatility

16 Pages Posted: 24 Feb 2017 Last revised: 28 Jun 2017

Jim Gatheral

CUNY Baruch College

Ivan Matic

CUNY Baruch College

Rados Radoicic

Baruch College, City University of New York

Dan Stefanica

Baruch College, City University of New York

Date Written: June 26, 2017

Abstract

We establish bounds on Black-Scholes implied volatility that improve on the uniform bounds previously derived by Tehranchi. Our upper bound is uniform, while the lower bound holds for most options likely to be encountered in practical applications. We further demonstrate the practical effectiveness of our new bounds by showing how the efficiency of the bisection algorithm is improved for a snapshot of SPX options quotes.

Keywords: Implied Volatility, Polya Approximation, Bisection Method

Suggested Citation

Gatheral, Jim and Matic, Ivan and Radoicic, Rados and Stefanica, Dan, Tighter Bounds for Implied Volatility (June 26, 2017). International Journal of Theoretical and Applied Finance, Forthcoming. Available at SSRN: https://ssrn.com/abstract=2922742 or http://dx.doi.org/10.2139/ssrn.2922742

Jim Gatheral (Contact Author)

CUNY Baruch College ( email )

Department of Mathematics
One Bernard Baruch Way
New York, NY 10010
United States

Ivan Matic

CUNY Baruch College ( email )

17 Lexington Avenue
New York, NY 10021
United States

Rados Radoicic

Baruch College, City University of New York ( email )

17 Lexington Avenue
New York, NY 10021
United States

Dan Stefanica

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

Paper statistics

Downloads
308
Rank
81,034
Abstract Views
682