In BS, if we know underlying strike days interest option price is there a way to calculate (any of the) Greeks without first iterating to the implied vol and then inputting this IV in the usual greek formulae? In other words, can we sail around explicitely computing IV if we don't need it but just need the Greek(s)? Thanks!
Sure, at expiration! I'm plenty rusty on this stuff, but you can't solve the normal density function without the volatility (probability of stock movement). You can, of course, get some info with general "rule of thumb" approximations (ATM option = delta ~ .5, etc) At least, I think that's how it is...
Not a problem. I was building some code when it occurred to me that it's a 2-step process --> first IV --> then Greek. The 2nd step of course is peanuts, the 1st is the time-consumer (when processing bulk). Wayne: it must be possible to aim directly at (to solve for) the greek and skip IV but it'll be the same kind of interative process. I guess against all odds, I was hoping for a closed form "implied greek". I mean, you never know......
IV is derived from the options price. the greeks are derived from the IV. I don't see how one can derive the greeks without knowing IV first. Please feel free (anyone) to jump in and correct me if I'm misunderstanding something here. daddy's boy
To be clear, you need an actual volatility together with underlyer price, strike, time and interest/dividend to calculate the fair premium and the relevant greeks. When the premium is known in advance you can calculate the volatility the would lead to, or imply that premium. Hence implied volatility. It is a subtle, but important difference. When you derive IV from current premium and use that IV to calulate the greeks, those greeks are based on the expected volatility, as implied by the current premium. Ursa..
You can solve for the different greeks, individually, but using the real implied volatility is crucial for accuracy AFAIK. You could generate a lookup table maybe. It would be a pain in the ass, but 45 strike call option for example, that is 9 days from exp, at 5.25% interest rate, that is 10% OTM, has an IV of 42.9, a delta of 0.8, and a theta of -$3, etc, etc. You'd have to generate a ton of entries for it to be useful, though. Make the table at runtime and find the values you need. Don't know if it would be quicker than iterating IV at, for example, 0.1 per loop (plenty accurate enough). Computing power is cheap these days.
Ursa, I think it gets even more subtle: strictly speaking there is no "actual" volatility, either you look back (historical, statistical) or you look forward (implied). Even in the advanced GARCH etc. business you need data *series* for volatility. But I do get your point, and realize I'm looking for "implied" greeks. Thanks. Wayne: Appreciate the idea, but it would seem quite a task indeed. An easier speed option might be a closed form IV approximation. Problem is these are difficult to test on all possible input data combinations: they may look promising at first but start performing poorly on short-term ITM puts with >$200 underlying and high interest (just an example). Guess I'll stick with the iterations and focus on efficient code
For all practical purposes you'r right. Theoretically though, take Delta. When we have underlying strike days interest option price we agree there is ONE delta that fits the bill here. Consequently we could somehow, somewhere set up search for this delta and iterate toward it within a certain error margin, similar to the usual IV search. There will be some math hurdles to take but it's all definitely *not* worth looking into I was just hoping for a miracle, that's all........