The nominal value of the notes in the derivatives market is extremely large. However, we can't equate $500B notional of e.g. CDS written against Apple debt with $500B of Google stock. The CDS represents (1) to the seller, an small initial premium and a large, extremely low-probability liability requiring some collateral, and (2) a stream of future payments from or to the buyer, depending on the cost of insuring the debt. Up until a credit event, the only money exchanged is the premium, and perhaps some collateral, both of which are (for highly rated debt) orders of magnitude smaller than the notional value of the contract.
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> and a large, extremely low-probability liability requiring some collateral
Having read up on the topic, the problem appears to be that this probability cannot be accurately determined, due to useless models being used (e.g. Normal distribution to model complex phenomena).
So the probability is often not so low as the financial experts think. Besides that, it does happen that the liability becomes due, as in the 2007/2008 GFC. People were shocked because their models indicated that such an event should practically never happen (due to it being of such low probability).
When the liability is due, the whole system collapses (as it did in 2007/2008) because the collateral that is held is often not worth what it's is marked up to be.
So the whole system is fragile and prone to systematic collapse. Sounds pretty rotten to me.
Well it gets more complex when you add mark to market into the mix. Plenty of the financial products that "blew up" in 2007/2008 were actually very profitable for those able to hold on to them.