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Watch Art Cashin: Stable oil prices support market

Art Cashin, UBS director of floor operations at the NYSE, said as long as oil remains above $82, it is supportive of the market.

Stabilization in oil prices, calmed Ebola fears and expectations the Federal Reserve will maintain its dovish, easy-money policy stance have all led to a decent recovery in stocks the past three days after last week's volatile action.

The CBOE Volatility Index, which is a gauge of market volatility, is down four straight sessions, tumbling 36 percent in that time frame after hitting a nearly three-year high Wednesday.

"The stable crude is really amazing," Cashin said. "That's keeping the markets very happy."

Read MoreWatch Art Cashin: Oil below $80 may cause selling

WTI crude oil tanked to a two-year low last week, dipping below $80 amid over supply, ebbing demand and a rising U.S. dollar. Oil does not usually drive the market, but falling prices highlight broader concerns about deflation, or declining prices.

"On the not-quite-as-contagious Ebola front, the airlines are flying again," Cashin noted. "They [traders] figure people will be flying."

Airlines, and transportation stocks in general, have led the market rebound since major averages bottomed Wednesday. Delta Air Lines and United Continental, for example, are up 14 percent over the past four sessions.

Read MoreWatch Art Cashin: Be wary of Ebola's effect

The Fed meets next week and market watchers are questioning whether it will remove a key phrase that says it will keep the Fed Funds Rate low for a "considerable time" as concerns about global growth heightened last week.

"This is a perfect opportunity for them to take that out," Cashin said. "They've had some internal discussion."

Stocks, which have benefited from the Fed's easy-money policy, jolted last week after St. Louis Fed President James Bullard said the Fed should consider prolonging quantitative easing, or QE, beyond the October meeting. Most market observers do not expect an extension of QE past October; however, they anticipate guidance may change on timing of a rise in rates.