By Doris Frankel

CHICAGO (Reuters) - Investors who believe LinkedIn Corp is overvalued after its explosive debut last week may get their first crack at proving that Friday, when options in the stock are set to be listed on U.S. exchanges.

The share price of the professional social networking company doubled in its first day of trading on May 19 after its initial public offering at $45.

The massive gain in shares early has some investors suggesting the stock will not be able to maintain that level if not for supply-and-demand issues holding up the share price.

"Supply just isn't enough to mount any kind of concerted short effort at this point. That's good for the stock," said Michael Quigley, technology analyst at Wedgewood Partners in St Louis.

With shares trading at $95.50, it is valued at about $9 billion, or more than motorcycle maker Harley-Davidson. LinkedIn's original IPO range valued it at about $3 billion.

But the small float -- just 7.84 million shares were sold in the initial public offering out of 94.5 million shares total -- means that the limited number of shares available for trade makes it difficult to borrow the shares to sell short.

"If it is hard to short, then the demand for options will be high since it's an easy way to have leverage for less capital," said Ryan Detrick, senior technical strategist at Schaeffer's Investment Research in Cincinnati, Ohio.

Underwriters, who have a large inventory of shares, are restricted from lending shares for 30 days. This also throws the expected supply-and-demand relationship out of whack.

"It comes down to a basic issue of supply and demand, and the supply of shares isn't enough for LinkedIn to be a safe long-term short," said Quigley.

That's not unusual for an IPO, but the sharp rise in LinkedIn shares may have whetted the appetite for bearish bets. It makes options more appealing for investors to speculate on price direction or hedge their risk in the shares.

"There will be a lot of put activity with speculators buying these contracts on the view that the IPO price was overblown," said Patrick Mortimer, director of options trading at stock and options block execution firm Pipeline Trading Systems.

Mark Sebastian, chief operating officer at OptionPit.com, an option education firm in Chicago, said the difficulty in borrowing shares could result in "huge amounts of conversion trading during the first few days of option activity."

Conversion strategies allow investors to create a "synthetic" short position against a real long position.

An investor would buy the underlying stock and offset this by buying a put and selling a call with the same maturity and strike price. The trader is then able to sell the real long position in the open market.

Not everyone sees a massive interest in put options. "I don't think that investors will necessarily be purchasing puts," said Joe Kinahan, TD Ameritrade chief derivatives strategist. "If the stock is hard to borrow, that will be priced in already because every time a market maker has to buy calls or sell puts he is going to sell stock as a hedge."

PAYING A PREMIUM

Premiums -- the price paid for options -- are likely to be high because of the anticipated volatility in shares. LinkedIn's share price hit an intraday high of $121.97 in its first day of trading.

When stocks are "hard to borrow," then put premiums also tend to be higher than normal because option market makers have difficulty completing reverse conversions -- the opposite of the "conversion" strategy investors use.

The Chicago Board Options Exchange, owned by CBOE Holdings Inc, Deutsche Boerse AG's International Securities Exchange and exchange operator NYSE Euronext plan to offer the options on Friday. Other exchanges are expected to follow suit.

(Reporting by Doris Frankel; additional reporting by Angela Moon and Ryan Vlastelica in New York; Editing by Andrew Hay)