Financial markets were staggered yesterday by the announcement that Paul A. Volcker would step down as Federal Reserve Board chairman and that economist Alan Greenspan would be nominated to succeed him.

But before the sessions was over, stocks recovered about half of their extreme losses, with the Dow Jones industrial average down 10 points after sagging 22 points in earlier trading.

The bond and foreign exchange markets sold off sharply, reflecting uncertainty on how quickly Greenspan would be able to show he is an effective and independent chairman of the Federal Reserve. The dollar fell from Monday's close of 145 yen to 141.20 yen, and from about 1.815 to 1.795 German marks.

In the bond market, the bellwether 30-year Treasury bond, which was at 100 1/2 -- or $1,005 for each $1,000 of face value -- just before the White House announcement, tumbled to 98

/ , as the yield rose to 8.92 percent from 8.71 percent. Corporate and municipal bonds also suffered sharp losses.

The Dow industrial average closed at 2278.22, with declining issues leading advancers by a 3-to-2 margin. The New York Stock Exchange composite index fell 0.71 to 162.77, and the price of an average share fell 17 cents. Big Board volume was 153.36 million shares, up from 149.34 million Monday.

"The bond and foreign exchange markets will want to take their measure of the man, and that won't be done overnight," said Goldman Sachs Vice President Robert Hormats. "But I suspect as they learn about him, the markets will develop more confidence in him."

Salomon Brothers chief economist Henry Kaufman added in a telephone interview: "If you ask me, 'If not Paul, who?', I would say 'Alan Greenspan.' But there's a difference. Paul's independence is never in question. For the time being, Greenspan's independence will be questioned, and that means closer scrutiny by the marketplace."

One positive effect from a financial market viewpoint, some observers said, is that Greenspan will be closer in tune with the administration's effort to promote deregulation than was Volcker.

A negative reaction in the markets had been widely anticipated as a response to a change in leadership at the central bank -- and in fact was advanced as an argument for retaining Volcker.

Ironically, the Federal Reserve had to intervene yesterday to prevent a further collapse in the exchange rate markets triggered by the resignation of its chairman. In Paris, trading was suspended for the first time since a false 1982 report that President Reagan had suffered a heart attack.

But at the end of the day, traders seemed gratified that the decline had touched off no panic. "The unthinkable has happened and the world continues to turn," said Dreyfus Corp. research director Monte Gordon. "The king is dead, long live the king. That's the way people are thinking."

The Volcker decision apparently came as a surprise to many market participants, despite widespread reports that the president might make a decision before next week's economic summit to remove uncertainties. There had been a series of published reports that the administration, earlier opposed to reappointing Volcker for a third term, was ready to do so because of global worries about debt and currency exchange rates. But the appointment, in the end, depended on Volcker's willingness to stay.

Some market analysts believe that the White House did not give Volcker the kind of assurances that would have induced him to stay on. For example, Jim McNeill, a Marine Midland bank economist, said that Volcker's withdrawal is "very bearish" for the dollar. "Everybody knows Volcker was offered the job, and he's turned it down. That means he probably wasn't given the correct support to do his job properly."

The administration said it had sought to persuade Volcker to stay on and Volcker himself said there were no monetary policy differences between him and the administration.

Treasury Secretary James A. Baker III predicted yesterday that the markets' initial bearish reaction to the change at the Fed will not continue "for a sustained period of time." He said the message to be taken from the appointment is that the United States' "fight against inflation is a commitment that is enduring; it is going to continue."

Greenspan, appearing with Volcker in the White House press briefing room, stressed that "under Paul's chairmanship, inflation has been effectively subdued. It will be up to those of us who follow him to be certain that those hard-won gains are not lost. Assuring that will be one of my primary goals."

The main question raised among financial experts about Greenspan is his relative lack of experience in international debt and money management.

"Alan, as chairman of the Economic Council under {President} Ford, was an economic adviser, but now he will have to be up-front as a decision maker," said Kaufman.