What are the best courses an aspiring Quant can take at university?

[Ronan Mullan]

Hi,

I'm an Applied Mathematics student about to begin my final year at Edinburgh University in the UK and am faced with various course choices.
I'm am currently intending to do a course in C++ but don't know what other areas of Mathematics would be best for an aspiring quant or most attractive to universities when applying for postgraduate study.

Any suggestions would be much appreciated.

 

[Daniel Duffy]

Applied and numerical maths.
Statistics


Python, C++.
Looks like databases are back in fashion.

My 2 cents.

 

[Philip_Mitterrand]

The hardest courses you can manange that will test your limits and improve your intellectual stamina....Advanced Probability, Algebraic Geomtery etc. C++ can be self taught.

Hi,

I'm an Applied Mathematics student about to begin my final year at Edinburgh University in the UK and am faced with various course choices.
I'm am currently intending to do a course in C++ but don't know what other areas of Mathematics would be best for an aspiring quant or most attractive to universities when applying for postgraduate study.

Any suggestions would be much appreciated.

 

[amraj]

I was in a similar position to you 2 years ago, although I was on a pure Maths BSc. I needed similar advice but only managed to research half of the useful modules in advance. I'm not sure whether you have access to the following modules, but it would be worth doing these on your own in advance if possible.

Probability theory - The pure side of probability which introduces the measure approach to probability. Useful for understanding the really pure stuff form stochastic calculus and Brownian motion theory.

Any PDE courses- Math finance is all about using an expectation to price something. However, we move from an expectation to a PDE (Girsanov, like in BS equation). Therefore, you will be tackling PDEs all of the time. I would probably say a computational PDE course is more useful than a pure PDE one. Most PDEs you come across will NOT be solved analytically, especially for exotics. Try to see things like finite difference methods beforehand.

Statistics - Do as much stats as you can. A lot of recent math finance is focused on modelling time series and other statistical models. The more experience you have with stats, the more comfortable you will be with playing with these things.

Any course on Mat lab and R, since these are tools which are useful for prototyping / playing around. All come in handy and save you learning these from fresh on the course.

Courses related to optimisation. This is useful for things like calibration and finding maxima etc.

Try to read through Hulls book beforehand. Don't worry if you don't understand the Maths in depth, but try to get a feel for the qualitative side of the products. It would be very useful to know in advance what different derivative products were, when they can be used, who would use them, and just general things like rates curves etc. Makes the ideas form the course 'come to life'.

 

[Daniel Duffy]

Most PDEs you come across will be solved analytically, especially for exotics.

Did you forget a 'not' somewhere?

 

[amraj]

Most PDEs you come across will be solved analytically, especially for exotics.

Did you forget a 'not' somewhere?

Haha good spot. I wish the original statement was the case. Would make calculations a lot faster and more accurate.

 

[Ronan Mullan]

I was in a similar position to you 2 years ago, although I was on a pure Maths BSc. I needed similar advice but only managed to research half of the useful modules in advance. I'm not sure whether you have access to the following modules, but it would be worth doing these on your own in advance if possible.

Probability theory - The pure side of probability which introduces the measure approach to probability. Useful for understanding the really pure stuff form stochastic calculus and Brownian motion theory.

Any PDE courses- Math finance is all about using an expectation to price something. However, we move fro an expectation to a PDE (Girsanov, like in BS equation). Therefore, you will be tackling PDEs all of the time. I would probably say a computational PDE course is more useful than a pure PDE one. Most PDEs you come across will be solved analytically, especially for exotics. Try to see things like finite difference methods beforehand.

Statistics - Do as much stats as you can. A lot of recent math finance is focused on modelling time series and other statistical models. The more experience you have with stats, the more comfortable you will be with playing with these things.

Any course on Mat lab and R, since these are tools which are useful for prototyping / playing around. All come in handy and save you learning these from fresh on the course.

Courses related to optimisation. This is useful for things like calibration and finding maxima etc.

Try to read through Hulls book beforehand. Don't worry if you don't understand the Maths in depth, but try to get a feel for the qualitative side of the products. It would be very useful to know in advance what different derivative products were, when they can be used, who would use them, and just general things like rates curves etc. Makes the ideas form the course 'come to life'.

Thanks, that's really helpful!
I'm doing courses on Stochastic Calculus and an applied course on PDE's this year too and have used Matlab a lot throughout my degree so far but I will definitely try and add some more Stats.
What kind of things does Hulls book talk about? I have a basic knowledge of various products (options, forwards, swaps ect.) from previous financial courses.

 

[Daniel Duffy]

Haha good spot. I wish the original statement was the case. Would make calculations a lot faster and more accurate.

That's the myth. And it is not true in general. Just because you have nice-looking formula does not mean it can be (easily) computed.
Pure mathematicians (and many quants?) seem to love closed/exact solutions. A waste of time, but very sometimes you can get lucky.

Sometimes the closed solution is more difficult than the original problem.

Your post will cause me to lose sleep tonight :D It's a bit depressing

 

[amraj]

Thanks, that's really helpful!
I'm doing courses on Stochastic Calculus and an applied course on PDE's this year too and have used Matlab a lot throughout my degree so far but I will definitely try and add some more Stats.
What kind of things does Hulls book talk about? I have a basic knowledge of various products (options, forwards, swaps ect.) from previous financial courses.

That's good to hear. Your in a better position than I was. I hadn't done any stochastic calculus, and had never heard of a BM. Although I had seen a lot of stats.

You have also seen a lot more products than me, and that will come in handy when trying to understand the intuition behind things. In your spare time, try to read up as much as you can on the basics of Math finance. That way, during your lecture / after class, you can make the most of your £30k fees and ask more in depth questions and actually challenge you professors. Last year, I spent most of my time trying to understand the basics because I wasn't well prepared, so I couldn't make the most of the professors around me to ask in depth stuff that wasn't available online.

where are you hoping to do your MSc?

 

[amraj]

That's the myth. And it is not true in general. Just because you have nice-looking formula does not mean it can be (easily) computed.
Pure mathematicians (and many quants?) seem to love closed/exact solutions. A waste of time, but very sometimes you can get lucky.

Sometimes the closed solution is more difficult than the original problem.

Your post will cause me to lose sleep tonight :D It's a bit depressing

Yes I guess you're right. I think people see it as though you will save some time on running simulations etc. But I reckon that if a small aspect of your original problem is altered, its much easier to alter some MC or FD code as opposed to trying to find a closed form solution.

 

[Daniel Duffy]

Can you imagine Leonhard Euler looking for closed solutions, no!

In solving optimisation problems in function spaces, Euler made extensive use of this `method
of finite differences'. By replacing smooth curves by polygonal lines, he reduced the problem of
finding extrema of a function to the problem of finding extrema of a function of n variables, and
then he obtained exact solutions by passing to the limit as n ! 1. In this sense, functions can
be regarded as `functions of infinitely many variables' (that is, the infinitely many values of x(t)
at different points), and the calculus of variations can be regarded as the corresponding analog of differential calculus of functions of n real variables.

Euler–Lagrange equation - Wikipedia, the free encyclopedia

 

[Ronan Mullan]

That's good to hear. Your in a better position than I was. I hadn't done any stochastic calculus, and had never heard of a BM. Although I had seen a lot of stats.

You have also seen a lot more products than me, and that will come in handy when trying to understand the intuition behind things. In your spare time, try to read up as much as you can on the basics of Math finance. That way, during your lecture / after class, you can make the most of your £30k fees and ask more in depth questions and actually challenge you professors. Last year, I spent most of my time trying to understand the basics because I wasn't well prepared, so I couldn't make the most of the professors around me to ask in depth stuff that wasn't available online.

where are you hoping to do your MSc?

Yeah, it would be nice to make the most of it if I'm paying that much!
Ideally, it would be Oxford or Imperial College London if I can keep my grades as high as their current level.

 

[amraj]

Yeah, it would be nice to make the most of it if I'm paying that much!
Ideally, it would be Oxford or Imperial College London if I can keep my grades as high as their current level.

They both have there own plus points. Imperials offers an internship instead of a dissertation, but the course was too pure for me. Oxford offers a data stream which allows you to see things like algo trading and machine learning. Its not in depth, but more of a taster to see what its like and you can take it further in your own time. I had offers from both, and decided to take Oxford. This was mainly for the brand name on the CV and Oxford experience which is good fun, but also because I did my BSc and Imperial so I wanted a change as well.

Good luck

 

[Ronan Mullan]

They both have there own plus points. Imperials offers an internship instead of a dissertation, but the course was too pure for me. Oxford offers a data stream which allows you to see things like algo trading and machine learning. Its not in depth, but more of a taster to see what its like and you can take it further in your own time. I had offers from both, and decided to take Oxford. This was mainly for the brand name on the CV and Oxford experience which is good fun, but also because I did my BSc and Imperial so I wanted a change as well.

Good luck

That's good to know- Thanks!