It's risk, not a certain loss. And you don't "transfer" it, you sell it to a party that wants higher risk (for a fee).

Derivatives are nice, in that sometimes its possible to separate the risk out from the asset. Consider a $50k loan at 5% with a 1% risk of default.

A pension fund and a hedge fund both have capital, but the pension fund have extremely conservative investors and the hedge fund have extremely risk hungry investors. That loan is not a good investment for either.

So a derivative is created: the hedge fund agrees to make the pension fund good if the loan-taker defaults for a one-time fee of $550 (the cash-value of the 1% risk + a $50 fee). The pension fund now has a $49,450 loan (actually, it will be booked as a $50k load both paying a bit less that 5% interest - the exact amount depends on the running time of the loan) and a $0 risk budget and the hedge fund just made $50 + a 99% chance of $500 more. All are happy, including the loan-taker who might have struggled to get someone to load him money.

(Numbers pulled from thin air for illustrative purposes and lots of details omitted)

That seems accurate, but it doesn't seem to account for the risk of the hedge fund going bust. It's a high risk fund so they either have the cash buffer we talked about or they transfer the risk to others. So the net effect is still null. The pension fund will be in much better position to take the 1% risk multiple times at sufficiently disconnected opportunities insuring each-other reducing the overall risk.

No, the risk costs $500 and the hedge fund has that. They can't book the $500 before the loan has been repaid in full. The problem is what happens if the default risk (1%) turns out to be 2% instead. See: The subprime crisis.