Exception:

FIELD_INTEGRITY_EXCEPTION, Every asset needs an account, a contact, or both.: [AccountId, ContactId]

Resolution:

This exception occurs when the Organization Wide Default of the Asset object is Controlled by Parent and the Asset record is created with AccountId and ContactId null.

Option 1:

Populate AccountId and/or ContactId on the Asset before creating the record.

Option 2:

Change the Organization Wide Default of the Asset object.