Black Scholes 101… When valuing an option that is either deep in or deep out of the money the BS model will provide a value that differs from the actual trading price. From my understanding, the BS model will be linear and the FMV will be convex. When an option is deep out of the money BS will have a really high vol and say its worthless (but its not) and when deep in the money the BS model will have a vol of almost zero (but its not)… What accounts for this discrepancy? Thank you.
" the BS model will provide a value that differs from the actual trading price"
BS breaks down for a distribution with fat tails, ie the events that would cause a deep OTM to become ITM. The market knows these events exist but the model does not account for them, thus you have trading prices vs theoretical prices.
for all practical purposes BS model is just a price-volatility converter.
Now it is, but the idea that option values should only depend on vol and not drift still strikes me as odd sometimes.