I think I know what you're saying, but you don't seem to understand - I am not talking about your chart showing delta changing - I am talking about the fact that Delta can change with any move, so if a Delta Calc shows .5 and then it actually appears to be .8 based on a move you are calling that "True Delta", but in reality, the delta just changed and wasn't really .5 anymore at the new moment of the stock movement. Maybe I am not explaining something right, I don't know? JJacksET4
So if the model calculates a delta of .50 from a 1 point move and the underlying moves .80 on that 1 point move the true delta is .80, the new calculation based on the new underlying price would be a new delta, and the delta is in constant change, the Gamma allegedly makes that calculation. I understand that. In my analysis I found times that the underlying moved down and the option moved up, or vice versa. or the delta was more than 100%. But this again gets back to my original premise, if the calculated delta is not the true delta, and by considerable amounts, then one must assume the other Greeks are suspect as well. There's no value in a price model that only produces new values and only predicts the past.
But surely you must realize that you're in proper "apples 'n oranges" territory? Is that an intelligent enough response for you? I am sorry to disappoint, but there's no reason to have an intellectual debate. You're misunderstanding the purpose of the Greeks and the BSM model. That's all there is to it.
Premium value is effected by factors other than changes in the spot price of the underlying. Delta predicts how changes in the spot price effect premium, as you have pointed out. One of the other first order Greeks, Vega, predicts the change in the premium value with every 1% move in implied volatility. It could be that the changes in premium you witnessed were brought about as a result of change in IV, in addition to change in the underlying price. Theta will also take its toll in a rather abrupt manner. It also could have been responsible for some of the changes in premium that didn't correspond to the delta. From what you wrote above, it sounded like you were expecting premium to change exactly by the amount of the delta for every 1$ move in the spot. Unfortunately or fortunately, there are many more moving parts than just the price of the underlier.
Perhaps only for some traders (such as directional and EOD): Hypothesis 1. The conventional Greeks of options are created for systematic analysis, however quite confusing/complicate to some traders. These conventional Greeks can be simplified since A - Kappa and Vega usually have same graphic pattern, and B - Theta usually has an opposite graphic pattern against Kappa/Vega. Hypothesis 2. Therefore the True Delta (plus the delta of it) would be usful against the convntional Greeks. Just 2 cents!
According to Gallacher: "The relationship of paramount interest to option strategists is the relationship between an option price and the variability of its underlying future isolated from all other variables. The variability of the option price itself is of secondary importance, for that is affected by factors other than the variability of the underlying future:... "
The devil is in the details. Stoic, you do not explain what option price and underlying price you are sampling. Is it the mark value, volume weighted average price, last price traded, bid, offer, midpoint...etc? Regardless of your sample set, there would need to be some smoothing function. Anyone who has watched positions mark out at end of day can tell you that the stock vs options marks do not have to be precise. Also a simple trade on the bid followed by a trade on the offer could send a rudimentary empirical delta calculation (such as yours) off the charts--which is exactly what we are seeing in your data. Using one set of data per day, and trying to extrapolate over a month will never work--especially if you are using mark values. Stoic's, your idea is correct, but his method is flawed, therefore any conclusions are meaningless. In comparison, my software measures empirical deltas. We take every options print and chart them vs the stock midpoint data (adjusted using a kalman filter functions), all of which we collect through our own exchange direct data feeds. We may then chart a set of options traded prices vs underlying midpoints over time to create a best estimate empirical delta. Greeks are tools that a trader needs to learn how to use. They are not a blueprint to success. Anyone learning about greeks will (or should rather) learn the weaknesses of bell curve risk modeling, and how to deal with these weaknesses at the same time. Traders use greeks because there has not yet been a better way to measure risk. It's as simple as that. A lot of novice traders have read Taleb's books and decide that learning greeks, and how to use them properly is wasted effort. These traders are doomed to failure. Taleb first attempts to discredit the BS/brownian risk modeling methods without presenting anything that wasn't known in 1989. His ideas are not new. They are not groundbreaking. Taleb is a great philosopher. However, his claim to fame amounts to nothing more than crowing on about weaknesses known to the entire financial world for the last 20 years.
Benoît B. Mandelbrot was a Franco-American mathematician. Born in Poland, he moved to France with his family when he was a child. Mandelbrot spent much of his life living and working in... you do know ben said bs was bs...