Great article by the St Louis Fed on bitcoins. The key question, which remains unanswered, is whether bitcoins have intrinsic value.
The answer is a resounding No! While computing work does go into solving the crypto-puzzles required for the issuance of new bitcoins, work alone, while a required condition, is not sufficient. The other side of the coin, pardon my pun, is utility. The source of intrinsic value is work that creates utility. For example, a bridge to nowhere in Alaska has no intrinsic value because nobody is using it despite the tremendous amount of work and resources that went into its construction. Regardless of how difficult the crypto-puzzle is and how much computing resources went into its solution, the fact remains that the puzzle itself serves no useful purpose. If it did serve an actual purpose, such as solving a math problem that has real-life application, the value of the bitcoin would be inextricably linked to such application and would not be subject to huge swings in value.