The price of gold, which has both soared and sagged in frenzied world markets this week, moved in both directions again today in nervous trading, finally closing in New York at $384.10 an ounce, up $8.40.

The markets were buffeted by a rumor that newly appointed Federal Reserve Board Chairman Paul A. Volcker had resigned -- a rumor denied vehemently by the Fed -- as well as continuing speculation that the United States was ready to announce a major package to support the dollar.

The dollar, for its part, weakened yesterday against most major currencies.

Foreign exchange traders said that trading in the dollar and other currencies was light, as no one seemed willing to take positions over the weekend because of rumors of a new administration package.

White House officials have no comment on whether a new dollar rescue plan is in the works.

New York analysts say that if the administration does not have a weekend announcement, the price of gold can be expected to rise again and the dollar would be weakened.

Gold trading all week was wild. Gold prices rose sharply Monday -- finishing above $400 for the first time in history -- and skyrocketed to more than $440 an ounce Tuesday when the first serious rumors of a U.S. dollar rescue plan surfaced. Then the gold boomlet turned into a bust.Gold closed Thursday in New York at $376 an ounce.

Traders believe that the package will contain a sharp increase in gold sales by the U.S. Treasury, among other things. A sudden, big increase in the supply of gold would depress the price, which has been bid up, at least in part, by hoarding.

"There is an absolute shortage of physical gold," said Andre Sharon of Drexel Burnham Lambert. "That's why the price is through the stratosphere. The price is totally unsustainable, assuming normal conditions."

Sharon said that if the frenzy died down and normal conditions asserted themselves, the price of gold would be about $250 an ounce.

However, Sharon said, if the administration does not come up with a package that is perceived to be strong enough, gold prices will shoot up again.

"The price is in a vacuum, with no reference. Either it will come tumbling down, or it will push through the stratosphere for good," he said.

When trading began in London today, there were still more sellers than buyers, and the price fell from Thursday's close of $384 to $367.50. But then the price began to move up again. By the afternoon fixing, the price was $385 an ounce, about where it closed today on the New York Commodity Exchange.

Other metals markets responded to the rebound in gold prices today, as they fell along with gold earlier in the week.

Copper closed up 2.8 cents a pound, at $1.017 and silver closed up 62 cents an ounce, at $15.92. While most of the focus has been on gold prices, which are nearly $200 higher than a year ago, silver prices have been rising even faster than gold.

In the nervous foreign exchange markets, the dollar fell against the West German mark and the Swiss franc, although analysts said the weakening did not reflect any new distaste for the dollar.

"That will come if the Carter package is too weak," one New York analyst said.

The dollar closed in Frankfurt at 1.7580, down from 1.7615 the day before. In New York it finished slightly lower at 1.7566 marks.

The dollar could buy 1.5785 Swiss francs today. Thursday it was worth 1.5850.

The dollar gained strength in Tokyo, however, and improved against the British pound.