How to pass a default value for argument from one function definition to a higher one

I'm searching for a good way to pass default values for arguments to a calling function. Let me explain this by example:

def greet(name, greeting='Hello', punctuation='!'):
    return greeting+' '+name+punctuation

def greet_with_hi(name, punctuation='!'):
   return greet(name, 'Hi', punctuation)

This is an example without use but here's my question: How can I omit the default value for the puncuation argument of greet_with_hi? A default value for this argument is already defined in greet.

Solutions I can think of:

• let it as it is, cons: changing the default value must be done on every function definition instead of only changing it in one place
• use None as value for default argument and handle None inside greet, cons: special handling
• use a global "constant" like DEFAULT_PUNCTUATION='!' and use this as value for the default argument, cons: seems not to be very pythonic

I haven't seen a common pattern in APIs and other code. How would you handle this pattern?