When will the real estate market make a comeback? Well, it seems that the Blackstone Group (BX) thinks it is already happening. The firm has won a bid for 588 U.S. shopping malls. The price tag? A cool $9.4 billion. In fact, the auction was heated, involving other top real estate investors like Starwood Capital.

The seller is Centro, which is based in Australia. The company has been trying to pare down its debt load since the financial crisis hit in 2008. After the sale of the assets, Centro will be left with 112 malls.

Only a year ago, the belief was that the private equity world was doomed. But as is common in the financial markets, this was big exaggeration. If anything, private equity firms have shown that they can adapt quite well.

Just look at KKR (KKR). In its latest quarter, the company posted a profit of $180.6 million or $0.86 per share. The consensus estimate was for $0.42 per share.

But private equity firms like to point to another metric: economic net income, which focuses on fees and gains from investments. This came to $714.6 million in the quarter. Yes, the private equity game can be wildly profitable.

Betting on the outcome of a buyout is no easy feat. Will there be a heated auction? Or will the bidders have doubts and want price concessions?

The result is often much volatility. Just look at Beckman Coulter (BEC), a top medical diagnostic instruments company. In early December, the company put itself up for sale and the stock price surged to $72. Since then, the shares have traded in band of $71 to $75.

Sara Lee (SLE) has rejected an offer from a group of private-equity firms that includes Bain Capital, Apollo Management and TPG Capital, the New York Post reports. Overall option implied volatility of 20 is below its 26-week average of 24, according to Track Data, suggesting decreasing price movement.

PepsiCo (PEP) is expected to report Q4 EPS on February 10. Overall option implied volatility of 17 is near its 26-week average, according to Track Data, suggesting nondirectional near-term price movement.

Options Update is by Stock Specialist Paul Foster of theflyonthewall.com.

For private equity firms, there was much anticipation of the Nielsen (NLSN) IPO. These funds spent huge amounts from 2002 to 2007 on buyouts and they want to get some liquidity, as well as pay down debt.

Well, based on today's trading, private equity firms should definitely be optimistic. Nielsen priced its IPO at $23, which was above its $20 to $22 price range (raising about $1.9 billion). The stock is now up to $25. In fact, this is the biggest private-equity IPO since 2006.

As the economy rebounds and credit markets warm up again, it looks like private equity firms are going back to work -- on big deals. According to Bloomberg.com, Apollo Global Management is prepared to offer $12 billion for Sara Lee (SLE). The transaction would also include investor C. Dean Metropoulos -- who bought Pabst Brewing in 2010 -- as well as Bain Capital and TPG.

It looks like this is a viable offer even though a strategic buyer is interested (which often can justify a higher valuation). This is JBS SA, a beef processor based in Brazil. An acquisition would certainly have lots of synergy, creating a vertical operation. Interestingly enough, JBS may seek the help of the Blackstone Group (BX).

Monday morning, the publisher of iconic adult magazine Playboy (PLA) announced that it will take the company private, thanks to a "sweetened offer" from the magazine's founder Hugh Hefner. The offer of $6.15 per share represents an 18% premium from the stock's Friday close. The total offer values the company at $207 million. Back in July, Hefner's Icon Acquisition Holdings LP offered $5.50 per share.

Playboy has had other offers, including an offer of $210 million from rival Penthouse magazine. That said, Hefner is Playboy's largest shareholder with roughly 70% of the company's voting shares and 28% of the company's nonvoting stock. Hefner noted that the "agreement will give us the resources and the flexibility to return Playboy to its unique position and to further expand our business around the world."

Since early September, shares of the major private equity firms Blackstone Group (BX) and KKR & Co. (KKR) have seen strong gains. Of course, part of the reason has been the bull move. But at the same time, the prospects for private equity are looking brighter. In fact, the upcoming year is shaping up to be strong for public offerings.

According to a report from Bloomberg.com, it looks like private-equity backed deals will account for roughly half the volume. And they will generally be massive transactions. Some that are on deck include HCA Holdings, Nielsen Holdings and Kinder Morgan.

Over the past week, the medical diagnostic instrument market has heated up. On Friday, there was a report that Beckman Coulter (BEC) was seeking a buyer. On the news, the shares spiked 27%

Now there may be another deal. Genoptix (GXDX), which develops cancer testing equipment, appears to also be on the selling block. It looks like the process is in its early stages.

Beckman Coulter (BEC), a top medical diagnostic instruments company, has been public over 20 years. But it looks like its days of independence may soon be over. According to a report in the Wall Street Journal, Beckman is in the process of selling itself. So far in today's trading, the shares are up 27% to $72.57, with the market cap at about $5 billion.

Beckman's products span many categories like biomedical testing and lab automation. The installed base is roughly 200,000. In fact, a large portion of the revenues come from recurring sources (such as refilling supplies for the machines). In other words, Beckman has sturdy cash flow stream.

J. Crew Group (JCG) was nearly 17% higher Tuesday morning thanks to rumors of a potential buyout.

The Wall Street Journal (subscription required) reported that a pair of private equity firms are closing in on a deal to purchase J. Crew for $43.50 per share cash, or $3 billion. One of the potential new owners is TPG Capital, a former owner of the company. TPG would hold a 75% stake in the company, with LA-based Leonard Green & Partners owning the remaining 25%. TPG previously owned an 88% stake in JCG in 1997.

Early Monday morning, trading was halted on Gymboree (GYMB) after an announcement that Bain Capital Partners would acquire the children's clothing company. Reportedly, the definitive agreement calls for Bain to pay $65.40 per share for Gymboree, or $1.8 billion.

According to the terms of the agreement, Gymboree stockholders will receive $65.40 cash for each outstanding share of Gymboree common stock owned. This price is a 57.4% premium to Gymboree's share price on September 30, 2010 -- the date that takeover rumors began. And the $65.40 is a 23.5% premium over Friday's closing price of $52.95.

ResCare (RSCR), which provides health services to the disabled, are up about 6% on Tuesday morning trading thanks to a sweetened buyout deal. The company got a $370 million buyout offer in mid August by Canadian private equity firm, Onex Corp.

After some negotiation, the parties came to an agreement this week; that is, a deal that is $14 million higher.

Back in 2002, Burger King (BKC) went private in a $1.5 billion deal (at the time, the food chain was owned by Diageo PLC). Then in 2006, the company came back to the public markets, providing a nice return for the private equity sponsors, which included TPG Capital, Goldman Sachs Capital Partners and Bain Capital.

OK, so how about going private again? Actually, this is the latest rumor making the rounds. Although, it sounds like the negotiations are in the early stages.