NEW YORK — Just last week, a bear market seemed inevitable. Since then stocks have surged four out of the past five days, bringing the S&P 500 index up 8.7 percent.

The latest jump came Monday after the leaders of France and Germany pledged to come up with a far-reaching solution to the region’s debt crisis by the end of the month.

The Dow Jones industrial average soared 330 points, its biggest one-day gain since Aug. 11. It has gained 7.3 percent over the past five days. Bank of America Corp. jumped 6.4 percent, the most of the 30 stocks in the Dow.

Sharp turnarounds in the market have become increasingly common. Last Tuesday, the S&P 500 traded 20 percent below its recent peak in April. Had it closed at or below that level, it would have met the definition of a
bear market.

Instead, the S&P began a rally that continued through Monday. The gains were extraordinarily broad; only 5 stocks in the S&P 500 index fell, and ten stocks rose for every one that fell on the New York Stock Exchange.

As in many recent days, a good part of the increase came at the final minutes of trading. The Dow rose 100 points in the
last half-hour.

German Chancellor Angela Merkel and French President Nicolas Sarkozy said Sunday they would finalize a comprehensive response to the debt crisis by the end of the month, including a plan to make sure European banks have adequate capital. Investors have been worried that European leaders weren’t moving quickly enough to contain the fallout from a default by Greece’s government.

Investors have been worried that a default by Greece could cause the value of Greek bonds held by those banks to plunge, hurting their balance sheets. U.S. banks would also be affected if Greece goes through a messy default, since they own Greek bonds and also have close ties to European banks.