Stock prices surged in early trading today, then levelled off for the rest of the day as investors digested the cut in the discount rate announced by the Federal Reserve Board late Thursday.

The Dow Jones Industrial Average of 30 major stocks closed at 892.69, up 8.84 points from Thursday's close. The Dow average was up 8.27 points in the first half hour of trading on the New York Stock Exchange, then bounced around that level for the rest of the day.

In the bond market--where prices rose early in response to both the Fed action and a sharp increase in the unemployment rate for November--prices sagged in late trading after the Federal Reserve announced a $900 million decline in the money supply.

William Sullivan of the Bank of New York said bond prices gave up most of the day's gains in the trading that occurred after the Fed's announcement at 4:10 p.m. of the weekly money supply data. He said investors had hoped for a steeper decline in the amount of cash and checking accounts in the economy.

Newton Zinder of E.F. Hutton & Co. said the increase in stock prices "basically was a response to the discount rate cut by the Federal Reserve." The Fed cut the interest it charges banks that borrow from it to reflect the recent sharp declines in interest rates. As the economy falls into a deeper recession, inflation is expected to subside and business borrowing is expected to decline. Both developments ease interest rate pressures.

Long-term rates such as those on corporate and government bonds also have declined. When rates decline, prices of bonds rise. Bond prices are sensitive to the outlook for inflation and interest rates. The bond market has been rising steadily for more than six weeks, although the continuing sensitivity of investors to inflation was pointed up by the decline in bond prices following the Fed's money supply announcement today. One week's figures are an unreliable guide to the future behavior of the money supply.

Trading was heavy on the New York Stock Exchange today. Nearly 55.4 million shares of stock changed hands compared with 43.8 million on Thursday. Nationwide turnover in NYSE-listed issues, including trades in those stocks on regional exchanges and in the over-the-counter market, totaled 65.05 million shares. The New York exchange's own index closed at 73.24, up 0.59 point on the day. Standard & Poor's index of 400 industrials rose 1.33 points to 140.99, and S&P's 500-stock composite index was up 1.14 points to 126.26.

The number of stocks that closed with higher prices on the New York exchange was about double the number that closed lower.

The American Stock Exchange market value index closed at 330.12, up 2.37 points. Roughly 5.3 million shares were traded on the Amex today compared with 4.25 million on Thursday.

The NASDAQ composite index for the over-the-counter market closed at 200.88, up 0.98 point.