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Shares in Aena, the world's busiest airport company, soared as much as 17 percent on Wednesday as the company listed on the Bolsa de Madrid, in Spain's biggest initial public offering (IPO) since 2007.

Aena owns multiple major airports across Spain, including in Madrid, Barcelona and the holiday resorts of Mallorca and Malaga, and claims to be the busiest airport company in the world by number of passengers. In December the company's airports handled some 12.3 million passengers. By comparison, the U.K.'s Heathrow airport handled an average of 6.1 million passengers per month last year, according to figures on the company's website.

Aena's 8.7 billion euro ($.9.8 billion) IPO on Wednesday was five times oversubscribed and shares jumped as high as 68 euros ($77) from the issue price of 58 euros.

A passenger looks out of the window at Aena-operated Barcelona-El Prat International Airport
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The company's CEO and chairman attributed the deal's success in part due to rising investor confidence that the Spanish economy was recovering.

"Our business is very much linked to the evolution of the domestic economy. What I have seen is that there is quite a strengthening confidence in the Spanish economy," CEO José Manuel Vargas Gómez told CNBC on Wednesday.

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The Spanish economy rebounded in 2014 to grow by 1.4 percent, after contracting by 1.2 percent in 2013. It is forecast by the International Monetary Fund to expand by 2.0 percent this year, above the euro zone average of 1.2 percent.

Gómez, who has chaired Aena since the start of 2012, said the Spanish economy had a "recognized competitive advantage."

He added that other attractions of the deal were the rarity value of a "global leader" coming to market, plus the fact that Aena had "quite visible" cash flow over the coming years.

Gómez also refused to rule out the chance of a future merger or acquisition.

"The company has already been expanding abroad; it has a number of positions abroad. We have to reconcile deleveraging and dividends for investors and M&A when we really find opportunities that make sense," he told CNBC.