Quote from Look4aSine:
If I buy a $400 call when AAPL is at $400 and I expect to hold it 1-week, then at any time, I can calculate $AAPL - $400 = intrinsic Profit/Loss. It makes sense to me - I know what to expect. But, when it comes to Time Value, whether, Black Scholes, the greeks, online calculators, etc. - it's all the same math, just rearranged algebraically - and, it's all analysis paralysis. None of it explains real-world Time Value in any meaningful dissected way.
Let's see if I can take a stab at this w/o riling you some more
There are multiple variables used in determining an option's price and since several are moving in either driection, a simple once size fits all answer doesn't exist.
Some of the variables can be eliminatated or ignored. Interest rates are a minor determinant since their day to day change has an infintessimal effect. Dividends are a PITA but assume none or the UL nowhere near ex-div so they can be ignored.
Price is simple. If AAPL moves above $400, every dollar above $400 is intrinsic value (stock price minus strike price). The options' price less the intrinsic value is the extrinsic value or time premium. It's that simple.
Or is it?
Each day there's time decay (theta). So while AAPL's price is rising, the extrinsic value is decreasing as time elapes.
In addition, because delta is less than 1.00, for every dollar that AAPL rises, the total premium rises by less than a dollar. That means that as intrinic value is rising, extrinsic value is decreasing.
For example (made up numbers), AAPL is $400, the Nov 400c is $30 with a delta of .55 (no intrinsic value, $30 of TP)
If AAPL immediately rises $1 (no time decay), the call will be worth approx $30.55 and that means that now there's a $1 of intrinsic value and only $29.55 of TP
The real wild card is implied volatility. The preceding example assumes it was unchanged, As Jerkstore mentioned, mplied vol is demand. As demand increases, IV rises and therefore time premium expands (increases). If IV drops, premium drops. One can assess various outcomes at different volatilities but there's no way to know what it will be at some future point in time. Again, it's the wild card.
Since all variables are accounted for in a pricing formula, premium can be easily calculated despite the aforementioned movement of multiple variables because it's snapshot of all at one moment in time. That's your "Real world time value".
Now if we go back to your original post, at any time one can use a pricing formula and calculate what an option's price "was" X-number of days ago. Well, sort of. IV fluctuates intraday and day to day. If you don't know what the IV was "X" days ago, you can only assume that it was then what it is now. The calculation will most likely be in the ball park but there's no guarantee of that since it's an assumption.
If you had the price of another of AAPL's options at that moment in time "X" days ago, you could determine its IV and use that for your option's IV but that assumption has numerous ways to be just as inaccurate.
I don't know how much of this makes sense to you or if it applies to what your asking but that's part of the view from this side of the fence where the same language is used
