# Black-Scholes fastest computation method

What is the fastest way to numerically compute Black-Scholes-Merton option prices?

I'm trying to find fastest and still precise method. Currently I'm using numerical approximation of Normal cdf with 10-9 precision and standard formulae.

Is there another way to compute them numerically using any programming language without built-in libraries for option pricing and cdf computation? If any what is the speed of the algorithm in comparison with standard method and what is precision of an answer?

There is a question about approximations to the Black-Scholes formula, but there are aproximations for ATM options. And it is not obvious that this methods would show better results.

• Make sure you do not over-engineer things. In the end nobody cares about implied vols beyond a single decimal digit and 2 for the option price. – Matthias Wolf Jun 25 '13 at 8:21
• @MattWolf Your warning is reasonable, but there are cases where precision is still valuable. For instance when using these prices/vols as inputs to more complicated models. If you round early, the effect is magnified by further calculations. So it depends on how the OP is going to be using the answers. – RaveTheTadpole Jun 25 '13 at 17:40
• Can you elaborate on what data you have given and what you intend to do with it? I don't really see need for a numerical method yet, but perhaps I'm just looking from the wrong angle here... – zuiqo Jun 25 '13 at 21:33
• @phi It is used in real time computatoin of option prices, as a part of implied volatility calibration etc. Performance is crucial. For example there is no analytical representarion of Normal cdf, that can be computed easily. Thus we use approximations with some polynomials rather then compute integrals each time. Thus I'm testing the fastest way to compute OP. – Ilya Jun 26 '13 at 6:11