Having hired a lot of quants and programmers in finance I can probably give a bit of background on what to expect:
Get this book, read it and understand it.
http://www.amazon.com/Heard-Street-Quantitative-Questions-In...
Quants tend to be in 1 of 3 categories:
1) pricing quants,
you work for a bank or investment house like Goldamn. You know stochastic calculus very well, you know finite differencing like the back of your hand. You'll know every way to look at a derivative product. You can program in matlab. You create the next big thing like CDO's or CDS's
If you love math, this is where you want to be.
2) Quants who trade
You work at a hedge fund. You can program in python with scikit or use R. You don't know calculus maybe as well as a pricing quant but you know some area of the market much much better. You know stats like its your mother tongue.
3) Risk quant/programmer. You do modelling all day for a trader or risk manager. You can take a portfolio and model any feature that someone ask for. Var, beta, greeks, you can spit them out quickly. You know C++, excel and R. You might have been an engineer in a former life.
This is often considered the low position in the quant hierarchy. This is how some programmers break into the industry.
4) I lied there is actually special category 4). This is the professors of quants. You sit around all day and think about the next big equation, or how to model derivatives better than black scholes. If you are one of these people chances are your name is known in the industry:)
EDIT someone asked if you can do these without a math degree. The short answer is probably not. YOu'll need a math, engineering, or physics degree, unless you really are driven to learn hte math yourself.
A comp sci degree might work but you would be the exception and you'd be fighting up hill. Ask your self honestly, how many branches of mathematics have you self taught yourself and you'll get your answer. For most the answer is none, for a select few the answer is yes.
Someone asked about brain teasers. They do get asked, you have to deal with it, whining in an interview that this type of question gives no useful hiring indicator won't get you hired. I don't ask them but they are common:(
We throw around brain teasers at work during the day trying to stump each other. I guess some of it is trying to look smart. Some of it is that we just really like to dissect any problem and figure it out.
I think the biggest reason for asking brain teasers is that at a hedge fund there are no rules for how to make money, excluding legal. They want people who can think outside the box. it turns out that its really tough to test for "can the candidate think outside the box"?
Trading is a higher stress job than most other math or programming jobs, what we are trying to see is not only are you smart, but can you think on your feet and not get stressed out, because if an interview stresses you out, whats going to happens when a $50,000,000 position that should be going up starts to go down.
Are you going to complain that the model says it should go up and the market isn't being fair, or are you going to accept what's happening and get back to work? You'd be surprised at the number of people who chose option 1.
I ask a bunch of questions that some people feel are brain teasers. In between questions I'l throw out what's the square root of 225 to see how the candidate reacts. Good traders seem to be exceptional at mental math, with very, very few exceptions.
I'll also ask alot of probability questions. Get ready to know what your expected payoff is if you gamble on dice games, its basically what you do every minute of the day when trading:)
Now if you are a programmer, how do you get into the industry?
You need to know stats, machine learning, and programming, really well.
And I don't mean know machine learning, like "I tool an nlp library and stiched it together to do sentiment analysis on a corpus of text". I will ask what algorithms the underlying library used. You used SVM, great talk to me about your kernel selection methods. I want to know that you understand the math, and more importantly the assumptions and limitations of the library you are using.
The reason is that when you trade on a model that is based on your machine learning, I want to know that you know when it breaks. Finance is an industry that loves to model but has crashes that are predicted to happen 1 in 1000 year events happen every 10 years.
I love helping programmers who want to become quants get into the industry. Please feel free to ask if you have questions!