International asset swap is a way by which a country can allow large domestic institutional investors to diversify their portfolio and gain an exposure to foreign assets. Simultaneously, both foreign institutional investors gain access to local assets and can add them in their portfolio. The difference between allowing cross-border transactions in the form of asset swaps and actual sale and purchase of assets is that the swap only results in a flow of funds across the border of the profit/loss made, with no transfer of ownership.
Let us assume an investment bank A based abroad and a local domestic fund B have created an international asset swap. The asset here is an investment in equity markets. If the local equity markets do better than the equity markets of the nation that A is based in, B sends the net profits to A. In the opposite case, B receives funds equal to the losses made from A.
The advantage of international asset swaps is that there is no initial capital flow in either direction, only the net profit/loss is exchanged at the end of a period which is specified in the contract created with the swap.