How much art is stockpiled in the 435,000 square feet of the Geneva Freeport? That’s a tough one. The canton of Geneva, which owns an 86 percent share of the Freeport, does not know, nor does Geneva Free Ports and Warehouses, the company that pays the canton for the right to serve as the Freeport’s landlord. Swiss customs officials presumably know, but they aren’t talking. Suffice it to say, there is wide belief among art dealers, advisers and insurers that there is enough art tucked away here to create one of the world’s great museums.

“I doubt you’ve got a piece of paper wide enough to write down all the zeros,” says Nicholas Brett, underwriting director of AXA Art Insurance in London, when asked to guess at the total value of Freeport art. “It’s a huge but unknown number.”

The number is about to grow. At the Freeport, construction has begun on a new, 130,000-square-foot warehouse that will specialize in storing art. It is scheduled to open at the end of 2013.

In the coming years, collectors and dealers will also have a variety of other high-security, customs-friendly, tax-free storage options around the world. Luxembourg is building a 215,000-square-foot freeport, scheduled to open in 2014 at its airport. In March, construction began on the Beijing Free Port of Culture at Beijing Capital International Airport.

There has also been talk of doubling the size of the freeport in Singapore, a gleaming, high-tech operation that is so sleek it’s hard to believe a “Mission: Impossible” sequel hasn’t been filmed there. It opened in 2010, next to Changi airport, and caters to Asian collectors who are ferried in white limos from the tarmac to the warehouse.

THIS construction boomlet is a novel way to gauge the art market’s strikingly swift recovery from a precipitous fall in 2008, when sales at auctions, the industry bellwether, shrank in the aftermath of the Great Recession. Global sales in 2011, both at auction and in private deals, were estimated at $64.1 billion, according to Clare McAndrew, an art economist, That total is just shy of the record high of $65.8 billion set in 2007 — and well ahead of the 2009 trough of $39.4 billion.

At the high end, some works are fetching prices that far exceed the heights of five years ago, when the phrase “art market bubble” was commonplace. In June, Christie’s sold a 1981 painting by Jean-Michel Basquiat for $20.1 million, a record for the artist at auction and a figure that far surpassed the $14.6 million it sold for five years ago at Sotheby’s. The same month, “Blue Star,” by Joan Miró, sold at Sotheby’s for close to $37 million, more than double the sum it earned at auction in Paris in 2007.