European shares closed 2.2% higher on Tuesday, after a five-day losing run.
The FTSEurofirst 300 index of leading European shares ended 2.2% higher at 834.36 points, having risen to a day's high of 851.17. The index is down by about 45% in value to date this year.
Volkswagen surged more than 80%, adding to a 146% rise on Monday, following news at the weekend that Porsche had bought more shares n the company. Porsche was up 9.9%.
However, banks took a fresh beating. Shares in French bank Societe Generale were down for a second day in a row, by more than 12%.
BNP Paribas was 10.4%, Credit Agricole down 13.4% and Deutsche Bank fell 13.3%.
Standard Chartered rose 2.9% , after saying it made good progress in the third quarter of 2008 despite slower economic growth in the Asian region.
The London-listed bank generates two-thirds of its revenues in Asia.
Across Europe: Germany's DAX was up 11.3%, boosted by Volkswagen, and France's CAC-40 was up 1.6%.
In Britain, the FTSE 100 was up 1.9%, 73.79 points higher at 3,926.38.
Big rise on US markets
Stocks in the United States ended sharply higher on Tuesday.
The Dow Jones industrial average shot up 889.35 points, or 10.88%, to end unofficially at 9,065.12, based on the latest available data.
Standard & Poor's 500 Index surged 91.58 points, or 10.79%, to finish unofficially at 940.50. The Nasdaq Composite Index jumped 143.57 points, or 9.53%, to close unofficially at 1,649.47.
The US Federal Reserve is to begin a two-day interest-rate policy meeting on Tuesday, and investors expect the Fed to cut rates - now at 1.5% - by at least a further 50 basis points.
The Bank of England is also widely expected to cut rates by another 50 basis points to 4% next week. The BoE has already cut interest rates twice this year.
European Central Bank president Jean-Claude Trichet said on Monday the ECB could cut rates at its next meeting on 6 November.
The bank cut its main lending rate by 0.50 percentage points to 3.75% on 8 October as part of a co-ordinated action by a number of central banks to avert a collapse of the banking system.