I have a Bachelor's in Mathematics from a state school with multiple NSF-funded research projects in probability theory and computer science. I've also taken the PhD qual sequence courses in Mathematics and Economics, including stochastic calculus, as well as a bunch of other graduate courses, so I'd say I'm in a solid place in terms of coursework. One of my research projects involved options-pricing, which I really found compelling, even though at the time I knew (and now still know) very little about finance.
Now that I've graduated and have been looking at job opportunities, I've started to consider finance as a potential field of work. Unfortunately, due to my lack of actual financial experience or knowledge (outside of what little is necessary to price certain options), I'm a bit hesitant to step into the field.
I was hoping for some direction from experienced members of the financial community here. What kind of jobs should I be looking for? Should I just go for a PhD before considering entering finance? What can I even do in the financial field, really? Any advice would be appreciated.
P.S. I have good algorithm developing experience. I can also program in a wide array of languages, although I can't say I'm an expert in any of them.