What Could Also Cause or Aggravate the Implicit ‘Smile’ and ‘Asymmetry’?
Applied Economics Letters, 2002 (9), 75-80
12 Pages Posted: 2 Oct 2012
Date Written: September 2, 2002
Abstract
This research note shows that the implied Black-Scholes volatility calculated using the bisection algorithm can have significant biases, which are more severe for in-themoney (ITM) options than for out-of-the-money (OTM) options. The biases are shown to have important implications as they could potentially aggravate the well-documented smile or smirk and asymmetry of implied Black-Scholes volatility for equity options. The findings caution the use of bisection algorithm for the calculation of Black-Scholes implied volatility. This research note also shows that the biases can be eliminated using the optimization algorithm which uses at least the first derivative of the objective function.
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