Try not to feel so guilty. :) We all can't always be working on something we believe in; mathematically, it's highly improbable. I'm sure there are also many people who work in your office who don't care for the firm's mission, although they have coping mechanisms to hide their apathy and vulnerabilities, so it can seem like they all love what they do and that you're the wrong one in the picture. Most people are naturally team players and maintain a certain image because they need the structure and support of the perceived team. I've never worked that way, so a lot of my life has been spent feeling out of place because my group's mission is clearly bunk but everyone else behaves as if it isn't. Believe you me, that's lead to a lot of depression.
These days I'm much more content and at peace with these things about people and workplaces that aren't going to change themselves. While I wouldn't say to never look up to other people whom have qualities you aspire to, comparing yourself to others is a losing game because the people we've been talking about are really just illusions; those team players who go with the flow and support bad missions, who seem to have everything we don't, are usually putting on an image. We usually don't know who these people really are, but I can assure you that most of them are living hum-drum lives and deal with their own sort of problems brought on by the baggage that comes with maintaining a conventional life. I don't begrudge them of this observation, as it's often just their calling to be this way, but their true selves are simply not my true self.
Ok, I'm going to get a little cliche here, but those who are exceptional are usually not the type of people who go along with hopeless missions or simply do what's expected of them. Now I'm not saying that I or you have to aspire to be exceptional, yet the reason I bring this up is that there is no shame in being someone like you, and not the people you work with.
I've found much more happiness in setting my own standards for who I want to be, not comparing myself to other people. It feels healthy because I've learned that such standards to only myself and not others has lead to much less disappointment in life; when I am disappointed with something, it's purely on me and I can take steps to try to resolve it.
In relation to that, you clearly have a strength in that you seem like a highly-driven person (that's how I'm interpreting what you said anyway). I normally don't like giving out advice, because everyone is different, but if I were you I would take that drivenness and direct it towards something else. I've not worked for a bank or a trading firm, but I imagine that the way that they function is extremely old-school. When companies and industries become highly-established, they will always tend towards a stable equilibrium that is less focused on efficiency or innovation, which can be hampering for people who want more than just the status quo but very hospitable to people who are willing to just go with the flow (i.e. are laid back and take things easy).