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Black Scholes


Espen Haug, “Black-Scholes” in Multiple Languages, here.

January 2008: After studying the literature (something many of the famous academics themselves obviously not have done properly) it is obvious that we option traders never have used the Black-Scholes-Merton formula in practice.( see also article in Frobes ) Only if you use close to continuous time delta hedging to remove close to all the risk all the time you are actually using the Black-Scholes (or the Black-Scholes-Merton) version of the option formula. The only problem this is impossible in practice.

If you remove most risk by hedging options with options, get immune for blow up risk by the way you construct your option portfolio then you are using the traders formula/method that was discovered before Black-Scholes-Merton by a series of traders and researchers, the first contribution form Bachelier 1900 and the last by Thorp 1969, so this is why we think it should be called the Bachelier-Thorp formula. In practice you can remove risk with discrete delta hedging (known long before Black-Scholes and Merton), but you can not remove enough risk to argue for risk-neutral valuation (and this is the main argument of Black-Scholes-Merton). See Chapter 2 in my book Derivatives Models on Models for a detailed discussion on how to hedge options in practice.

You naturally know the so called “Black-Scholes-Merton” option formula, that actualy not is the Black-Scholes-Merton formula (BSM was a theoretical hedging argument related to risk-neutral valuation), but in how many languages? Just like me I guess you speak Norwegian, French, Russian, English, Swedish and Danish, but what about really interesting languages like (now in more than 30 languages):

Objective-C/iPhone, F#, Autoit, Fortress, Lua, APL, SAS, Mathcad, J, MEL, Postscript, VB.NET, Clean, Ruby, Lisp, Prolog, PL/SQL, LyME, ColdFusion, K, C#, HP48, Transact SQL, O’Caml, Rebol, Real Basic, Icon, Squeak, Haskell, JAVA , JavaScript, VBA, C++, Perl, Maple, Mathematica, Matlab, S-Plus, IDL, Pascal, Python, Fortran, Scheme, PHP, GNU, gnuplot…

If you have implemented Black-Scholes in another language I would be happy to get a copy of your source code to put it on this page!


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