Last year five homes sold around the world for more than $100 million, including a $146 million French Riviera mansion.

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WASHINGTON — The poshest of luxury homes are acquiring the cachet of a masterwork by Picasso or Matisse.

Rather than settle for garages of antique cars or a museum’s worth of paintings, billionaires are increasingly willing to pay $100 million for homes that can serve as showcases for their fortunes, according to an analysis issued Thursday by Christie’s International Real Estate.

“It tells you that there is a new class of collectible — they’re trophies now,” Dan Conn, CEO of Christie’s real-estate brokerage, said of the most lavish homes being acquired.

The luxury-housing market has shifted in the past year as the dollar has strengthened. Sales in global hubs such as Manhattan, Los Angeles, San Francisco and London are stabilizing after having rocketed in 2013, when many buyers cashed in on stock-market gains. Now, multimillionaires and billionaires are seeking estates overseas and at resort destinations, the report said.

The dollar has appreciated 20 percent against the euro the past year, making pied-a-terres in Paris and wineries in Bordeaux more affordable for wealthy Americans. Sales are also surging by averages of more than 20 percent along the beaches of Turks & Caicos and the slopes of Telluride, Colo.

Five homes sold around the world for more than $100 million in 2014, and a record 18 were listed for sale at that level, according to the Christie’s report. Last year’s purchases include a $146 million French Riviera mansion. Each square foot of the home cost $22,577 — roughly equivalent to a new Honda Accord.

This is the new top tier for billionaires scouring the globe for signature homes, a market that Conn said should continue to prosper because the world minted 200 new billionaires from 2013 to 2014.

“You’ve got this club of billionaires who just like to have unique assets,” Conn said. “But it’s also, truthfully, that they like to entertain their friends and say, ‘This is mine.’ ”

Some luxury developers say the stronger dollar has cut into sales. There has been a 25 percent drop in Manhattan’s monthly sales pace and a 50 percent drop in Miami Beach, said Kevin Maloney, a developer whose firm, Property Markets Group, works on luxury buildings.

Global buyers have become more patient. They are seeking value because their incomes, earned in euros, pesos and reals, now buy less in dollars. Real-estate magnates are coping with the same challenge facing manufacturers trying to sell their products overseas.

“If I had my druthers, I’d like to see the dollar weaken against other currencies,” Maloney said.