Given that Bank of America's (NYSE:BAC) share price has more than doubled over the last two years, does this mean that its stock is no longer a buy? Not necessarily. Here are three reasons why.

1. Franchise value
First, it has a great franchise. I mean, think about it for a second: Its name is Bank of America.

Love it or hate it, everyone has heard of the nation's second largest bank by assets. Its branches and ATMs are scattered throughout the vast majority of the United States. It holds approximately 11% of the nation's deposits. And it has some of the biggest and best-known credit card and wealth management operations in America.

In other words, if this country does well, so will Bank of America.

2. Innovation
Second, it's surprisingly innovative. This may come as a shock to you, but it's true.

In this day and age of Internet and mobile banking, it's imperative that the nation's traditional banks make progress on these fronts lest competitors like Bank of Internet (NASDAQ:BOFI) continue to take market share. Just since 2008, for instance, Bank of Internet has nearly doubled the size of its balance sheet as customers flock to its above-average savings account yields.

More than any other too-big-to-fail lender, however, Bank of America has grasped this. If you're a customer of the bank and have used its mobile app, then you know what I mean. It's far and away one of the best in the industry, second perhaps only to U.S. Bancorp (NYSE:USB), which regularly ranks at the top of the heap in this department.

And you don't have to take my word for it. As I discussed here, a recent survey of the state of mobile banking found that Bank of America is one of the "premier offerings" in the industry, using terms like "best-in-class" and "highly efficient" to describe its mobile app.

This is why so many of Bank of America's customers have readily adopted the practice. While "over 10 million customers actively" use the mobile platform at Wells Fargo (NYSE:WFC), Bank of America boasts 13.2 million active users. Those figures equate to adoption rates of 26.4% and 15.3%, respectively.

3. It's cleaning up its act
Finally, Bank of America is cleaning up its act. While it's true that the Charlotte-based bank still has significant progress to make on the reputation front, it's come a long way over the last few years in terms of atoning for its sins (or, rather, largely the sins of Countrywide Financial) from prior to and during the financial crisis.

Over the last five years, it's paid out upwards of $50 billion in legal fees and settlements, and it's currently litigating a number of other related matters. But once these things work their way through -- which they should over the next year or so -- the bank's CEO has said that all capital above what is necessary to run the bank will be returned to shareholders via dividends and buybacks.

The Foolish bottom line
My point is this: Yes, Bank of America's shares have performed admirably over the last two years. But the facts on the ground suggest that they could very likely continue to head higher.

John Maxfield owns shares of Bank of America. The Motley Fool recommends Bank of America, BofI Holding, and Wells Fargo. The Motley Fool owns shares of Bank of America, BofI Holding, and Wells Fargo. Try any of our Foolish newsletter services free for 30 days. We Fools may not all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy.