The stock market surged to a record high yesterday as market-driven interest rates continued to fall and expectations mounted that the Federal Reserve soon would cut its discount rate.

Falling oil prices and some good corporate earnings reports also helped boost the Dow Jones industrial average to a 38.32-point gain, the fifth-largest daily advance. The 2.1 percent rise in the average left it at 1,847.97. Details on Page E4.

Bond prices also shot upward, with some long-term government bonds rising three points, or $30 per $1,000 of face value. Corporate and municipal bond prices also rose, but by somewhat lesser amounts.

Analysts attributed the big rally to a growing belief by market participants that the recent string of weak economic statistics makes a cut in the Fed's 7 percent discount rate likely -- even if the West German and Japanese central banks do not agree to cut theirs at the same time, as they did early last month. The discount rate is the interest rate a central bank charges when it makes loans directly to financial institutions.

However, there were some indications that a discount rate cut may not come as quickly as the market seems to expect. It was not clear that the Fed is prepared to move if the foreign central banks do not, and they may not do so right away.

In Tokyo, Gov. Satoshi Sumita, head of the Japanese central bank, yesterday denied reports published there that he and Federal Reserve Chairman Paul A. Volcker have reached agreement to cut their respective rates. Sumita said that, at the recent meetings of finance ministers and central bankers in Washington, Volcker did not ask him to cut the Japanese rate and that he did not have the impression that the Fed chairman would trim the U.S. rate anytime soon.

Meanwhile, in Europe, the French Economics Ministry said in a statement that the recent decision by the French central bank to lower its key rate by half a percentage point "was in line with an international agreement between France and its major partners," who also will cut their rates in coming weeks.

However, in a telephone interview from West Germany, an authoritative official source flatly denied that there is any such agreement. "I find it astonishing that a government would issue such a public statement when it is not based on any agreement," the German official said.

These international considerations are important because Federal Reserve officials remain concerned that a renewed sharp decline in the value of the dollar could add to inflation later, and in the meantime make foreign investors less willing to put money in the United States that is needed to finance this country's large trade deficit.

A cut in the discount rate here that is not accompanied by lower rates in Germany and Japan might cause such a drop in the dollar, although the currency recently has not been declining as fast as it was even a few weeks ago.

In any event, financial markets have raced past the Federal Reserve and its current discount rate. Yields on short-term U.S. Treasury securities dropped yesterday to a point that was more consistent with a 5 1/2 percent discount rate than a 7 percent rate, analysts said.

Thus, the Federal Reserve Board could argue legitimately that it is only following the market if it cuts the discount rate, analysts said. With market rates already so low, a discount rate cut might not put much downward pressure on the dollar, they added.

Economic activity clearly is running below the pace many Fed officials anticipated for the first half of this year, partly because of the very sharp cutbacks in oil industry activity that have accompanied the recent big drop in crude-oil prices.

Oil futures prices fell yesterday by $1.27 to $11.43 per 42-gallon barrel in New York. The price decline was linked to a growing feeling that the current meeting of the Organization of Petroleum Exporting Countries in Geneva will reach no agreement to stabilize prices by cutting production.

The evidence of continued economic sluggishness mounted yesterday with the report from the Commerce Department that its latest quarterly survey of business intentions to invest in new plant and equipment shows such spending likely to be up only 0.9 percent this year, after adjustment for inflation. Although recent declines in interest rates could encourage businesses to increase their capital spending, the oil industry is rapidly cutting back its spending plans because of falling oil prices and a lack of cash.

A speech by Volcker late Tuesday afternoon in St. Louis encouraged traders in the government securities market and contributed to yesterday's rally. The traders were particularly cheered by his comment that "concerns about a resurgence of inflation seem to be receeding, rather than the opposite. That has helped set the stage for strong increases in both bond and stock prices, and interest rates have returned to their lowest level in many years."

The decline in interest rates has been little short of spectacular. For instance, on March 1, when the discount rate was still 7 1/2 percent, three-month Treasury bills were yielding about 7 percent. By yesterday, the yield had plunged to about 5 3/4 percent, while the discount rate was 7 percent.