Bitcoin prices on the Bitstamp exchange. (Bitcoincharts.com)

The word "bubble" comes up a lot in discussion of Bitcoin. Bubble talk last peaked in April of this year, when the value of one Bitcoin soared from less than $100 at the start of the month to an all-time high of $266 on April 10.

And in the next few weeks, it appeared that the skeptics had been vindicated. Bitcoin prices tumbled, falling to a low of about $50 before stabilizing back around $100. Bitcoin critics argued that the Bitcoin-buying public had fallen prey to irrational exuberance, and that one unit of the crypto-currency couldn't possibly be worth $266.

But then something interesting happened. After a few months of relative stability, Bitcoin prices began rising sharply again. Since the start of October, Bitcoin prices have doubled from $125 to $250. That's just shy of the all-time high of $266.

That poses a problem for those who called the high prices of last April a bubble. When people describe a market move as a "bubble," they're generally referring to more than a rapid price increase that's followed by a decline — that's just garden-variety volatility. Rather, the term "bubble" refers to appreciation that is driven by hype rather than a sober consideration of market fundamentals.

When bubbles pop, they tend to stay popped, as the market comes to its senses and realizes that the earlier, higher price was irrational. So if a price returns to its earlier highs a few months later, that suggests that the original appreciation might not have been so irrational after all.

And that's especially true in this case, because the price increases of the last few weeks haven't been driven by the kind of media hype that contributed to April's price surge. To the contrary, much of the media coverage of Bitcoin in recent weeks has been relatively negative, including coverage of a federal raid on the Silk Road drug market and a study claiming that the currency has a serious architectural flaw.

That's not a news environment you'd expect to generate rapid price increases. But prices are rising anyway, driven by (among other things) increasing investment in the currency by venture capitalists and growing demand for the currency in China.

This isn't the first time that Bitcoin has had a "bubble" that turned out not to be so frothy. In 2011, Bitcoin prices skyrocketed from about $0.30 to what then seemed like an astronomical price of $32, before falling back to a low of about $2. In retrospect, it seems clear that the bulls of 2011 were right: Bitcoins were actually undervalued, even at the $32 peak. But it would take a couple of years for the rest of the market to recognize this fact.

We can't yet be sure that the bears of 2013 will look equally foolish. Maybe the market will crash again right after I post this article. But the rising price ought to cause people who cried bubble back in April to have second thoughts.

Update: On Tuesday evening Bitcoin prices reached a new record high of $267.40.