Of the above 3, the Indemnification Method and the Formula Method are not used as frequently. The Agreement Value however, is used fairly extensively and is the most common method.
A termination in a premature manner for a swap may occur in case of events like tax payments, illegal actions of one of the parties involved in a swap, in case of merger, acquisitions and credit events.
There are 2 parties to a swap. In case of a premature termination, one of the 2 parties calls for it. This affects the counterparty although there was no intention to exit the swap. This would entail the need for a replacement swap by the counterparty. This does not come without additional costs and that is the basic principle behind the need to be compensated, that which is calculated using the Agreement Value Method. The termination payments would mostly be different compared to as calculated since the contract initiation since there could be changes in market conditions, interest rates and therefore mean that the initial terms of the swap be no longer available.
It can also be looked upon as the penalty to be paid by the party that exits the swap, thereby creating a disincentive for exits from a swap.