jQuery .val change doesn't change input value

Use attr instead.
$('#link').attr('value', 'new value');

demo

Changing the value property does not change the defaultValue. In the code (retrieved with .html() or innerHTML) the value attribute will contain the defaultValue, not the value property.

to expand a bit on Ricardo's answer: https://stackoverflow.com/a/11873775/7672426

http://api.jquery.com/val/#val2

about val()

Setting values using this method (or using the native value property) does not cause the dispatch of the change event. For this reason, the relevant event handlers will not be executed. If you want to execute them, you should call .trigger( "change" ) after setting the value.