Wall Street turned in another stunning finish Thursday and extended its unprecedented streak of volatility — this time, to the upside — with the Dow Jones industrial average making a 780-point swing during the session.

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NEW YORK — Wall Street turned in another stunning finish Thursday and extended its unprecedented streak of volatility — this time, to the upside — with the Dow Jones industrial average making a 780-point swing during the session.

The Dow closed up 401.35, or 4.7 percent, at 8,979.26, after falling 380 points in the opening minutes of the session.

Microsoft, one of the 30 Dow stocks, gained $1.53, or 6.8 percent, to close at $24.19 a share. Boeing, also a Dow stock, soared $2.46, or 5.8 percent, to $44.79.

Broader stock indicators also were higher. The Standard & Poor’s 500 index gained 38.59, or 4.3 percent, to 946.43, and the Nasdaq composite index rose 89.38, or 5.5 percent, to 1,717.71.

It is clear that investors are reacting in the extreme to negative economic news, including disappointing numbers Thursday on industrial production. But traders are also reacting to the market’s declines, and were piling in to buy late in the session.

Analysts expect this extraordinary volatility to continue, and warned that just as Monday’s huge 936-point surge in the Dow was overdone, there was little reason to trust that Thursday’s gains would hold.

“I don’t think the markets have a clear sense about the economic environment as of yet. They’re clearly nervous,” said Subodh Kumar, global investment strategist at Toronto-based Subodh Kumar & Associates.

Kumar said the volatility buffeting the markets reflects investors tinkering with their portfolios to match their more sober take on the health of the economy and some investors simply cashing out. That means some vehicles, such as mutual funds and hedge funds, are entering a market already short on buyers and being forced to sell.

Wall Street’s fear gauge rose to a record level Thursday. The Chicago Board Options Exchange Volatility Index, known as the VIX, rose to an all-time intraday high of 81.17, its first-ever move over 80, before settling at 67.25. The VIX, which usually trades below 50, tracks options activity for the companies that make up the S&P 500.