Stock prices soared today as investors waxed euphoric over recent big takeover attempts of major natural resource companines.

The 22.15-point climb in the Dow Jones industrial average -- its biggest one-day climb in 1981 -- also was helped late in the afternoon by Chemical Bank, which announced it would cut its prime lending rate to 17 1/2 percent from 18 percent. Most banks, including Chemical, cut their prime rates one-half point to 18 percent on Tuesday, and today's cut was unexpected because of its swiftness.

The Dow average of 30 industrial stocks, the most-closely-watched indicator of stock market activity, finished the day at 989.82. Volume on the New York Stock Exchange rose sharply. More than 55 million shares changed hands today, compared with 47.4 million on Wednesday.

But even today's volume is well below the 70-million-share days the market registered regularly in the first few weeks after President Reagan's election last November.

"I look for 20 million shares to be traded in the first hour tomorrow [Friday]," said Larry Wachtel of the big brokerage firm, Bache Halsey Stuart Shields Inc.

He said that expensive takeover attempts by Standard Oil of California (which wants to buy Amax) and Joseph E. Seagram & Sons (which is trying to acquire St. Joe Minerals Corp.) caused many investors to believe that stock prices, especially among companies that own raw materials, are too low.

"Here are assets for which they are paying an enromous premium," Wachtel said. "And two companies are saying the offers are not adequate."

On Wednesday, Seagram's offered to pay $45 a share, about three times St. Joe's book value of $16.50 a share, or about $2 billion. St. Joe's, a leading lead producer, said the offer was inadequate. Federal officials are looking at a surge in trading activity Tuesday in both stocks and options in St. Joe's minerals.

St. Joe's closed today at $47.50 a share, and some analysts think another, higher bid will be forthcoming.

Last week, Standard Oil of California for a company, to buy Amax Inc., a major metal producer. Socal said it would be willing to pay about $78.50 a share for Amax. Amax was trading at about $38 at the time.Amax also rejected the bid as too low.

Today Amax closed up $1 to $57 a share, while Socal rose $2.375 to $43.125 a share.

Today, after the market closed, Standard Oil of Ohio announced it had reached agreement with Kennecott Corp. to acquire the copper producer for about $1.7 billion, or $62 a share. Kennecott had been trading at about $27 a share.

While oil and natural resource companies were the early leaders in stock market performance today, their strength spread to nearly all other areas, including chemical companies, transportation companies and retail corporation.

Nearly 1,200 stocks on the New York Stock Exchange closed higher in price, while 348 declined. The NYSE index of its stocks closed up 1.73 points to 76.26.

Standard & Poor's index of 400 industrials was up 3.75 points at 151.11, and S&P's 500-stock composite index gained 3.24 points to 133.19.

On the American Stock Exchange, the index closed up 7.04 points to 343.43. Amex volume was 5.6 million shares, up from Wednesday's 4.4 million shares Wednesday. The Amex reported that 409 shares rose in price, while 185 fell.

The NASDAQ composite index for the over-the-counter market closed at 76.27, up 1.74 points.