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

2015 ◽  
Author(s):  
Dan Stefanica ◽  
Rados Radoicic
Keyword(s):  
Option Prices ◽  
Sharp Approximation

A sharp approximation for ATM-forward option prices and implied volatilites

2016 ◽  
Vol 03 (01) ◽  
pp. 1650002 ◽  
Author(s):  
Dan Stefanica ◽  
Radoš Radoičić
Keyword(s):  
Implied Volatility ◽  
Standard Normal Distribution ◽  
Approximation Formula ◽  
Option Prices ◽  
First Results ◽  
Approximation Formulas ◽  
Sharp Approximation ◽  
Standard Normal ◽  
Relative Errors ◽  
Uniformly Bounded

In this paper, we provide an approximation formula for at-the-money forward options based on a Pólya 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.

New Bounds on American Option Prices

2007 ◽  
Author(s):  
In Joon Kim ◽  
Geun Hyuk Chang ◽  
Suk-Joon Byun
Keyword(s):  
American Option ◽  
Option Prices

Option Prices, Takeover Announcements, and Stock Returns

2011 ◽  
Author(s):  
Edward J. Podolski ◽  
Cameron Truong ◽  
Madhu Veeraraghavan
Keyword(s):  
Stock Returns ◽  
Option Prices

Psychology, Stock/FX Trading, and Option Prices

2012 ◽  
Author(s):  
Alan Beilis ◽  
Jan Dash ◽  
Jacqueline Volkman Wise
Keyword(s):  
Option Prices ◽  
Fx Trading
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