* Apple rallies, lifting S&P 500 and Nasdaq
* S&P 500 finishes above 14-day, 200-day moving averages
* Stocks boosted by report of possible ECB bond buying
* Indexes jump: Dow 1.31 pct, S&P 1.96 pct, Nasdaq 2.4 pct
By Yasmeen Abutaleb
NEW YORK, Oct 21 (Reuters) - U.S. stocks rallied on Tuesday, with the S&P 500 notching a fourth straight session of gains boosted by strong corporate results, including Apple's.
The S&P 500 and Dow Jones were up more than 1 percent while the Nasdaq rose more than 2 percent, thanks to better-than-expected results from several major tech companies.
The bullish tone was helped by a Reuters story that said the European Central Bank is considering buying corporate bonds. It led to active futures trading before the opening bell and helped lift European stocks from last week's 13-month low.
"That is allowing the market to breathe a little sigh of relief," said Kevin Caron, market strategist at Stifel, Nicolaus & Co in Florham Park, New Jersey. "The market has come to fear the absence of central banks."
The S&P 500 has gained more than 6 percent from its session low last Wednesday, when the benchmark nearly reached correction territory. It closed Tuesday above both its 14-day moving average and its 200-day average.
The Dow Jones industrial average rose 215.14 points, or 1.31 percent, to 16,614.81, the S&P 500 gained 37.27 points, or 1.96 percent, to 1,941.28 and the Nasdaq Composite added 103.40 points, or 2.4 percent, to 4,419.48.
Apple Inc rose 2.7 percent to $102.47 a day after revenue topped expectations, helped by strong iPhone sales. It also gave a strong outlook for the holiday quarter.
The largest percentage gainer and decliner on the S&P 500 were both related to earnings. The top gainer was Waters Corp , which rose 9.9 percent, while the largest decliner was Chipotle, down 7 percent.
The largest gainer on the Nasdaq 100 was Illumina Inc , which rose 9.2 percent and the largest decliner was Starbucks, down only 0.5 percent.
While earnings have largely come in strong so far this quarter, concerns continue to swirl over the pace of global economic growth. China's gross domestic product grew 7.3 percent in the third quarter, the slowest pace since the first quarter of 2009.
"This rebound is going to be short-term in nature," said Mohannad Aama, managing director at Beam Capital Management LLC in New York. "The reasons for the market meltdown from last week are still there."
U.S. existing home sales rose 2.4 percent in September, above expectations, hitting their highest level in a year. The PHLX Housing index rose 1.2 percent.
Advancing issues outnumbered decliners on the NYSE by 2,557 to 538, for a 4.75-to-1 ratio on the upside; on the Nasdaq, 2,008 issues rose and 668 fell for a 3.01-to-1 ratio.
The benchmark S&P 500 index posted 24 new 52-week highs and 1 new low; the Nasdaq Composite showed 45 new highs and 30 new lows.
About 7.2 billion shares changed hands on U.S. exchanges, below the 8.3 billion October average, according to BATS Global Markets. (Additional reporting by Rodrigo Campos; Editing by Nick Zieminski)