I have a static variable declared in the run() function and I initialize it to 0 - static var Price = 0;

From the help menu it implies that the value cannot be set there after - "keeps its content when the function terminates or when another instance of the function is called.".

However, I then issue a set of the static variable - Price = priceHigh();
and the static variable is set to the value returned.

Why? This is not supposed to happen.

A static variable is more like a global variable, insofar as its existence and value is maintained between function calls. You can still change its value after initialization.

If you do not want a value to change, use const.