Trading on the New York Stock Exchange soared to a record 84.08 million shares yesterday and the Dow Jones industrial average rose about 16 points as financial markets around the globe reacted with an initial, sharp burst of optimism to the election of Ronald Reagan as the next American president.

However, there were some early hints that the apparent euphoria may be short-lived. As one analyst described it, "It was an ardent, if brief, honeymoon."

It won't take long for investors to realize that President-elect Reagan cannot stop the upward spiral of inflation and interest rates, said traders in Washington and New York. That may discourage small investors who were out buying blue chip stocks yesterday in what brokers said was unprecedented numbers.

Indeed, Dean Witter Reynolds chief analyst Robert Stovall forecast yesterday that the Federal Reserve Board will boost the discount rate from 11 percent to 12 percent in the next few days and that the prime lending rate of banks -- charged to the most credit-worthy businesses -- would jump to 15 percent on Friday, from 14 1/2 percent level that has lasted one week.

And, after the market closed, the government announced that $3.75 billion of 3 1/2 year notes sold at auction yesterday had a record 13.31 percent yield. (Story on Page B5)

But earlier yesterday, investors were caught up in post-election optimism, partly because so many persons were surprised by the landslide proportions of the GOP White House and Senate victories.

Stock prices surged on Wall Street in one of the most chaotic days in trading history. Sharp increases by energy and defense companies paced gains in all market indicators. Volume easily topped the old record of 8196 million of Oct. 10, 1979. Composite volume of nationwide trading of NYSE in all markets was a staggering 92.64 million. There were 1,210 advancing stocks on the NYSE and 424 on the downside, as the Dow Jones average of 30 industrial blue chips rose 15.96 to 953.16, after being ahead nearly 30 points in the early day.

The NYSE composite index rose 1.28 to 75.64 and Standard & Poor's 500-stock index rose 2.29 to 131.33. Most of the investor interest was in blue chip issues, with little attention to speculative stocks that have gained attention recently. The American Stock Exchange index was up a modest 0.06 at 338.81 as volume rose to 12.4 million shares from 7 million on Monday, while the NASDAQ composite index of over-the-counter stocks rose 2.88 to 196.03.

The Big Board volume leader was International Business Machines, up 1 7/8 to 68 1/2. Boeing, typical of the defense-aerospace group, jumped 1 7/8 to 38 1/2 even though it didn't trade until just before the market closed because of an imbalance in buy and sell orders. General Dynamics did not trade at all. United Technologies was up 3 7/8 to 56 3/8. Texaco, Gulf, Mobil and Atlantic Richfield were among the big oil gainers, each a dollar a share.

In the bond markets, prices soared in the first reaction to election news but subsequently fell to levels lower than on Monday. Bond prices move in the opposite direction of interest rates and short-term interest rates began to move higher yesterday. By the end of trading, according to the investment firm of Salomon Brothers, industrial and utility bonds were down 1 point in moderate trading while government issues also fell.

The rate for federal funds, which banks trade overnight among themselves, soared as high as 16 percent even though the Federal Reserve was active in the market by injecting funds from overnight purchase agreements. The Federal Home Loan Mortgage Corp. also had bad news on interest rates, reporting that the average yield of $11.3 million in mortgages it agreed to buy was 14.224 percent, up slightly from the week of Oct. 28.

Overseas, stock prices rose in London and Tokyo while the American dollar advanced strongly and gold prices were modestly higher. The dollar closed in London at 1.9420 German marks compared with 1.9133 late Tuesday as the U.S. currency had the biggest single-day gains since April.

Gold rose $11.50 a troy ounce to $657.75 in London but closed later in New York about $20 below that level.

Sharp, upward gains in the stock market have been the norm after most recent presidential elections; in the case of Carter, his Wall Street honeymoon period, with prices generally rising, lasted about two months.