Supposing such a currency is technologically feasible, could Bitcoin survive the creation of a competing alternative currency that incorporated cryptoderivatives? Why did you pick your answer?
Recent security breaches at Mt. Gox have shown how vulnerable bitcoin is to counterparty risk at exit points (the risk that Mt. Gox or other another counterparty loses your money, the high fees you pay to insure Mt. Gox against this risk).
If a cryptocurrency with derivatives was created, the security of Bitcoin could be duplicated in derivatives market that allowed significant speculation on future price movements within a p2p system.
The only counterparty risk would be the integrity of the block chain (which exists in the current system already).
For a proposal on one way in which cryptoderivatives might be set up, see http://forum.bitcoin.org/index.php?topic=19130.0