IMO, in this case, "exchange" does not refer to an institution but to the act of swapping financial interest (an exchanging of equities, not the XYZ Equity Exchange). If your house is worth $500,000 and you owe $400,000 on it, you have $100,000 of equity in your house. If you also have $10,000 in credit card debt (which the bank owns) you can swap that debt for part-interest in your house.
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