Why in FX and EQ world rates are usually deterministic?

Variability of interest rates contributes to FX/EQ products by a smaller order.

What is the difference between discount factor and ZC bond price?

Discount factor Unknown macro: formula. Click on this message for details.
The [formula] macro is not in the list of registered macros. Verify the spelling or contact your administrator. is a random variable at time t depending on the future evolution of Unknown macro: formula. Click on this message for details.
The [formula] macro is not in the list of registered macros. Verify the spelling or contact your administrator.. ZC bond price Unknown macro: formula. Click on this message for details.
The [formula] macro is not in the list of registered macros. Verify the spelling or contact your administrator.is a value of a contract at t paying 1 at T.

Unknown macro: formula. Click on this message for details.
The [formula] macro is not in the list of registered macros. Verify the spelling or contact your administrator.can be seen as expectation of the random variable Unknown macro: formula. Click on this message for details.
The [formula] macro is not in the list of registered macros. Verify the spelling or contact your administrator.under T measure.