are you suggesting you have a model at least as good as B-S but different? is there anything published as good as B-S out there? i am not an option guy. i am just curious.
All the time. Most wealthy option traders cannot distinguish from a 3rd or 4th moment risk. Suppose you're short gamma and neutral delta to 270 on AAPL for August expiration. Vanna is less than half of rho under 2 sigmas on vol and price on flies, calendars and diagonals. Understanding that vanna is cheap is certainly worthwhile information. I get your point, and it's on topic. Honestly, there is little point in arguing as "delta depreciation" is the title of the thread.
First of all, would you please answer my own, on page 11 "What is the point ? I may miss something so please forgive me if I'm wrong but : Would you please tell me what is the value of a 0.5311 delta 3 years call strike 47 with a spot at 47 5% volatility using BSM with IR set at 0.1% and the same call value using what you call your trick ?" Finite variance assumption makes in a zero rate and carry world delta of an ATM call be the same as a twice vol ATM call with 1/4 maturity. In this world, a 20% vol ATM 1 year call has the same value as a 40% vol 3 months ATM call. Hence, vol is synthetic time, and time is synthetic vol. In this world, ATM call delta can vary between 0.50...something and 1, as far as vol varies from 0.1% to 15000% . Great, once again I may miss something, but there is no news here and more, no mystery.
Since you are still analyzing the question, I had the comment below which I did not post in previous responses: "So, It did not occur to you that in case of interest you could also use as strike the forward price?"
Course 'it occurs to me'. I derived it for you on page 7 ! If I did, there is no quantitative mystery. So no news here and no guru. So you got what you called "your trick" that gives you a call value stroke at the forward price given a delta and a stock price. Nothing wrong with that. I think it's useless and makes things much more complex than simple.
Since you say it did (but there is no evidence it did,but there is demonstrated potential it did not), then what was your point with the interest-related example?
My man, I understand that you're angry I posted the derivation what you called a mystery. Sorry Mister Guru. Again, with Donnap's example an IR set to 1%, you got a strike at 48.43136. Do you see that strike on the market ? Does it occur to you that you can't always find a strike that equalize forward price ? Hence my point "with the interest-related example" is that you got a fast trick, but NOW with additional computation needed to find a forward strike, to find a value for a strike that doesn't exist. Once again, Great ! Don't you finally find it much more complex and a waste of time thus for a trick useless ? Be serious ! Try a real pricer, you would get a real answer. So right now, what you need to find an option value are, spot/strike, delta and rates. Go ahead, in twenty minutes you will find that with maturity volatility strike interest rate and spot you got a trick to find an option value (Yes I know, people call it BSM, you can call it your trick).
1. Now that you mention strikes and not interest rates, why you did not raise your issue as strikes issue, but yet raised an interest rate issue? 2. Furthermore, if it occurred to you, why you did not present it in your derivation ?