In the case of global nuclear war, would stocks go to zero or would algorithms keep the market alive

In the case of total nuclear war and wall street and NYC being completely destroyed, would the price of SPY go to zero or would there still be algorithms trading after humanity is gone? Like the price of SPY could be like 3 dollars a share with just algorithms trading after everybody has died. Or would the markets hit circuit breakers and just permanently remain closed?

Would spy puts pay out anything? (Yes I know money would be worthless in such a scenario)