Shares of the world's second-largest cruise operator were up 10.4 percent in Thursday morning trading.
In January, a ship operated by larger rival Carnival Corp & Plc, the Costa Concordia, ran aground off the coast of Italy, killing 32 people and leading to a reduction in bookings and prices industry wide.
But Royal Caribbean said that the effect of that accident "has continued to wane" and that bookings in the third quarter were stronger than expected, even in Europe, where the Costa Concordia accident made headlines for months and where many customers have been hit by government austerity measures.
"There are still challenges in Europe, especially Southern Europe, but solid demand from other regions appears to be more than offsetting this," Royal Caribbean Chief Financial Officer Brian Rice told analysts on a conference call.
Royal Caribbean, whose other lines include Celebrity Cruises did not provide a forecast for 2013, but said it was "encouraged" by what it is seeing for bookings for next year.
In July, the cruise operator cut its profit forecast citing the need to slash cruise prices, and forecast net yields, a gauge of how much each cabin generates, to fall in the third quarter.
Instead, net yields rose slightly, helped by firmer prices and stronger demand in every region.
Royal Caribbean now expects 2012 earnings of $1.85 to $1.95 per share, 15 cents higher than its previous forecast range and above the $1.78 that analysts were expecting, according to Thomson Reuters I/B/E/S.
The company also expects revenue yield, which reflects how much money each cabin generates beyond the cruise ticket itself, to be up 3 percent for the year, excluding the effects of currency.
"We are still seeing price increases in a year marked by so many external pressures," said Chief Executive Richard Fain.
Carnival, whose shares were up 3.2 percent, similarly said last month that prices and demand were both on the rise.
Royal Caribbean's third-quarter net income fell to $367.8 million, or $1.68 per share, on revenue of $2.26 billion, from $399 million, or $1.82 per share, on revenue of $2.32 billion a year earlier.
(Reporting by Phil Wahba in New York; Editing by Lisa Von Ahn, Gerald E. McCormick and Sofina Mirza-Reid)
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