rate
In a very general sense the interest rate r is a number that tells us how much income can be earned by lending money, or equivalently how much cost is associated with borrowing money.
The higher the r is, the more income one expects to earn by lending money.
It is not possible to define the r mathematically so that it applies to all sorts of lending/borrowing transactions.
One should rather speak of an interest rate in relation to a specific lending/borrowing contract.
The simplest example of such a lending/borrowing contract is a simple loan or depsosit, of which the associated spot rate is represented in Deriscope by the type Term Rate
A Term Rate pertaining to an interbank loan is represented by the type ibor rate
There also exist more complex rate definitions, such as the interest rate pertaining to interest rate swaps, which is represented by the type swap rate
Although not existing in the actual market, the spot interest rate pertaining to a theoretically conceivable instantaneous riskless deposit is defined appropriately and represented by the type short rate
Given a specific lending/borrowing contract C, the associated interest rate r depends on the time t, when the value r is agreed between the parties entering into the contract C.
If we treat the time t as variable, we end up with a function r(.) that maps each time t to the respective interest rate value r(t).
Assuming t = 0 designates the time now, the value r(t), t > 0 is not a simple number but rather a random variable, since it is not possible to know with certainty the interest rate that is going to prevail at the future tinme t.
It follows, the function t -> r(t) maps the number t to some random variable, and therefore is a stochastic process.