In the case of nuclear apocalypse, would the S&P 500 hit zero or just outright close?

Let's say that Putin presses the big red button. Nuclear war starts and New York City along with all the other major cities in the world are obliterated in nuclear hellfire. Would the stock exchanges immediately close upon hearing news on the outbreak of nuclear war? Or would SPY hit a price of zero? Maybe algorithms would still be able to trade if the stock market doesn't close after everybody has died?