The Dow Jones industrial average gained 420 points, and investors sent stocks soaring to their highest gains in five years, as shares of financial firms surged in the hopes that the Federal Reserve has finally taken hold of the credit crisis.

Two big investment banks, Lehman Brothers and Goldman Sachs, delivered stronger-than-expected earnings.

At the end of trading, the Dow was at 12,392.66, a gain of 420.41 points, or 3.51 percent. The Standard & Poor’s 500-stock index advanced 4.24 percent, its best performance since October 2002. It was up 54.14 points, to 1,330.74.

The Nasdaq composite index also gained 4.2 percent, or 91.25 points, to 2,268.26.

In Europe, indexes in London, Paris and Frankfurt all closed more than 3 percent higher, a full recovery from Monday’s declines.