NEW YORK - US stocks rallied for a second straight session on rising optimism about a Washington deal to avert a debt default. The Dow Jones Industrial Average on Friday jumped 111.04 (0.73 per cent) to 15,237.11. The broad-based S&P 500 rose 10.64 (0.63 per cent) to 1,703.20, while the tech-rich Nasdaq Composite Index tacked on 31.13 (0.83 per cent) to reach 3,791.87. Investor anxiety eased on Thursday after Republican leaders offered President Barack Obama a short term extension of the US government's borrowing authority so as to stave off a possible debt default. By Friday, there was still no deal, but markets appeared encouraged by continued talks. LONDON - European shares rose on hopes of a deal to break the US budget deadlock, while London has been lifted by an impressive stock market debut for Royal Mail. Frankfurt's DAX 30 rose 0.45 per cent to end Friday at a record high of 8,724.83 points. In London, the benchmark FTSE 100 index rose 0.88 per cent to 6,487.19 points, while the CAC 40 in Paris edged up 0.04 per cent to 4,219.98 points. Madrid added 0.08 per cent and Milan climbed 0.24 per cent. The euro firmed to $1.3541 from $1.3520. HONG KONG - Asian markets rallied on hopes the US will avoid a default as President Barack Obama and Republican leaders held their first talks on resolving a budget impasse that triggered a partial government shutdown. The gains on Friday followed Wall Street's best day since January as dealers welcomed progress on ending the crisis with less than a week before Washington runs out of cash to pay its bills. Tokyo rose 1.48 per cent, or 210.03 points, to 14,404.74, Sydney climbed 1.63 per cent, or 83.8 points, to 5,230.9, while Seoul was 1.17 per cent higher, adding 23.50 points to 2,024.90. Shanghai was up 1.70 per cent, or 37.22 points, at 2,228.15 and Hong Kong advanced 1.16 per cent, or 267.02 points, to 23,218.32. WELLINGTON - The NZX 50 Index gained 23.390 points, or 0.5 per cent, to 4740.770.