If you had a time machine, could you have bought the option at the price your model outputted? If so, have you tested this? Or do you get historric implied vols and plug them into your model?
I'm not sure if we talk about the same thing. What do you think is the goal of these calculation? Asked differently: what kind of result or answers do you expect from such calculations?
He didn't actually say that he derived BS without ito's lemma, which is obviously possible (though obviously, doubtful that he can). He said he 'eliminated' it from the formula (or, 'automaton' as he called it in another thread). The fact that he tried to post some code showed that he meant the implementation, not the derivation of BS. With that, I asked him to point out where in the formula is ito's lemma (or ito-lemma, as he called it), at which points he started with the whole "it's my IP", and "it's irrelevant" tangent... ..because, as is so common on ET, he's a crank. Come on mutluit, is it really that hard to put up your claim? Show us exactly where in that two line BS formula is your so-called 'ito-lemma'?
Ito's lemma is indeed missing in my code because I purposely eliminated it! Got it now? I'm currently a part-time trader, not a researcher. As said it would take me some time to understand my own work after 3 years, that's normal in programming. One just needs to study the old code, but I don't have time for that wholly academic stuff at this moment. And: WHY ON HELL SHOULD I POST MY CODE TO YOU?
I don't want your code. I want you to take the standard BS formula, from wikipedia, and highlight the part that you think is 'ito-lemma' that you eliminated. That's it. No private information you need to give up. You can't do that because ito's lemma is part of the derivation, not the formula itself. And since you keep talking about code, you are talking about implementation, not derivation. Again, to be clear - I don't want your IP; I don't want your 'code'. I just want you to point out where in the standard wikipedia listing of the BS formula is this 'ito-lemma' you keep claiming that you've made 'unnecessary'.
Yes, I'm talking only of an implementation w/o Ito's lemma. If you can't come up with a solution w/o Ito's lemma, then, hmm. it's obviously your own problem I would say... Here are the steps (in German): // step0: stddev_for_t berechnen // step1: z ermitteln: // step2: z0 berechnen, d.h. halben stddev_for_t <-- das ist der KEY von BS ! // step3: z1 und z2 berechnen // step4: Call berechnen // step5: Put berechnen using Put/Call-Parity
I don't know what sle's 3rd column is supposed to tell us, but when I do the same calculation I get different values (year=253 trading days in my engine): Code: Period(253 days) : Vola=20.00% +1SD=22.14% -1SD=-18.13% C/+1SD=22.14% C/-1SD=0.00% P/+1SD=0.00% P/-1SD=18.13% Period(253 days) : Vola=50.00% +1SD=64.87% -1SD=-39.35% C/+1SD=64.87% C/-1SD=0.00% P/+1SD=0.00% P/-1SD=39.35% Period(253 days) : Vola=80.00% +1SD=122.55% -1SD=-55.07% C/+1SD=122.55% C/-1SD=0.00% P/+1SD=0.00% P/-1SD=55.07% Maybe sle can comment on these differences in the calculation results.
1 std = 0.2, agreed? atm call price approximately 0.08, agreed? B/E = price / stdev = 0.08/0.2 = 0.399
Yeah sorry, duration is the only sensible usage. Anyway, rates are low, but any model that results in that input is flawed as you could trade the conversion at zero rates. Obviously not going to happen in reality, but it makes the model output GIGO. So I fail to see the utility of backtesting a model that reflects zero rates. Like modeling XOM at zero dividend (inside the payout period). In the 100C/P listed... the model trades the conversion at par which implies the 40-day fwd is at par as well. IIRC it's worth $0.07 or so. Maybe I am missing something as I have only glanced at this thread. What is the sheet supposed to show us?