Mathematical prereqs for mfe programs

[tunatuni]

I took multivariable, lin alg, ODEs and stats do i need to take pdes? (Is it a prereq for mfe programs) also when is the best time to take the gre test?

 

[Daniel Duffy]

Some MFE do ask for pdes. ode w/o pde is possible but why not do pdes, especially when it is for Black Scholes?

 

[junos]

Linear Algebra, Numerical Analysis, Partial differential equation, and Calculus

 

[noether-skolem]

I never took PDE in undergrad and got a C+ in ODE, but I was an applied maths major, so I guess I somewhat managed to convince the admission officers (at least for a few schools) that I'd still be able to cope with the MFE courses.

Honestly you probably won't need everything taught in a pure/applied maths PDE course for MFE (or at least not to the same level of rigour/formality), but I'd still strongly recommend it to anyone interested in doing MFE or similar programs. Not having PDE or any of the core courses would be a red flag, and you don't want too many of those in your profile - and especially so if you didn't have a strong maths/quantitative background.

As for GRE, take it early if possible, so you have time to retake in case you're not happy with your first scores.

 

[lolalin]

Not a hard pre-req per se, but wouldn't hurt to know some econometrics/some machine learning

 

[Daniel Duffy]

I never took PDE in undergrad and got a C+ in ODE, but I was an applied maths major,

I can kind of understand that pure maths don't do PDE (and at the same time not) but for applied maths PDE theory + numerical PDE would be essential. Maybe I'm missing something.

 

[tips]

Depending on the program, you don’t need to have taken a PDE course at all, though I agree with sentiment that you should have a strong math background I.e at least stats, Lin alg, calc 3, and programming if you’re not taking a pde class. Off tangent, but I feel like this forum over emphasizes PDEs. I got into the fin econ program at Columbia which goes through their PhD curriculum, MIT, and UChicago + got interviews at some other places and I’ve never taken a PDE course.

Most programs, that are more applicable to modern quant work don’t require you to know pdes because, to be frank, you don’t really need it for your day to day work all the time. The most important skills these days as a quant (which programs also care about more) IMO are good research skills, ML, programming, and an ability to pick up financial context quickly.

 

[Daniel Duffy]

Off tangent, but I feel like this forum over emphasizes PDEs. I got into the fin econ program at Columbia which goes through their PhD curriculum, MIT, and UChicago + got interviews at some other places and I’ve never taken a PDE course.

PDE knowledge is taken from other backgrounds. An econ student would not do PDE because there are yuge prerequisites. Just saying.

One possible reason for the fact that PDE is not so widespread as it should be is that there are other more accessible methods (binomial, trinomial) for doing the same things. These methods are limited (range of applications, mathematically, numerically) and getting long in the tooth and PDE/FDM can do it all and more. The reaction is to use Crank Nicolson and ADI but even these are not the best, as we shall soon publish in a new PDE/FDM book.
A case in hand is the 1-factor, 2-factor Hull White model model which is predominantly using lattices. This would be a good MSc project.

 

[Onegin]

Getting into a program is a different objective from getting a job, which is different from succeeding in a job.

I really wish I had done PDEs before CMU; I kind of encountered them, but any useful applications (simulation, risk management, derivative pricing) requires enough knowledge to be able to reformulate the PDE to the relevant conditions. For those that had PDEs, this was quite trivial.

 

[tips]

Yeah, I don't disagree with your assertion. I just don't think missing out on PDEs keeps you from being a successful quant in this day-and-age. I say this as VP quant researcher at a pretty big prop desk in fixed income, so I have some credibility I feel like, but I could be wrong about the day-to-day for other groups. Like it was suggested above, there's a bunch of alternative forms for doing the same thing, that work pretty well, that require less background knowledge, and ultimately get the job done
In any case, OPs question was about getting into a program so I think I would stand by the assertion that you don't need PDE knowledge to get into a MFE program

 

[Onegin]

Yeah, I don't disagree with your assertion. I just don't think missing out on PDEs keeps you from being a successful quant in this day-and-age. I say this as VP quant researcher at a pretty big prop desk in fixed income, so I have some credibility I feel like, but I could be wrong about the day-to-day for other groups. Like it was suggested above, there's a bunch of alternative forms for doing the same thing, that work pretty well, that require less background knowledge, and ultimately get the job done
In any case, OPs question was about getting into a program so I think I would stand by the assertion that you don't need PDE knowledge to get into a MFE program

Agree with your points.

From my point of view, you don't need PDE's to get into an MFE, but PDE knowledge makes it easier to get out of the MFE.

 

[Daniel Duffy]

Like Johnny von Neumann said, maths is about learning the symbols. My way is ODE -> bit of ODE numerics -> PDE theory -> Black Scholes -> BS numerics ->(optional) small BS project in C++ or Python. Ready to go.
Trajectory takes 2-3 months for student entering MFE/MSc.

Euler, Gauss, Lagrange, von Neumann, Laplace were numerics guys.

No PDEs we would be living in mud cabins and eating nettle soup.

 

[noether-skolem]

I never took PDE in undergrad and got a C+ in ODE, but I was an applied maths major,

I can kind of understand that pure maths don't do PDE (and at the same time not) but for applied maths PDE theory + numerical PDE would be essential. Maybe I'm missing something.

I encountered a lot of PDE through other courses (numerical analysis, approximation theory, all the finance-related stuffs), but I never took the course formally named "Partial Differential Equations" which actually goes through all the rigorous derivations and whatnot. Of course different universities require different things, but mine had PDE as an elective.

From my point of view, you don't need PDE's to get into an MFE, but PDE knowledge makes it easier to get out of the MFE.

I feel similarly but about stochastic. Continous time models and to a lesser extent Monte Carlo simulations would've been less of a pain if I had better prep in stochastic.

Some of my classmates felt the same about measure theory (probability theory is just measure theory where the total measure is 1 anyway, right?).

 

[m_s]

Getting into a program is a different objective from getting a job, which is different from succeeding in a job.

I really wish I had done PDEs before CMU; I kind of encountered them, but any useful applications (simulation, risk management, derivative pricing) requires enough knowledge to be able to reformulate the PDE to the relevant conditions. For those that had PDEs, this was quite trivial.

Do you guys use Green's function and its properties? I found that the most complicated part in PDEs, it's either that, or my professor doesn't really know how to explain it well.

 

[m_s]

I feel similarly but about stochastic. Continous time models and to a lesser extent Monte Carlo simulations would've been less of a pain if I had better prep in stochastic.

I feel like I need to take a stochastic calculus, cause when I took the pre-mfe Math course, that part was the hardest part by farrrrrr. I mean the PDE stuff we covered in the pre-mfe course was like Chapter one of the PDE course I'm takin.

 

[Daniel Duffy]

Do you guys use Green's function and its properties? I found that the most complicated part in PDEs, it's either that, or my professor doesn't really know how to explain it well.

I have found Green's function to be not so useful. On the one hand it is PDE theory (existence of a solution) and on the other hand it produces a solution as an integral. It is limited to simpler problems. Still. it gives great insights into PDEs.
The book by Stakgold (1998) is worth a read.

The way I do it for PDE is as follows:

1. PDE qualitative properties and unambiguous specification (well-posedness, maximum principle, smoothness, energy inequality etc.) without actually having to produce a solution.
2. Transform PDE to a computationally-friendly PDE form without actually having to produce a solution.
3. Map PDE in 2 to a finite-dimensional (quantitative, computable) form, e.g. FDM, FEM etc.

 

[Daniel Duffy]

I feel like I need to take a stochastic calculus, cause when I took the pre-mfe Math course, that part was the hardest part by farrrrrr. I mean the PDE stuff we covered in the pre-mfe course was like Chapter one of the PDE course I'm takin.

I feel for all the students who have to learn this stuff. I had at least 3 courses as undergraduate related to measure and it was super abstract. What SDE books need IMO is more applications and numerics on top of the theory.

 

[sumalya bhattaacharyaa]

hello

I feel for all the students who have to learn this stuff. I had at least 3 courses as undergraduate related to measure and it was super abstract. What SDE books need IMO is more applications and numerics on top of the theory.

hello daniel sir,
this is sumalya.
what are the skills required to be able to generate investing signals following quantitative statistical practices?
I have masters in finance.

 

[Daniel Duffy]

No idea.

 

[sumalya bhattaacharyaa]

thank you sir