According to reports in the Japanese media, American and British intelligence agencies are also involved.
Yesterday Axa, the French insurance group that will have to pay out hundreds of millions of pounds for the damage caused by the terrorists, asked the French stock market regulator to find out whether its shares had been sold by people connected with the attacks.
The financial watchdogs will examine whether there were any other unusual movements in the share prices of companies directly affected by the attacks, which would suggest that "short selling" took place.
This practice allows investors to sell shares that they do not own in the hope that the stock will fall in value in the future, so they can buy it at a lower price and pocket the difference.
Short selling is not illegal but doing it on the basis of insider knowledge is.
The idea that bin Laden or his network speculated on the stock market ahead of their assault on America is considered to be far-fetched by most experts but others were taking it seriously.
Italian Defence Minister Antonio Martino said: "I don't think it would be exaggerated to think that the terrorist organisations were among those who speculated on international markets."
A report in an Italian newspaper, Corriere della Sera, said that the multimillionaire bin Laden had played the stock market before, using an unidentified Milan broker.
In Europe, speculation that short selling was carried out by people with prior knowledge of the terrorist attacks has centred on Munich Re, which stands to pay out £630 million ($2.2 billion) because of the New York catastrophe.
The attacks triggered a fall of about 15 per cent in the value of Munich Re shares.
Sabine Reimer, a spokeswoman for Germany's federal securities regulator, said it was looking at the possibility of share price manipulation as part of its regular monitoring of the market.
If terrorists did speculate on shares, it is likely that they would have used frontmen and gone through many different brokers to cover their tracks.
Britain's Financial Services Authority began investigating the possibility last Thursday.
"It is incumbent on us to look into this," an FSA source said. "But it is like looking for a needle in a haystack."
Kimberly McCloud, research associate at the Monterey Institute of International Studies in California, said: "Based on what we know about how bin Laden handles his money through different organisations, he probably is sophisticated enough to do something like that."
Steven Emerson, who heads the Investigative Project, a counterterrorist research institute in Washington, said Bin Laden had several astute financial advisers.
"Do they have the capability of selling short? That's pretty sophisticated," he said.
"On the other hand, I have no doubt that he has access to people who could that. His network is more than just crude, gun-toting terrorists. It includes some very sophisticated people."
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