Question Regarding Mathematics for Quants

SRQuant

I'm a CS PhD student with good exposure to Machine Learning and a few years work experience in Software Engineering. I have a good understanding of ML techniques, Optimization, Linear Algebra, basic calculus, statistics and probability. I'm hoping to make my transition into quant finance but it's unclear where my skills will be most applicable.

From what I understand, the sell-side quants deal mostly with PDE, FDM and numerical methods like Monte Carlo sampling etc. , and the buy side quants deal more with statistical modelling, prediction, Machine Learning and statistics. Am I correct in making this assumption.

It doesn't help that there are many quant titles such as Risk, Front Office, Pricing, Fixed Income, Equity, Algorithmic Trader etc. I'm very confused as to which position I should apply for. I want to get my foot in the door as a quant.

Could someone please help point out which Quants require what skills in mathematics and if it's easy to transition between these positions once you're in the door.

Daniel Duffy

C++ author, trainer
In general learning PDE and such with a CS background is almost impossible. It's part of maths and a different skill and mental training. That's all.

SRQuant

In general learning PDE and such with a CS background is almost impossible. It's part of maths and a different skill and mental training. That's all.

Thanks but that's what I'm trying to gauge here i.e. which quant position will leverage my strengths the most. I'm trying to find out which quant positions deal more with ML, statistics, probability, optimization etc. I do have a decent understanding of Monte Carlo methods too. Given my background, I'm hoping I can get up to speed at some of the different quant positions as the banks usually have a training programme of sorts.

Daniel Duffy

C++ author, trainer
I cannot say really .. how long is a piece of string. But all that ML stuff is hot these days and not just in finance. I assume you can program in an imperative language?

my 2 cents

SRQuant

I cannot say really .. how long is a piece of string. But all that ML stuff is hot these days and not just in finance. I assume you can program in an imperative language?

my 2 cents

Yes I have many years experience as a software engineer. I'm quite familiar with the CS side of things including Data Structures, Programming Paradigms etc..
ML is a hot subject nowadays and if I didn't want to go the finance way, I'd probably try for Data Scientist positions in the IT industry. What makes a difference is that I'd like to apply my skills in an domain which actually interests me. I'm fascinated by applied mathematics although it's not my educational background. My experience with ML and optimization techniques exposed me to applied mathematics. I'm trying to find that niche where I can combine my CS experience with my Mathematics experience and leverage both the skills.

Daniel Duffy

C++ author, trainer
Personally I think applied maths includes both discrete maths (all the stuff you know) as well as the applied continuous maths like hard real and complex analysis, fluids, PDE, numerical methods and so on. This latter category is not in the remit of a CS education. It demands a maths degree IMO (3-4) or PhD in astrophysics in the recent past.

My experience with ML and optimization techniques exposed me to applied mathematics.
A subset of applied maths. The skills don't necessarily translate to other areas.
ML is mainly matrix ADTS, graphs and algos?

my 2 cents.

SRQuant

Personally I think applied maths includes both discrete maths (all the stuff you know) as well as the applied continuous maths like hard real and complex analysis, fluids, PDE, numerical methods and so on. This latter category is not in the remit of a CS education. It demands a maths degree IMO (3-4) or PhD in astrophysics in the recent past.

My experience with ML and optimization techniques exposed me to applied mathematics.
A subset of applied maths. The skills don't necessarily translate to other areas.
ML is mainly matrix ADTS, graphs and algos?

my 2 cents.

Thanks for your input. So do all quant positions expect the latter category of mathematical skills? Is there a quant position amongst the myriad of titles that I would fit in with my mix of CS and ML?

Daniel Duffy

C++ author, trainer
Thanks for your input. So do all quant positions expect the latter category of mathematical skills? Is there a quant position amongst the myriad of titles that I would fit in with my mix of CS and ML?
I don't know, sorry. Maybe some research, asking around.

tjk

From what I understand, the sell-side quants deal mostly with PDE, FDM and numerical methods like Monte Carlo sampling etc. , and the buy side quants deal more with statistical modelling, prediction, Machine Learning and statistics. Am I correct in making this assumption.

I believe it may be an incorrect bucketing of things into "buy-side" vs "sell-side"... Any position (whether it's on the buy-side or sell-side) that heavily involves derivatives will require expertise in PDE, stochastics, and all the areas of advanced math used for derivatives modeling that you don't have... ML and optimization (at least as of now) generally seem to be more in line with coming up with strategies to model and trade everything else (commodities, equities, fixed income etc)... You're probably not a good fit for a derivatives job, but if you were to go on eFinancialCareers and do a search on "machine learning" I think a fair number of positions would show up at small buy-side shops that focus on asset classes other than derivatives.

The drawback is that these jobs are often pretty tough to get, and since there seems to be a pretty fair amount of speculation lately about whether "machine learning is just a fad in finance," a lot of these small shops could conceivably end up blowing up at some point.

donny

I'm also learning the different categorization of applicable math in finance but I'll comment on what I know.

I think the area where you'll find ML, statistics and probability most helpful are those 10 to 20 employee ~1b hedge funds. That would be a good place for you to break in.

I agree that investment banks that price derivatives get the Math PhDs who have worked on stochastic calculus, PDE. At the same thing, I would also think that you can price derivatives using a Monte Carlo approach and MC is more empricial thus under the ML umbrella.

Take for example what I deal with. You could attempt to find a close solution of the first passage time modeled by a SDE. Or I could just program the SDE in R and run multiple solutions to find an expected hitting time. Besides, if most SDE do not come with closed solutions, shouldn't an empirical solution the default option.

tfors

There are jobs at banks' risk/trading departments for MC type of jobs for sure.

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