Shares of the embattled London-based oil company bounced back Thursday, as BP said it doesn’t know why its stock went into free fall a day earlier and Wall Street analysts agreed as they often do that now is not the time to panic.

Among the BP (BP) boosters was Bank of America Merrill Lynch analyst Alejandro Demichelis, who rates the stock buy with a $49 price target. He said Wednesday’s 16% plunge, which took BP to a 14-year low at $29 and change, represented the long-awaited “market capitulation.”

BP shares tumbled Wednesday, as Fortune reported an oil industry guru predicted the company’s bankruptcy and investors worried about mounting cleanup costs. Some concluded BP would have to eliminate its dividend under congressional pressure.

But Demichelis doesn’t buy that notion. He put the cost of cleaning up the Gulf of Mexico spill at $28 billion and said BP, whose annual pretax profits in recent years have ranged from $26 billion to $36 billion, has the financial flexibility to “maintain its annual dividend — albeit with potential changes to quarterly profile.”

That is, BP could keep paying a dividend, though one substantially lower than the $10 billion annual rate shareholders have gotten used to.

Another factor perhaps involved in Thursday’s revival is that the plunge yesterday took the stock down within a few beats of a key technical level.

Looking at BP’s share price in London, CMC Markets strategist Ashraf Laidi notes that Wednesday’s retreat means the stock has given back more than three-fifths of its 1992-2006 rally — nearly completing the technically huge and all-important so-called Fibonacci retracement.

Should the stock hold its recent gains, a rally could be ahead, he writes in a note to clients.

“Bulls will want to see the this level hold for the week, which could see a subsequent bounce back,” Laidi said.

Thanks to Fortune’s Scott Cendrowski for the bit on the BofA Merrill guy.