ll11

Incorrect I believe. Have a look at what you're written again.

Just in terms of value to your portfolio:

1. Rate

If long a put and rates rise, option value falls, portfolio keeps upside sensitivity
Long a call and rates rise, option value could rocket. Portfolio overall however doesn't gain any upside sensitivity.
Short a call: If rates go to the moon it's brown trousers time.
Short a put: No change in PF value (well, small increase) as rates rise. You pocket the premium and go to the lappies after work.

2. Bonds

Long put&increase in rates: You don't lose $$$
Long a call&increase in rates: option value falls
Short a call and interest rates rise. Pocket premium, you don't lose $$$
Short a put and rates rise: Brown trousers time. Loss capped at value of underlying.