Global stock markets soared in a massive relief rally yesterday after EU leaders agreed a deal to solve the eurozone debt crisis and data showed the US economy growing faster than expected.

Dealers said there may be many reservations about the deal but the immediate reaction was one of relief that European leaders had finally come up with a coherent response to a crisis threatening to sink the euro and the world economy.

The banks performed best, having been under intense pressure on concerns over their exposure to Greek government debt, with private sector creditors now agreeing to take losses of 50 percent on their holdings of Greek bonds.

This is combined with more than €100 billion in funds to help the banks cover their losses, ensuring the European banking system escapes the worst of any fallout.

Dealers said figures showing the US economy grew 2.5 per cent in the third quarter, up sharply from the second and ahead of forecasts for around 2.3 per cent, also gave sentiment a boost.

In London, the FTSE-100 index of top companies closed up 2.89 per cent to 5,713.82 points while in Paris, the CAC-40 jumped 6.28 per cent to 3,368.62 points. In Frankfurt the DAX 30 gained 5.35 per cent to 6,337.84 points.

Other European markets posted similar sharp gains after months of turmoil driven by worries the eurozone debt crisis could torpedo the euro and push the global economy back into recession.

In late trade, the euro was at $1.4190, up sharply from $1.3908 in New York late Wednesday. The dollar fell to ¥75.77 from ¥76.21.

In New York, the blue-chip Dow Jones Industrial Average was up 2.53 per cent at around 1600 GMT and the tech-heavy Nasdaq Composite added 2.35 per cent.

Analysts there welcomed the US growth figures.

The report was “encouraging,” said Peter Newland of Barclays Capital, noting that “the bulk of the rebound... was centred in personal consumption, which was up 2.4 per cent”.

The prospect of the US consumer spending again raised hopes of a more firm-footed recovery after measly growth rates of 0.4 and 1.3 per cent in the first two quarters sapped confidence.

“The bottom line is that the third quarter turned out to be a period of underlying strength,” said Stephen Stanley, chief economist for Pierpont Securities.

“Decisions have been made in Europe, and even if we are short on detail Europe’s leaders are talking the right game and the markets seem to like it,” said said Kathleen Brooks, an analyst at traders Forex.com.

In Asian trade earlier yesterday, Tokyo closed up 2.04 per cent and Hong Kong rallied 3.26 per cent, helping set up Europe for a positive day.

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