As Wall Street traders cautiously predicted the beginnings of a summer rally, the nation's stock and bond markets surged broadly higher today amid speculation and prayer for lower interest rates.

The Dow Jones industrial average jumped 9.14 points to 814.12, bringing that barometer of stock market activity up more than 17 points for the week. Most of those gains came since lunchtime Thursday, when the DJI hovered at 789, just one point above its low mark for the year.

But the markets continued rallying today, picking up from where they left off yesterday. There were 1,118 advancing stocks on the New York Stock Exchange, while 367 declined.

Standard & Poor's index of 400 industrials picked up 1.44 points to 121.76, and S&P's 500-stock composite index added 1.30 points to 108.83.

Volume continued on the upsurge as trading reached 65.9 million shares, up from 63.2 million shares Thursday. Nationwide turnover in NYSE-listed issues, including trades in those stocks on regional exchanges and in the over-the-counter market, totaled 75.87 million shares.

The American Stock Exchange index was up 3.33 points to 248.50, with volume up from 4.18 million shares Thursday to about 4.7 million today.

On the over-the-counter market, the composite index rose by 1.27 points to 168.07, as the NASDAQ industrials were up 1.89 points to 192.57. Advancing OTC stocks outpaced declining issues by just under 3 to 1, although more than 70 percent of the issues there were unchanged.

"The market has been holding its breath and crossing its fingers for quite a long time now," said Leslie M. Alperstein, senior vice president and research director at Bache Halsey Stuart Shields Inc. "Everything seems to point to the OK sign. There are signs the recovery is upon us, and the market always preceeds economic recovery."

As federal borrowing rates fell, Chemical Bank lowered its broker loan rate to 15 1/2 percent from 16 percent, although the prime lending rate remained at 16 1/2 percent at the nation's money center banks. Quoted Treasury bill rates also dropped slightly, though not as sharply as Thursday, when rates for three- and six-month bills dropped by more than one-half percentage point.

The rally appeared to be broad, with across-the-board gains particularly in blue chip stocks. General Electric, for example, was up 1 1/8 to 65 7/8, and General Motors was up 5/8 to 44 7/8. But analysts such as William LeFevre, vice president for investment strategy at Purcell, Graham & Co. Inc., called the rally "more technical than fundamental."

Analysts also expressed concern about the overall state of the economy, which several said is likely to blunt a broad rally. LeFevre said he did not think the interest rates were set to drop significantly, and Alperstein warned that the "nonfinancial corporate sector is in the worst conditition it's been in since the 1930s."

Market analysts also continued to say that the market might rise through much of the summer, with Newton Zinder of The E.F. Hutton Group Inc. predicting that it will continue "to rally to mid-800 and then shoot down again" as part of a "sequential bottoming-out pattern."

Meanwhile, more than 1.5 million shares of Continental Bank stock were traded, leading the New York exchange, while a large trade in Washington Post stock resulted in trading of 808,000 shares to lead the American Stock Exchange.

The $3.7 billion increase in the nation's money supply resulted in more modest gains in the bond market, with corporate bonds up about one-half point.