How Is the Concept of a Pool Fee Analogous to an Options Premium?

The pool fee is analogous to an options premium because it is the price paid to the pool operator for providing a service and, in the case of PPS, for absorbing risk. In PPS, the fee is the premium paid for the guaranteed, fixed payout (like an insurance policy).

In PPLNS, the fee is the premium for the service of aggregating hash power and managing the reward distribution.