November 10th, 2007, 9:20 pm
At first blush, this is insane. Mind you, I've had plenty of insane thoughts myself, so I guess I can't say that insanity is really unusual or bad. Just don't do anything "financial!"Seriously, what are you trying to do?If you are trying to find a quick and easy metric that points toward option values/valuation, think about it: this is what Black-Scholes volatility is supposed to do! However, it was found that this is inadequate for the full complement of option prices; in other words, we need many vols to describe all these option prices - hence, vol loses its "explanatory" power and becomes just some sort of index, relevant for each option, one at a time. Ok, now introduce the next idea: how about stochastic volatility / Heston. Now we have a new set of parameters; inst. variance, long variance, speed of mean reversion, level of mean reversion, vol of vol...however, guess what? You'll find this model does a pretty poor job of describing all of the option prices you mentioned. So, how about Heston with Jumps? Hmm, this works really well, but now there are more parameters...Savvy?