durrrr, you don't need/want to calc second and third moments; you run a stress x time and vol. The fact that you cannot pick a date in the future and scenario-test is not a problem with the model. Yeah, (all of) the shit has convexity and that's how you deal with it. You test cross-sectionally x time x vol. You screen build a position. Price spot 2% lower with 100 beeps added to the vol-line. Price spot 2% higher and shift (globally) the vol-line by 100 beeps. Are you horrified? Don't trade the thing. The only input you need to change is vol x strike and day count if you're very close to expiration. Most front ends offer you the option of skew approximation or strike vols. Understand s-strike and s-delta. Vol-corr inverse to price. If you buy a bunch of bear calendars then you can assume that you're not going to lose on_vol_ if the position trades neutral to delta. If the market rallies you'll lose to (obv delta) and vol-corr but mitigated somewhat by skew (moneyness/trades away). You factor vol locally when approaching macro events (long or short into CPI? NFP?) etc. So in that case when modeling say a risk-reversal you may want to add 100 beeps downside and pull 90 beeps upside (inside a sigma). Just an example. Barefoot and dumb is no way to go through life, son.
Agreed, predicting the future is quite hard. That's not what the models are for though. The models excel at determining the MSRP. Then buy or sell the vehicle(s) of your choice.