Numerical Approximation of the Implied Volatility under Arithmetic Brownian Motion
8 Pages Posted: 4 Jun 2007 Last revised: 16 Nov 2016
Date Written: June 1, 2007
We provide an accurate approximation method for inverting an option price to the implied volatility under arithmetic Brownian motion. The maximum error in the volatility is in the order of 1e-10 of the given option price and much smaller for the near-the-money options. Thus our approximation can be used as a near-exact solution without further refinements of iterative methods.
Keywords: implied volatility, arithmetic Brownian motion, ABM, Bachelier, rational approximation, closed form approximation
JEL Classification: C63, G12
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