I just want to add myself to the handful of people who thought highly of your comments and the points you raised. Keep posting and ignore the nasty comments. Sometime ago, in two other threads, I tried to discuss the point you raised but the crowd put the winds out of the sail. Volty is just an artificial variable. Measured delta and option price are real things. So you are dealing with reality, and therefore you are doing the right thing. Did you test the measured deltas of spreads vs. their modeled deltas? If a model-delta has a chance to be closer to reality, it would be for ATM. The model-delta of OTM options, should be garbage for any single option, but I am not sure about the spreads. That is why, I would be interested to see the results for spread. For a spread, I would not be surprised if garbage cancels out (assuming one to one ratios). Regards, TJ
Agree. Delta is the probability of the option ending up in the money not the probability that the price will end up on the strike.
There can be no corroboration because your premise is incorrect... To put it simply, I don't know what your "true delta" is. I have no idea what an "independent price model" of yours is. So you're essentially comparing a well-specified, albeit not perfect, quantity (the analytical delta) against something that, for all effects and purposes, is an arbitrary measurement that you fancy. So what sort of a meaningful corroboration do you expect to see if you have provided no details on the exact method you use to compute your "true delta" and its parameters? At any rate, feel free not to listen to me. Maybe other knowledgeable option folks will help here, if you're willing to listen to them. Otherwise, you're stuck with tj .
No no no, you're agreeing for the wrong reasons. Delta is roughly the probability of the option ending up in the money, but not exact because, simply put, it's weighted by payoff. The delta of a binary (digi) is exactly the probability of it ending up ITM. Also what are you talking about saying an ATM option is not 50 delta? Back to the main topic, OP you have not listened to most intelligent reasons. I gave you a more complex one that no one even noticed (smile/skew), other simple ones are implied volatilities change constantly, you never seemed to implement gamma and you're looking at it at one point every day instead of very frequently. B-S is based on continuous hedging, which of course is not possible, but if you are a market maker you are updating spots/vols constantly if the market is moving.
If you had any basic reading comprehension you'd know. The True delta was what the option did in relation to the underlying, the real world numbers. simple as that. The calculation were done using the online model @ CBOE Nothing arbitrary about it. Nothing that I "just fancy" just the facts.
There's no need to be rude... When you say it's "what the option did in relation to the underlying", what horizon are you referring to (with respect to the time used to calculate the B-S delta)? Is that "what the option did in relation to the underlying" during the next hour, the rest of the trading day or the rest of the year? How do you know that during this period the price of the option wasn't affected by a change in something other than the price of the underlying? Would you not agree that, if something else could affect the price of the option during your sampling period, your comparison between "true delta" and B-S delta makes no sense, given the definition of B-S delta? As to the calculation, are you saying that the B-S delta calculations were done using the CBOE online model? If so, that's most wonderful and not arbitrary at all. It's also not what I was referring to (if you read my previous post a bit more carefully, you'd see that). The arbitrary bit is the method by which you arrive at your "true delta" number. If you clarify that, maybe we could get a bit more specific.
The truth is: http://www.elitetrader.com/vb/showthread.php?s=&postid=2885059&highlight=delta*#post2885059 Prices of EOD Options?! Or such as: http://www.elitetrader.com/vb/showthread.php?s=&threadid=174213&highlight=delta*