Stock prices continued to rise today during the third-heaviest trading day in the history of the New Ork Stock Exchange.

The 3.93-point gain in the Dow Jones industrial average capped a week in which that heavily watched barometer jumped 53.93 points. The average closed the week at 986.35, the highest it has been since Jan. 10, 1977.

Jerry Hinkle, the chief trader at Sanford C. Bernstein & Co., said that, barring an unforeseen development, the Dow average could cross the magical 1,000 barrier early next week, a level it has not reached since New Year's Eve 1976.

Investors have become excited about stocks because they feel that interest rates have reached peak and will decline soon.

After the stock market closed today, the Federal Reserve Board announced that it had boosted its discount rate -- the interest it charges member banks that borrow from it -- to 12 percent from 11 percent. Hinkle said that investors long have anticipated a discount-rate increase -- in large part because interest rates in the open market are much higher than 12 percent -- and today's increase should not dampen investor enthusiasm.

By only increasing the rate to 12 percent when a much higher discount charge could be justified, the Federal Reserve seems to be saying that it, too, expects interest charges to come down. Because Federal Reserve policy is one of the chief determinants of the level of interest rates, investors might take the small discount-rate increase as an encouraging development.

However, if the economy is headed into another slide, as many economists believe, the strong rally in the stock market will be pinched some time in the future. Economic downturns result in lower corporate profits, which in turn usually hurt stock prices.

About 72.1 million shares changed hands on the floor of the New York Stock exchange today.

On Nov. 5, the day after Ronald Reagan was elected president, 84.3 million shares were traded -- the biggest one-day volume in history.

Individual investors fueled the rally most of the week, although big institutional investors such as pension funds were major participants Thursday and today.

A midafternoon surge in stock prices was cut short as many investors decided to sell and take some of the profits they had realized during the week. At 2:30 p.m. the Dow average was up 8.96 points.

The number of stocks closing higher topped the number closing lower, 855 to 700.

Texaco led the active list, up 1/2 at 44 3/8 on a volume of close to 1 1/2 million shares; Mobil gained 1 1/2 to 79 1/2; Occidental Petroleum 3/4 to 33 3/8; Conoco 1 5/8 to 70 3/8; Exxon 1/2 to 82 3/4; and Superior Oil 3 to 211.

Mobil reported good results from a well off the coast of Newfoundland.

The day's biggest losers were Jefferson National Like Insurance, which fell 18 to 48 bid, and Jefferson Corp., owner of about 27 percent of Jefferson National Life, which lost 12 3/4 to 28 bid, in the over-the-counter market.

A swiss company dropped its previously announced plans to acquire Jefferson National for $73 a share.

The American Stock Exchange market value index was up 4.04 points to 352.21. On the Amex, 344 issues gained in price while 316 declined.

Hinkle said that investors also have been heartened by the prospects of a tax cut next year that would give incentives to both businesses and investors.

Another factor that helped boost stock prices was the large number of stock traders who were "short" this week -- that is, had commitments to sell stock they did not own. As prices rose, the so-called shorts bought stock to cover what they owed (before prices went up further). That buying action pushed up prices even more.