Hi John.
Although many of us would like to argue that we work in a competence-based field, we ultimately work in finance, and finance is a lot different from tech. There are more networking and marketing aspects to getting a job in finance than in tech, even for quants.
If you want your son to become a quant on the cheap, and he is entering undergrad, have him study CS at a Big Ten school- wherever is in-state for you. UIUC would be perfect in a lot of ways with the proximity of Chicago and the CS program; UMich, UW Madison, Minnesota, and Perdue are all excellent choices as well.
I am less familiar with Ohio State and Iowa. For these schools, I would consult the US News rankings and pick the engineering program with the highest US News rank. I might also do a double major in mathematics if it had a higher rank.
For grad school on the cheap, you can go to UIC, establish residency, and crank out an MS in Stats or Mathematics. This allows you to be in the city and recruit for jobs. This strategy also works for Baruch in NYC, although NYC is a lot more expensive. If your son has the grades, he can also apply for a PhD program; most of these programs are fully funded and even provide a stipend.
Learning stochastic calculus and statistical analysis on ARMA models is non-trivial. Some on quantnet have argued that it can't be fully learned with a two year MFE, and I would tend to agree with them.
Also, there aren't a lot of textbooks on this stuff, and this field is a little more nascent and specialized. Frequentist statistics is only about 70 years old. Ito's lemma wasn't really published until the 1950s. The Girsanov Theorem (required to derive Black-Scholes) wasn't proven until 1960. Stuff is still being discovered and worked on and stochal and time series analysis don't really have their own books yet. This is not like linear algebra or calculus where theory and methods have been around for 150 or 300 years, respectively. There are not textbooks galore on this and there is not a gigantic section on Khan Academy devoted to teaching this. Most of the people capable of teaching stochal have thick French or Chinese accents and very little patience for us mortal Americans- even the smarter engineers. They will produce their own (horribly typed) lecture notes and act like the class is a review of what everyone should have learned in eighth grade.
So far I have not been able to find a good textbook that teaches Ito's Lemma, Girsanov Theorem, and Feynman-Katz, and also offers a multitude of sample problems. I also haven't been able to find any texts on ARMA/GARCH models, although it is my understanding that J. Fan is working on one. If anyone can contradict me on this, I would be grateful.
