Following an idea of Peter Jäckel ("Probably the most complicated trivial issue in financial mathematics: how to compute Black's implied volatility robustly, simply, efficiently, and fast") it is shown, how an initial guess has to be taken to backout volatility from given option prices - with an astonishing good quality. The original uses more numerical computations, which I replace by Lambert's W function, Maple is of great help for that. In a second part the guess is refined to a numerical solution using Newton's method, where only some steps are needed to achieve machine precision: Through Lambert's function and an appropriate scaling about 3 steps are enough by using a higher order method. Download 102_which_volatility_was_paid.mws
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