A Sharp Approximation for ATM-Forward Option Prices and Implied Volatilites

International Journal of Financial Engineering, Vol. 3, No. 1 (2016)

20 Pages Posted: 15 Jul 2015 Last revised: 24 Sep 2016

See all articles by Dan Stefanica

Dan Stefanica

Baruch College, City University of New York

Rados Radoicic

CUNY Baruch College

Date Written: November 30, 2015

Abstract

In this paper, we provide an approximation formula for at the money forward options based on a Polya approximation of the cumulative density function of the standard normal distribution, and prove that the relative error of this approximation is uniformly bounded for options with arbitrarily large (or small) maturities and implied volatilities.

This approximation is viable in practice: for options with implied volatility less than 95% and maturity less than three years, which includes the large majority of traded options, the values given by the approximation formula fall within the tightest typical implied vol bid-ask spreads.

The relative errors of the corresponding approximate option values are also uniformly bounded for all maturities and implied volatilities.

The error bounds established here are the first results in the literature holding for all integrated volatilities, and are vastly superior to those of two other approximation formulas analyzed in this paper, including the Brenner-Subrahmanyam formula.

Keywords: implied volatility, Black-Scholes model, ATM-forward options

JEL Classification: C60, C63

Suggested Citation

Stefanica, Dan and Radoicic, Rados, A Sharp Approximation for ATM-Forward Option Prices and Implied Volatilites (November 30, 2015). International Journal of Financial Engineering, Vol. 3, No. 1 (2016), Available at SSRN: https://ssrn.com/abstract=2626589 or http://dx.doi.org/10.2139/ssrn.2626589

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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