Stock and bond markets, buoyed by the prospect of lower interest rates, rallied sharply today with the Dow Jones Industrial Average up nearly 20 points.

The markets appeared to be reacting to the latest indication that a recession is underway. Although a recession will mean higher unemployment and lower corporate profits, it also will result in a reduction in the near-record interest rates that have been crippling the economy.

The Dow average, the most widely watched indicator of stock market behavior, climbed 19.60 points to 852.55. Trading on the New York Stock Exchange was heavy, as 59.69 million shares changed hands. On Thursday volume was 40.2 million shares.

Bond prices rose as well. William Sullivan of the Bank of New York said the average long-term bond rose $20 for each $1,000 of face value.

At the same time, short-term interest rates continued to decline from their peaks of last August. Rates on three-month certificates of deposit, a major device that big banks use to raise money they then lend to their customers, closed at about 14.7 percent today, down from 15.1 percent on Thursday and 15.35 percent a week ago.

Late trading in the bond and money markets was given a further shot in the arm when the Federal Reserve Board, whose tight-money policies have been blamed for causing much of the interest rate crunch, reduced its so-called discount rate from 14 percent to 13 percent. The discount rate is the interest the central bank charges commercial banks that borrow from the Fed. A cut in the discount rate represents an acknowledgement by the central bank that rates are on the way down and it does not want to stop them.

The Fed made its announcement after the New York Stock Exchange stopped trading at 4 p.m. and after most stock and bond traders had stopped for the day.

Donald McKee of the brokerage firm Sanford C. Bernstein & Co. said that now that all the bad recession news is out, the stock market shrugged and improved on anticipation of lower interest rates.

"The market looks like it is ready for a rally," McKee said. But he added that he thought the rally would be technical in nature--due more to the stock market's internal dynamics than anything else--and would not signal the start of a sustained "bull" market, as investors and traders call a steady, long-term increase in stock prices.

When interest rates go down investors are more likely to put their money in stocks than in interest-bearing securities such as Treasury bills. Also, investors find it cheaper to buy stocks on credit.

The rise in stock prices was broad based. More than 1,200 stocks closed higher in price today, while about 300 closed lower. The New York Stock Exchange's own index closed at 70.64, up 1.55 points. On the American Stock Exchange, the index closed up 5.80 points to 312.02.

Oil company stocks gained today, after Mobil Corp., unsuccessful in a three-way fight to acquire Conoco Inc. last summer, bid $85 a share for Marathon Oil. Many second-tier oil companies like Marathon (which did not trade all day) rose in price as investors figured they might become takeover targets themselves. Cities Service jumped $4.375 to $48.375 a share; Superior Oil gained $2 to $36.25 while Mesa Petroleum was up $2.25 to $22.125.

Mobil itself declined 25 cents to $26, as investors worried that the nation's second biggest corporation might face antitrust problems--an issue that was never resolved in its losing quest to buy Conoco, the ninth-largest oil company in the country--and that other oil companies with big war chests might bid for Marathon as well.