So I'm a sophomore declaring a math major (with all those probability and programming goodies) yet if I fail miserably at MFE admissions two years from now I'm curious as to what other options there are. I'm sure plenty of people have asked this very same question.
I have broad interests. I like math (but have not touched the probability courses yet) and from the limited C++ I did as of now enjoy that as well. I like economics (considering a minor) and my current perception of the financial world. I would also be interested in doing research, just not in academia. I really imagine myself doing serious programming in the future but because of my lack of exposure it is too early to tell. All of my interests seem to converge inside the general scope of anything "quantitative," but it is impossible to say what exact job or position I would want to do. I really want to land a solid career by the early 20s so I feel pressure to figure out whether pursuing a quant finance type degree (ie MFE) will not have me at a disadvantage for other more finance oriented positions, or more positions reserved for compsci-philes.
Have you considered the world of Utilities/Commodities? The world of energy is complex and many 'types' of quants come to work here; i.e. Power Systems, Economists, Programmers, Quants. Derivatives and valuation become much more complicated because markets are illiquid and the market structure is constantly changing.
Beware though, depending on the ISO you may find heavy state regulation, so that adds another complication. But what is a limit for one, may mean opportunity for another. If you're looking for pure quant/programmer, then consider opportunities in the commodities divisions of large investors.
I am a person with a computer science background in the University of Washington Computational Finance program. So I have some biases.
From my point of view, you can't have too much software background. I would leave economics alone (or at least economics courses that are not cross-listed finance courses). I would take as much software engineering as you can. You should get as solid a background as possible in Java, C++ and Python. Ideally you should also get experience with software testing (things like JUnit and the continuous build and test environments like Hudson). If you're not already a Linux user, I'd get experience with Linux.
If you're interested in finance I would see if you can focus your math courses on statistics. Advanced linear regression and machine learning would be good. R programming....
One thing to keep in mind: there is not a lot of difference in the job prospects for someone who majors in math without any software experience and an english major.
That's a bit of exaggeration comparing the job prospect of a Mathematician and an English major.
Yes these days you do need programming background but a good degree in Mathematics will still provide you more job opportunities than one in English. Your chances will be better depending upon your university, grades and obviously the amount of preparation for the job.