Three academics say there was a bubble in LinkedIn Corp's shares during the first four days of its trading, which they have determined definitively using a model they designed.

The three have devised a model they say can establish in real time whether prices in a market are doomed to collapse.

If investors can spot speculative excess in short order, they can avoid overheated markets and better allocate their capital, said Cornell University finance professor Robert Jarrow, who wrote the paper along with Ecole Polytechnique's Younes Kchia and Columbia University's Philip Protter, both mathematicians.

If enough people think there is a bubble and not enough people want to hold it, maybe the bubbles will disappear before they get too large, Jarrow told Reuters.

The model, described in a paper currently being peer-reviewed for publication, compares the size of price fluctuations, known as volatility, with the volatility of a normal stock, which is a stock whose price is what you would pay if you held it forever. If the volatility in the stock you are testing is higher than that of a normal stock, there is a bubble.

Take social networking company LinkedIn Corp, for example.

The company's shares more than doubled on their first day of trade on the New York Stock Exchange and closed on May 24 -- the fourth and final day of trade run through the model -- at still more than double their IPO price.

The shares have since given up some of their gains, but closed on Wednesday, after just 9 days of trading, at more than 70 percent above their IPO price.

Some people would intuitively argue that the speedy share gains indicate a bubble. But the model can prove it: it shows that as LinkedIn's stock price increased, the rate of increase of volatility was abnormally large.

The model has been successfully tested against some of the stocks believed to have been bubbles in the 2000 to 2002 dot-com era, according to the paper.

HELP FOR THE FED

Investors aren't the only ones who stand to benefit from knowing when bubbles are arising. The Federal Reserve could use its regulatory power to tighten rules for lending in markets that seem to be overheating.

Federal Reserve Chairman Ben Bernanke noted in Congressional testimony in 2009 that it is extraordinarily difficult to tell in real time when a bubble is arising, echoing statements from former Fed Chairman Alan Greenspan.

The issue even came up, recently, in relation to LinkedIn.

When LinkedIn shares jumped 109.4 percent on their first day of trade, Chicago Fed President Charles Evans said he was withholding judgment over whether a new dot-com bubble was under way.

I have no way of knowing that those aren't just exactly the right valuations, Evans told reporters after a speech in Chicago. (Additional reporting by Jennifer Saba; Editing by Dan Wilchins and Muralikumar Anantharaman)

Ben Bernanke