Global disaster in terms of economic wise or political wise but might not really affect the value of bitcoin because it has proven strong over past years after several breakings from top economics analyst. But in regards of natural disaster I think it will really affect the market price in every sector be it bitcoin or any other assets outside cryptocurrency but it's now left with we the community holders on how we want to use it to our favour and to help mankind.
If there is a global catastrophe, people will simply fight for their survival. The price will be the most simple physical things and even ordinary currency will lose its value. With a global catastrophe, the Internet is likely to disappear, and with it the cryptocurrency will disappear. Even if the Internet remains, virtual money will no longer interest anyone. Then, most likely, 10,000 bitcoins will be offered to you again for the pizza, or even more.