> higher vol [...] makes the option worth more. > Similarly having more time to expiry makes the option worth more [...] These two observations become unified

> higher vol [...] makes the option worth more. > Similarly having more time to expiry makes the option worth more [...] These two observations become unified when one observes that the two variables sigma (vol) and (T-t) (time to expiry) only ever enter the Black-Scholes formula together, as sigma^2 (T-t) (which is the variance of the log return to expiry). (That leads to the observation that the unit of vol is 1/sqrt(time), normally a^(-1/2) [a=annum=year]). Next, you alluded to it, but let's make explicit the way to trade implied vol: Suppose (WLOG) that you think implied vol is too low. Then you buy it (buy cheap, sell expensive...) in the market (buy buying calls and/or puts). Now you're long gamma, but short theta, and long vol in two senses: a) if the stock doesn't move, but implied vol goes up, you can turn around and sell the option back for a profit. b) you can delta hedge the option. Every day, you lose money on theta, but gain money on the movements of the stock. If it doesn't move at all, you lose the theta. If the stock moves "as expected" (=as implied by the implied vol), you'll just break even. But if the stock moves more than expected (that is, realised vol is higher than the implied you bought it at), then you make money. If the market comes around to your estimate of the future vol, you can then sell the option at a profit, or you can hold it to the end and keep delta hedging, and that will be profitable if realised vol turns out to be higher than implied.