Sears boasts more than 2,000 stores in its retail footprint, when accounting for both its Sears and Kmart nameplates. Amazon, on the other hand, only operates domestic fulfillment centers in 14 states.
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"What Eddie [Lampert, Sears CEO] gets in such a sale is a potentially profitable exit strategy that many analysts, myself included, believe he is pursuing," Lewis said. "This could fall nicely into Bezos' hungry little hands. Amazon might be able to cut an incredible deal, at least far less costly in time and capital, than building or leasing its own nationwide distribution centers/stores."
A Sears spokesperson said the company does not comment on speculation and rumors. Amazon did not immediately respond to a request for comment.
Sears shares rose about 12 percent to $37.60 on Thursday, after news broke that director Thomas Tisch bought 475,000 shares of the company.
Andrew Wilkinson, chief market analyst at Interactive Brokers, noted that not only are the shares moving, but there is some notable options activity as well, with indications of higher implied volatility, a key driver of options premiums. This could imply traders are betting on a change of ownership, he said.
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"There is a jump in implied volatility moving in the same direction as the underlying share price. There is call-option activity that was non-existent prior to today's share price move," he added.
"I would say options are pricing quite defensively here, so we've got sizeable positions, or action in May, or at the money," Wilkinson said. "Not only are shares rallying, but options are pointing to a greater chance of a sharp move up or down in the very near term."
According to Wilkinson, 16,000 contracts traded for Sears, most notably the May 16 expiration.
"A potential bid would [substantiate] that," Wilkinson said.