NEW YORK (TheStreet) -- Stocks are rising Wednesday now that oil prices have started to recover from falling below $50 per barrel. As long as oil prices stop dropping 4% per day, the stock market should  be able to stabilize, said Jon Najarian, co-founder of optionmonster.com and trademonster.com, on Wednesday's CNBC "Fast Money Halftime" show. 

If oil is done with those types of trading sessions, at least for the foreseeable future, then a short-term bottom may be in for equities, he added. Lower energy prices are good for the economy and most businesses, as well as the U.S., Chinese and Indian economies. 

The stabilization in oil prices has allowed investors to refocus on good news, such as analyst upgrades and the solid retail sales numbers released earlier in the day, said Pete Najarian, co-founder of optionmonster.com and trademonster.com. He used the recent weakness to buy shares of JPMorgan Chase  (JPM - Get Report) . 

The low in oil is at $46.83 per barrel, pointed out Joseph Terranova, chief market strategist for Virtus Investment Partners. The correlation between stocks and oil needs to abate in order for equities to move higher. While Terranova believes oil prices are headed lower, he did acknowledge the decoupling of stocks and oil is possible, as crude prices continued to decline in December while stocks rallied. 

While it's good to see the market rally, it's doing so without a whole lot of conviction, argued Josh Brown, CEO and co-founder of Ritholtz Wealth Management. Key momentum stocks such as Netflix (NFLX - Get Report) , Amazon (AMZN - Get Report) , Google (GOOGL - Get Report) and Priceline (PCLN) are all in negative territory, he noted.

There could easily be more downside ahead for the broader markets, Brown added, as the S&P 500 is only about 3% off of its all-time high. Junk bonds and financials continue to show weakness, while consumer discretionary stocks, which are supposed to benefit the most from lower energy prices, should be higher on the day. 

Oil still looks like it's headed lower, said Michael Harris, president of Campbell & Company. He has been short oil now for nearly a year and thinks the break below $50 per barrel, a key psychological level, paves the way for $40 oil. That price is an important level that has acted as support several times in the past 15 years. The Middle East is not worried about oil prices at this time, while a lot of traders are remaining cautious and are waiting for a bottom to form in oil before getting long, he said. 

One thing investors should watch is the rig count, according to Terranova. In 2009 oil didn't rebound until the rig count dropped. Last year at this time the rig count stood at 1,378. Currently, the count is over 1,400, he said. In order for oil prices to go up, production -- and thus the number of rigs -- has to go down. Preferably, a count below 1,000 would be ideal. 

Robert Peck, an analyst at SunTrust Robinson Humphrey, still thinks former Yahoo! (YHOO) interim CEO Ross Levinsohn should be the new CEO of Twitter (TWTR - Get Report) . On Tuesday's "Fast Money Halftime" show, Levinsohn didn't entertain the idea of becoming the next CEO but did say Twitter should acquire Yahoo!, which would combine to make a "very powerful" duo. 

Peck agreed, saying after Yahoo! spins off Asian assets Alibaba  (BABA - Get Report)  and Yahoo! Japan the core business would be worth about $9 billion. With a premium, Twitter would likely have to pay $12 billion for Yahoo!, which it could do with a combination of cash and stock or debt. Combining the two companies would make sense, Peck said, given the synergies between media, video, mobile, search and user base. 

John Chen, CEO of BlackBerry (BBRY) , said the demand for his company's Classic smartphone "looks pretty good" so far. However, his attention is on the "Internet of things," where everything from the connected car,to health data to "smart" features in a home will need to be on a private and secure network. BlackBerry, known for its secure network solutions, could be in prime position for this market. Chen said it will take "a little while," but not too long ,before those revenue start to boost the top line. 

For their final trades, Pete Najarian is buying PepsiCo (PEP - Get Report) and Jon Najarian is a buyer of Juniper Networks (JNPR - Get Report) . Brown is buying TriNet Group (TNET - Get Report)  and Terranova said to watch Exco Resources (XCO) as a tell on where energy junk bonds may be headed. 

-- Written by Bret Kenwell 

Follow @BretKenwell

This article is commentary by an independent contributor. At the time of publication, the author held a position in GOOGL.