The stock market yesterday recorded the largest one-day jump in its history, amid signs that the high interest rates that have plagued the economy finally may be heading down.

The Dow Jones Industrial Average soared a record 38.81 points as trading volume on the New York Stock Exchange was a near record 92.86 million shares. At day's end, the Dow stood at 831.24.

Citibank lowered its prime lending rate a half point to 14 percent. It was the second drop in as many days. Monday, Citibank lowered its prime rate from 15 percent to 14.5 percent. Chemical Bank also lowered its prime rate to 14 percent.

Much of Wall Street's excitement yesterday was generated by the continued signs of falling interest rates, with an optimistic forecast by Wall Street analyst Henry Kaufman leading the way. Kaufman, the widely watched Salomon Brothers Inc. economist, abandoned his earlier predictions of rising short- and long-term interest rates in favor of the prediction that the current drop in rates will continue.

"Recent events in the economy and financial markets require a new look at the prospect for interest rates," Kaufman wrote in a memo to Salomon clients. "On balance, these events suggest that the decline in interest rates now under way will continue, irregular to be sure, with perhaps dramatic interruptions."

The Reagan administration was quick to accept at least some of the credit for yesterday's market results. White House spokesman Larry Speakes suggested that the president's address to the nation Monday night may have had some impact on investors.

Treasury Secretary Donald T. Regan credited the administration's overall economic program with helping to set the stage for the rally. Speakes was careful to point out, however, that it is "risky to assign a motive to changes in the stock market."

On Wall Street, Charles Comer of Bache Halsey Stuart Shields said, "There is a panic to get back in the market." Another Wall Street analyst said, "We're sitting here, drinking champagne."

Kaufman, in his memo, wrote, "The immediate threat that would have driven interest rates back to their 1981 peak yields -- a smart business recovery in the second half of the year -- is now much less likely to materialize than a few months ago."

The economist predicted that long-term government bonds, now yielding 12.5 percent, might fall to 9 to 10 percent, while the federal funds rate might fall from the current 9 to 10 percent to the 6 to 7 percent range.

But a market analyst at Merrill Lynch Pierce Fenner & Smith Inc. warned that "nothing about today is conclusive." Richard McCabe, the firm's vice president and manager of market analysis, said that rallies "can look very impressive for a few days and yet not prove to be the start of a new major advance."

McCable and Bache's Comer agreed that the rally may continue because interest rate declines make investment instruments other than stocks less appealing.

"Rates are coming down like a ton of bricks and many money-market type investments aren't as attractive any more," Comer said. "There is a lot of cash in the hands of investors."

Like the stock market, the bond market also soared yesterday, as bond trading volume jumped more than 50 percent to $56.2 million, while the Dow Jones 20 bond index rose 0.76 to 61.36.

The stock market's leap was broad, with the Dow industrials continuing to gain momentum after gains of more than 15 points in the last two days of trading. More than 1,500 New York Stock Exchange issues advanced and only 155 fell in per share price. There were twice as many new highs as new lows, with 108 stocks reaching new tops.

The American Stock Exchange index jumped sharply to 244.30 up 6.43, as did the key indicators on the Nasdaq, or over-the-counter market. The Nasdaq index jumped by 2.60 to 162.28.

In another bit of good economic news for the Reagan administration, the Commerce Department reported a 33.7 percent rise in July housing starts. Analysts said the news had little impact on the market, however, as much of the rise was attributed to multifamily housing construction.