A lot of folks aspiring to be quants have the incorrect impression that real quants work with mathematical models all the time. They probably got this impression from reading some books purporting to tell them what quants do, and they probably got this impression from hearing about interview questions that cover stochastic calculus or real analysis or topology.
The truth is, I know of no quant jobs that rely purely on mathematics. Some quant jobs require the mastery of math in addition to statistics, but by far, statistics (including simulation techniques like MC) is the primary modeling tool used by quants.
The reason is simple: Wall Street only cares about real-world results. It doesn’t matter how beautiful a math model might be. You need to test it with real-world data and convince others that your statistical test is valid. In fact, when Black and Scholes wrote their famous paper, they tested their theory with data.
Moreover, it’s extremely difficult to come up with a purely original and purely theoretical model. This only happens once every decade or two. If you’re the person who is lucky enough to create such an idea, someone will still need to test it, which means someone must know what statistical methodology to employ, and someone must write a computer program to implement the model and the test. I seriously doubt any Wall Street firm, big or small, is willing to pay you six figures a year to just sit around and imagine mathematical models. In fact, the vast majority of quants are paid to implement other people’s models, which usually are found in academic literature or simply based off a boss’ ideas.
So, if you’re considering what courses to take or what books to read to prepare yourself for the quant job search process, I highly recommend you get some fundamental mathematics knowledge first — after all, math is foundation of everything quantitative — but instead of studying advanced topics like stochastics or string theory just so you can hope to impress your interviewers, you’ll do better by studying statistics, and its cousin of econometrics, in-depth. Time series, for example, is used almost everywhere on Wall Street.