One suggestion that often crops up is to create an exchange for derivatives, such as credit default swaps. In my view, this probably would solve the problem of counterparty risk. However, the more important problem, systemic risk, would be left unsolved, or perhaps worsened.
A credit default swap is an insurance contract or bet that is tied to a company's credit performance. If I think that XYZ's bonds may default, I might want to buy a credit default swap that pays off in the event of an XYZ default.
Counterparty risk means that if I buy my default swap from ABC, I have to worry that ABC might not perform in the event of an XYZ default. Having an exchange step in to guarantee the transaction would be an improvement.
However, the larger problem is systemic risk. That is the risk that the contingency plans of individuals cannot be executed collectively in practice.
Suppose we had an exchange-traded default swap on XYZ. What are the sellers' contingency plans if they think that XYZ may be headed toward default and the option that the sellers have sold may be in the money? My guess is that the each seller's plan is to hedge its short option position by dynamically hedging, which means taking short positions in the bonds and stock of XYZ. These short positions will get more and more aggressive the closer XYZ gets to default.
The problem with these contingency plans is that they cannot be executed collectively. Collectively, they start a run on XYZ that drives it out of business before everyone can execute the hedge.
The problem with credit default swaps is not (just) that they are traded over-the-counter. The more serious problem is that they entail huge systemic risk. Getting rid of counterparty risk does not solve the problem. The issue is not that any one party is unable to meet its obligations. The issue is that in the aggregate, credit default swaps allow the market to sell more default risk protection than it's possible to produce. This false sense of security leads people to pile on risk, and then when the crisis comes, their protection fails.