I'm by profession a programmer, but also a mathematician/researcher. I contributed even research results to an academic book, and even have been mentioned in the book. Why should I? It's my thread, and I would like to see to keep trolling idiots off the thread, since they don't contribute anything but off-topic crap, and wasting people's time by their lack of intelligence and by their ignorance.
So why don't we go over some of your "obvious facts" and take them apart. Options with higher volatility are, surprisingly, also more volatile. This means that it makes more sense to measure the payoff not in percent, but in number of standard deviations needed to break even the option price. So, lets take a simple 1y call ATM and use general BS (no divs, no interest rate) at different volatility levels (first column is volatility, second is atm call price and third is price/stdev): 20.00% 7.97% 39.85% 50.00% 19.75% 39.49% 80.00% 31.09% 38.86% 100.00% 38.30% 38.30% 120.00% 45.15% 37.63% 200.00% 68.27% 34.14% Do you feel that this contradicts your "fact" that option on less volatile stocks are better value? What you care about is a proportional increase in implied volatility and yes, for lower implied vol the proportional increase in premium is higher (which is consistent with the fact that higher volatility does not grow the option price in liner manner). This one is sort-of correct. The main reason why there is no edge in buying calls and selling puts (which is obvious, as put/call parity still holds) is that the risk neutral expectation of the underlying is actually below the current forward. For really volatile stocks/assets this correction becomes pretty meaningful.
The idea is to buy when relative risk premium is low and sell when it's high, if I understand correct. Kind of contradicts the notion to "buy low vola" and "sell high vola", but when you think about it, it makes sense.
If you believe in any general respect that buying low vol or selling vol in high or low vol stocks is so ambiguous that you obviously have no edge. Generalities in this respect are so worthless.......
Can you show us how you've made ito's lemma (why did you put a dash?) unnecessary? Show us the math please. I (and sle and others know) the standard derivation well enough, so impress us with your brilliance. Let the math speak, please.
<<< - An increasing of Implied Volatility (IV) is very valuable (for both Calls and Puts), so buy at low volatility. >>> All things being equal, i would obviously prefer to buy a call at low IV. But in the investment world, all things are rarely equal. If I had the choice: To buy a call on a stock with low IV, relative to its HV, but my analysis indicated the stock would remain flat or trend down to tech support..... Or to buy a call on a stock with moderate or mod high IV, relative to it's HV, but my analysis indicated the stock was at L-T tech support, and likely to rise in value over the near term..... Guess which trade I'm more likely to initiate. Thus the issue is not simply a matter of IV. The IV must be evaluated in the "context" of ones analysis of the trade as a whole.