LONDON — The price of bitcoin surged through $10,000 on Wednesday, adding to its ten-fold jump in value this year and fueling a debate as to whether the virtual currency is gaining mainstream acceptance or is merely a bubble waiting to burst.

But as soon as bitcoin went through $10,000, it surged past $11,000, only to plummet from those lofty levels. The cost of buying one bitcoin as measured by the website Coindesk was hovering around $9,800, and was as low as $9,300 on Wednesday afternoon. A price of one bitcoin had been roughly $1,000 at the beginning of the year.

The vertiginous rise in the price of bitcoin and other virtual currencies this year has divided the financial community on their merits and whether — or when — the value might come crashing back down.

The CEO of JPMorgan Chase has called bitcoin a “fraud,” as it is not based on anything other than software code and is not backed by any monetary authority.

Other executives, including International Monetary Fund chief Christine Lagarde, say virtual currencies should not be dismissed and could have useful applications, such as a means of payment in countries with unstable currencies.