Lets say you sell short VXX calls expiring in 2 weeks. A major global conflict breaks out and the markets end up being closed for the next month. What happens to your short VXX calls? Had the market been open, those options would have skyrocketed and you would have lost your shirt. But since the market was "closed" during the period the options were to expire, what actually would happen? Do you keep the proceeds as the options expired and couldn't be exercised? Do the exchanges set a new "expiration" date for when the market is open?
I think you would be a very lucky man... they can't just change the contract specs, so it would expire as is. But I'm sure any large participant with an interest in this would try to make the exchange to open....
Even during the second world war the London Stock Exchange appears to have been closed only briefly (https://en.wikipedia.org/wiki/London_Stock_Exchange#Second_World_War). Remember that in 1940 invasion of Britain was expected and it doesn't appear to have closed abnormally at all that year. A month-long closure is basically unthinkable these days unless all major financial infrastructure took nuclear sized hits. In which case you've got worse things to worry about.
I think it's more interesting to think about what would happen when a government suddenly nationalizes a company. Say stock trades at 5, you are short a bunch of puts... and it gets nationalized. Stock is basically worthless instantaneously... but how are options settled? Fair value (= stock at 0). Previous close? Intrinsic value at previous close? Shit like this has happened....
OCC has a process for arriving at a settlement value and it varies by what is available data. This one reason why they worked so hard to get the markets open the week after 09/11. I don't recall all of the choices, but you can read the disclosure document online. It would be much more of a challenge today with all of the short dated stuff. I'm not saying it's fair, but there is a process
Just read the risk disclosure again and it is remarkably vague - it looks like OCC gets to figure it out and they have the authority to delay the settlement