Seems some of the problem of volatility is that stocks are too liquid.
I think part of the problem is that the costs of active trading are too remote from the activity. The tax system has a few rewards for long-term thinking, but they really only show up a year later at income tax time.
A tax closer to the event would tend to make people more hesitant about giving in to panic. And a tax that was tied to the market itself is a fun thing to contemplate. Although politically impossible, it would be interesting to consider a tax that went up when the markets were in free fall, and that disappeared when the market was flat. That would give a direct incentive to wait out the storm and take the long view of things.
It should be your right to sell a stock that you believe is devalued and unlikely to go up without consequence. Sure, most are panic selling, but the option to get rid of crap should be there without having to lose more. Plus, if nobody panic sells, how will I get dirt cheap shares? 
A tax on what? The very volatility argues against it, since the event would have passed by the time people filed their forms. (I’m not assuming once a year.) There is a tax on the money you make in the more or less long run already, you wouldn’t want to tax every gain when you couldn’t give back on every loss.
Tobin tax. Some variants are two tiered to target periods of greater volatility. My view - FWIW - is that the problem is real and serious but the proposed solution faces difficulties (of measurement, timing, free-riding, rent-seeking etc) so large as to make it not a good idea.
Not annual. No forms. It would be applied like sales tax, and appear after the line for broker’s fees.
And, sure the calculation could be done based on current market conditions. After all, that’s how foreign currency purchases are done, the rate is subject to change at any time.
I like that one. Tobin only applied it to currency speculation, but it could apply just as readily to any other market.
If people can’t sell their stocks when the market goes down without a penalty, they’re going to be less likely to invest in the first place. That’s not something we really want.