Charlie Bean, who retires next month after 14 years at the Bank, said current low levels of volatility were "eerily reminiscent" of the run-up to the financial crisis, but argued that banks were now better able to withstand shocks.
But he warned that with rising interest rates the value of some financial markets could plummet as investors shift away from risky assets.
He also voiced concern that the Bank's as-yet-untested watchdog role may not prove effective especially given some banks may look for ways to get around restrictions on risky but highly profitable activities.
Bean said: "Compared to the impact of changes in interest rates, we have relatively little experience of deploying macroprudential instruments... So, there may well be times when monetary policy is the only game in town to guard against incipient financial stability risks."
But he played down the potential for a re-run of the banking collapse, arguing that banks had built up large reserves to protect themselves.
He said: "It is inevitable that at some stage market perceptions of uncertainty will revert to more normal levels. That is likely to be associated with falls in risky asset prices".
But because "banks are better capitalised, leverage is lower and we are better placed to deal with financial institutions that get into trouble, the risk of major financial problems crystallising in the advanced countries should be much lower".
Speaking at the London School of Economics, Bean conceded that he had been complacent leading up to the financial crisis, believing that the past seven years "marked by financial instability and a deep recession" was a "salutary lesson for those, like me, who thought we had successfully cracked the problem of steering the economy".
Last week Bank governor Mark Carney said Bean was renowned as one of the world's most respected economists and a great loss to the Bank.
An academic who moved into policymaking, Bean is one of the UK's most published economists and ranks as one of the most in demand at conferences around the world.
He last hit the headlines in 2010 when he urged Britons to go out and spend to help invigorate the economic recovery. In unusually unguarded comment for a banker, Bean told Channel 4 News that people should stop themselves from building up cash savings that generate little income in a period of historically low interest rates.
Bean, who sits on the Bank's monetary policy committee that sets the base interest rate, found himself defending headlines such as "Bank deputy says spend, spend to save economy" only months after the coalition came to power urging households and businesses to save to reduce their debts.
His stance, which spelled out the benefits of consumers using the gains from low interest to spend on the high street, was respected in Keynesian economic circles but caused consternation in the Treasury.
Bean told students at the LSE: "The bottom line is that we may yet encounter a few potholes on the way to the exit. But the good thing is that banks are better capitalised now than in the run-in to the crisis, leverage is lower, there is better visibility of counterparty exposures, and we are better placed to deal with financial institutions that get into trouble."
He referred to the exodus of funds suffered by Turkey, Brazil and other emerging nations after the US Federal Reserve threatened to taper its programme of quantitative easing last year and argued that there could be worse to come.
"So the risk of major financial problems crystallising in the advanced economies should be much lower. Those emerging economies that have financed large external deficits through the accumulation of foreign currency debt may be more vulnerable, however," he said.
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