The correct term is "Ito's lemma".Quote from CT10Gov:
Can you show us how you've made ito's lemma (why did you put a dash?) unnecessary? Show us the math please.
I (and sle and others know) the standard derivation well enough, so impress us with your brilliance.
Let the math speak, please.
It's been some years ago when I did this. Below is a comment from the source file. Sorry, it's in German, and at the moment I don't have time to translate or comment it further. Suffice to say, that Ito's lemma is eliminated, and that it still gives 100% the same result (had verified this with many tests). Below is only function hdr + the relevant comment, but not the rest of the implementation:
Code:
static double BlackScholes_sub_MY(const bool AfCall, const double S, const double K, const double t, const double r, const double s, const double d = 0.0, const double AdbDivider = 2.0)
{ // 0 < AdbDivider <= 2 (2 ist BS-default)
// s.a. myoptiomethod.cpp fuer Analyse von BS und dies alles unten
// !!!!!!!!! SO FAELLT DER ITO-TERM WEG: !!!!!!!!!!!!
// Der Trick ist anzunehmen dass "K = S * exp(z * s * sqrt(t) + u * t)" (method 1)
// bzw. "S = K * exp(z * s * sqrt(t) + u * t)" (method 2)
//
// Die Methode unten ist von mir (2009-09-12-Sa), see also tests in myoptiomethod.cpp
// Es liefert exakt das gleiche Ergebnis wie BS mit Ito (s.o.)
// Der Vorteil meiner Methode ist dass es einfacher nachzuvollziehen ist, ausserdem hat es einen optionalen "Divider" - Parameter (vielleicht kann es in Zukunft wichtig werden...)
...snip....
with you? Can you tell me this?