Billionaire Hiroshi Mikitani, Japan's fourth-richest man, is building a house in central Tokyo that is estimated to cost at least ¥2.3 billion, underscoring a shortage in the city's luxury housing market.

The two-story house is on an 880-sq.-meter site in an exclusive neighborhood in Shibuya Ward, according to a registration filing with the Legal Affairs Bureau. Land prices in the neighborhood have risen 20 percent this year, broker Century 21 Sky Realty estimated.

"There are few luxury homes for sale at the moment," said Yukiko Takano, manager of international sales at List Sotheby's International Realty, a real estate brokerage unit of the New York-based auction house. "Demand is rising at a time when supply remains unchanged."