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MFE v. M.S.

Have received offers for several top MFE (CMU, Cornell, etc.) for fall 2020, and have also received offers to NYU M.S. in Mathematics / Columbia M.S. Applied Math. Applied to both kinds thinking that with an M.S. you can either get a Ph.D. or get a quant job. (By which I mean, one of the more well-known varieties of MBS/modeling job at one of the big banks in NYC, but probably not a small HF where you need the kind of in you would get from MFE program.)

Experience indicates that if a (highly theoretical) Ph.D. can't answer the interview questions but an MFE can, the MFE gets the job. Question is, at this point in the proliferation/market penetration of MFE programs, how much work does the NYU M.S. student (quite theoretical, to the extent curriculum matters) have to do to be competitive for MFE jobs that MFE's consider desirable (buy side, etc.), or even "quant jobs" interpreted in more general kinds of senses. Is it just a matter of making sure you get stats/stochastic calculus/finance/machine learning in the M.S., or is it basically an entire MFE degree worth of work.

Am trying to piece together an answer to this from program alumni, but maybe someone here can also speak to it.
I'm in a program now, mid-career with experience on a (linear) derivatives desk and buy-side quant. I'm a little shocked at how theoretical the MFE is relative to my experience - I'm essentially having to learn everything new from scratch. That said, it's entirely applicable. I'm not sure how an MS in applied math would work - maybe all of your projects would be in finance? If you're going to do an MS in applied math, why not spend a few extra years for the PhD? Given the market situation, it might be a good place to park until things clear up.
Thanks for the perspective, these are good points. I am not mid-career but few years of non-quant.

Distinction you made between "theory" and "theoretically substantive but applicable" really gets to the heart of the problem/question. Did stochastic calculus/Black-Scholes/stochastic processes/simulation/stats/time series as an undergrad, but didn't touch ML and didn't really touch stats/time series in a good way (theoretically intense but without applications in R, python, etc.), so presumably would have to find a way to address those (the "applicable" part). Guess the question is, can you get all that in a convincing way without an entire MFE.

For Columbia M.S., 5 of the 10 courses are electives and you can do courses from CS dept. (ML) or the hard side of the MFE program, but there's no big project for the degree (thesis). For NYU there is no ML/stats in the required courses or electives (stochastic calculus and probability limit theorems would be the most relevant), but presumably you could take those courses additionally and try to write the optional thesis in one of those areas. Not sure how salable either of these scenarios would be.

Your point about Ph.D. is well-taken. Current turbulence/hiring freezes aside, I tend to think that if you are going to spend the money, there's an argument for real investment in technical STEM area as against an MFE program, especially if you are younger.