From Greenspan's speech to the National Italian American Foundation:
Conceptual advances in pricing options and other complex financial products, along with improvements in computer and telecommunications technologies, have significantly lowered the costs of, and expanded the opportunities for, hedging risks that were not readily deflected in earlier decades. The new instruments of risk dispersal have enabled the largest and most sophisticated banks, in their credit-granting role, to divest themselves of much credit risk by passing it to institutions with far less leverage. Insurance companies, especially those in reinsurance, pension funds, and hedge funds continue to be willing, at a price, to supply credit protection.
These increasingly complex financial instruments have contributed to the development of a far more flexible, efficient, and hence resilient financial system than the one that existed just a quarter-century ago (right before Greenspan took office in 1987). After the bursting of the stock market bubble in 2000, unlike previous periods following large financial shocks, no major financial institution defaulted, and the economy held up far better than many had anticipated.
If we have attained a degree of flexibility that can mitigate most significant shocks--a proposition as yet not fully tested--the performance of the economy will be improved and the job of macroeconomic policymakers will be made much simpler.
Translation: Chances are, the banking system has everything under control, so don't worry about my successor even if you've never heard of the person before.