Assignment and Nomination are two different terms.
Nomination - Your nominee, who would receive the benefit when some thing happened to you.Eg. LIC Policy nominee
Assignment - You have assigned the benefits of the policy to anybody to get something. For eg. You have taken a loan and as security you have assigned the LIC policy.

Nominee can be changed anytime. Just get the form from nearest LIC office. It has to be submitted at the branch where the policy was issued.
Regarding Assignment - Usually one assigns a policy to a bank or lender. For that you have to fill up the necessary forms and the policy will be handed to the assignee after endorsement.

You do not have to assign your policy to your parents. Just change the nominee.