Econometrics, Finite Difference Methods, Continuous Stochastic Processes & Stochastic calculus in 1 semester manageable?+background advice

Hello guys,

I would please like to ask for your advice on whether I should take the 3 graduate courses above in 1 semester (along a standard undergrad course in computer architecture, the remaining 2 have negligible workload). I would like to have the skills needed to work as a quant intern by summer but I am not quite sure if I need all 3 of those courses above to get an internship. Do you think its a good idea to just push through it or to postpone 1 of those for next year?
The stochastic calculus course roughly covers Shreve 2, finite difference methods course is quite rigorous(functional analysis is a prereq) and covers finite element and finite volume discretizations & time-dependent problems. The econometrics course covers parameter estimation and hypothesis testing in a linear regression model. General least squares and its applications (e.g. heteroskedasticity, autocorrelation, multivariate regression), GMM estimation, simultaneous equation models and panel data models. Note that in spring I will be taking stochastic partial differential equations, time series analysis, Machine learning, and parallel programming in c++. Would my background be considered good enough for top institutions this summer?
 

Daniel Duffy

C++ author, trainer
How much maths do you know now?

"finite difference methods course is quite rigorous(functional analysis is a prereq) and covers finite element and finite volume discretizations & time-dependent problems."
This is overkill. You don't need FA for FDM and no one uses FEM/FVM in finance (mainly because most do not have the necessary background).
BTW FA is very useful for FEM.

"parallel programming in c++."
Do you know single-threaded C++?

Your list is way too ambitious?
 
How much maths do you know now?

"finite difference methods course is quite rigorous(functional analysis is a prereq) and covers finite element and finite volume discretizations & time-dependent problems."
This is overkill. You don't need FA for FDM and no one uses FEM/FVM in finance (mainly because most do not have the necessary background).
BTW FA is very useful for FEM.

"parallel programming in c++."
Do you know single-threaded C++?

Your list is way too ambitious?
Currently, I know real analysis and am studying functional analysis. As for stat, I know probability theory(non measure-theoretic), parametric inference, and I finished some of Chris brooks econometrics for finance book(up to chapter 4). As for c++ I do not consider myself proficient in the language(But I do know OOP, functional programming, and am familiar with some software design patterns singleton-factory-builder ). By spring I assume I can probably learn enough c++ to not feel disadvantaged in the course.

The thing is I do not know what specific courses do I actually need to get an internship this summer and will probably exhaust myself during fall. If you were in my shoes would you consider postponing the finite difference methods course (and)/or econometrics? As for measure-theoretic continuous stochastic processes and stochastic calculus, the instructor knows that there are 4 undergrads taking the course without any background in measure so he will explain the ideas as needed(There is no syllabus yet since it is the first time he will offer such a course). I personally would prefer not to take all 3 courses at once but I am not sure how severely would that impact my chances to get(and make the full use of) a good internship in quant trading. Thank you for your advice.
 

Daniel Duffy

C++ author, trainer
"(There is no syllabus yet since it is the first time he will offer such a course)."

Does the instructor know measure theory and has he/she already taught MT?

I thought quant trading was quantitative, computational etc.??
 
Maybe FEM can also be taught without FA? Check out Gilbert Strang's treatment of teaching FEM.


He starts with 1D, then expands to 2D, 3D. He didn't use much FA, but he still got the ideas across to audiences. It wasn't limited to mechanics. Gilbert's teaching is an art.

How much maths do you know now?

"finite difference methods course is quite rigorous(functional analysis is a prereq) and covers finite element and finite volume discretizations & time-dependent problems."
This is overkill. You don't need FA for FDM and no one uses FEM/FVM in finance (mainly because most do not have the necessary background).
BTW FA is very useful for FEM.

"parallel programming in c++."
Do you know single-threaded C++?

Your list is way too ambitious?
 
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No, he did not teach MT as far as I know.
I did not understand this: "I thought quant trading was quantitative, computational, etc.?? ". Should I post some job descriptions to clarify? Some topics were: portfolio risk management, market impact, market making, and market signals.
 

Daniel Duffy

C++ author, trainer
Maybe FEM can also be taught without FA? Check out Gilbert Strang's treatment of teaching FEM.


He starts with 1D, then expands to 2D, 3D. He didn't use much FA, but he still got the ideas across to audiences. It wasn't limited to mechanics. Gilbert's teaching is an art.
This is 1d elliptic diffusion PDE?
The jump to Black Scholes PDE would be yuge.. You need functional analysis for error estimation stuff etc. Unfortunately, I think a degree in maths is needed for FEM and deep knowledge of PDE.

You can learn FEM by a recipe approach but it will take years to appreciate (as I have experienced). And for Black Scholes it is a challenge for newbies. And .... FEM not much used in finance.
I can train MSc students in FDM for computational finance in a few months


BTW Gil Strang was supervisor of my supervisor.
 
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It's nice to know you are Gilbert's academic descendant! I'm Gilbert's fan...
Thanks a lot for sharing your experiences and insights. It's appreciated.


This is 1d elliptic diffusion PDE?
The jump to Black Scholes PDE would be yuge.. You need functional analysis for error estimation stuff etc. Unfortunately, I think a degree in maths is needed for FEM and deep knowledge of PDE.

You can learn FEM by a recipe approach but it will take years to appreciate (as I have experienced). And for Black Scholes it is a challenge for newbies. And .... FEM not much used in finance.
I can train MSc students in FDM for computational finance in a few months


BTW Gil Strang was supervisor of my supervisor.
 
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