Oil prices shot up Monday in a late rally fueled by rumors of hostilities in the Persian Gulf, after falling in the morning on the belief that the Bush-Gorbachev summit made Mideast war less imminent. ``This is such a strange market,'' said Stephen Smith, an analyst with Bear Stearns & Co. ``You're down a dollar and a half, and then you're up a dollar and a half.'' Light sweet crude closed up $1.26 at $31.30 per barrel for October contracts in light trading on the New York Mercantile Exchange. Oil had opened down $1.49 as traders were calmed by the weekend summit in Helsinki, Finland. President Bush and Soviet President Mikhail S. Gorbachev agreed that Iraq should get out of Kuwait, but Gorbachev indicated an unwillingness to resort to a military solution to the crisis. Crude fell another 20 cents before beginning a steady climb in all contract months. Unleaded gasoline and home heating oil also fell in the morning and rose across the board in the afternoon. On October contracts, gasoline closed up 1.50 cents at 94.56 cents per gallon, while home heating oil closed up 1.91 cents at 85.89 cents per gallon Natural gas futures were mixed. The swings in oil prices sent stocks moving in opposite directions. The stock market opened higher and closed lower. The Dow Jones average of 30 industrials, up about 30 points at its peak of the day, finished with a 3.96 loss at 2,615.59. After oil opened with its sharp decline, the price began rebounding on news that Iraq and Iran were re-establishing diplomatic ties for the first time since their extended war of the 1980s. The conciliatory move was viewed as a bid by Iraq to try busting the international embargo of its oil that was put in place after it invaded Kuwait on Aug. 2. The markets paid brief attention to Iraqi President Saddam Hussein's announcement that he would provide free oil to Third World countries as a gesture of good will. But Saddam said the recipients would have to pick up the oil themselves, which would force them to get past the U.S. Navy. ``When he came out with his statements, they were construed as bearish,'' said Ed Kevelson, a trader with Dean Witter Reynolds Inc. ``Initially, he came out with `free oil,' so people said, `Sell it.' Then they started thinking you had to transport it. That was pretty much discounted throughout the day as Hussein gibberish.'' The late afternoon rally was spurred by rumors that did not turn out to be valid, according to Ann-Louise Hittle, a senior oil analyst with Shearson Lehman Brothers Inc. ``Some people were trading on a rumor that Iraq had moved troops into Jordan,'' Hittle said. ``Another rumor was some Saudi rigs were hit. Another one was some shots were fired.'' Officials in Washington said there was no information to confirm any of the rumors.