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The method described in Hallerbach (2004) always worked well for me. We derive an estimator for Black-Scholes-Merton implied volatility that, when compared to the familiar Corrado & Miller [JBaF, 1996] estimator, has substantially higher approximation accuracy and extends over a wider region of moneyness.


The only special function needed for computing Black-Scholes option prices is the cumulative normal function ("N" or "Phi") or equivalently the error function ("erf"). These are very widely available with good standard library implementations. The erf function in single and double precision is part of the c99 and c++11 math standard libraries. For your ...

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