Critique my choice of courses

[Zaubertrank]

So I'm customizing a masters in applied math at UCSD with the intent of going into the math heavy areas of quant finance.

The masters is two years and I get to take 48 units, each class is 4 units, here is what I've got:

Math 272, Numerical Partial Differential Equations I
Math 272, Numerical Partial Differential Equations II
Math 272, Numerical Partial Differential Equations III

Math 281, Mathematical Statistics I
Math 281, Mathematical Statistics II
Math 281, Mathematical Statistics III

Math 280, Probability Theory I
Math 280, Probability Theory II

Math 294, The Mathematics of Finance

Math 286, Stochastic Differential Equations

Math 287A, Time Series Analysis

Math 287D, Statistical Learning

Note, I already have a year of grad analysis, a year of grad algebra, a few courses in DiffyQs, an introductory class on numerical analysis. As for Programming, I intend to continue to learn that on my own.

Here is the link which lists the math courses which UCSD offers. As you can see I already have a strong background in math, but I'm still pretty ignorant of the nitty-gritty of how all this math relates to finance, so maybe some of you could help me improve this list. Thanks.

 

[quotes]

If you want to learn derivative pricing well, here are road map to its knowledge needed

Mathematical Finance or Stochastic Calculus - The first and foremost thing you need to understand, and any other knowledge serves it.

And from here you can dig into 2 areas:

Stochastic Process - the probabilistic explanation on the Martingale approach for pricing.
PDE approach - the PDE approach for solving a derivative.

It is devided in this way because of Feyman-Kac theorem:
A stochastic differential equation can sometimes be transformed into an equivalent partial differential equation.

I suggest you focus on the probabilistic approach since the development of PDE method is very limited, you need only to know numerical method and that is 90%.

However, there are recently another approach through Fast Fourier Transform. Many advanced models need complex analysis. You can put some effort on it for a solid foundation for models beyond Black-Scholes geometric brownian motion. This is the future of quantitative analysis.

So long that you have mastered stochastic process and complex analysis, you can study advanced models like variance-gamma, heston, etc. However it seems that they are not provided by your school, but you can self-study it at least.

Last but not least, you need a solid econometric background from the basics to time series. Learning time series without econometric background is not recommended.

Besides, you may need to learn analytic background for probability, but it is better if the stochastic process class already includes it.

 

[quotes]

On numerical methods,
you only need an R and some Monte-Carlo books to develop your own algorithm.
You can self-study numerical methods on probabilistic approach.

 

[Zaubertrank]

Thank you quotes for your informative response, could you clarify why you mention derivative pricing in particular, and also make clearer which courses you think are redundant, and those I should maybe add in their place.

I don't know much about how the various areas of quantitative finance differ, I feel like the right way for me to choose is based on what type of math I enjoy the most, is this a stupid way to go about it? I like fourier and complex analysis a lot so if derivatives pricing is where signal processing is being used that might be a good fit.

 

[quotes]

Simply put,
To come up with an option valuation, a quant either computes stochastic probability model or partial differential equation model, but may use Fourier transform method for more complex calculation. Stochastic Calculus tells you why and when to use the two and is the first class you need to take.

Numerical methods in either area both broaden the set of solvable options and enhance the valuation accuracy. You can learn Monte-Carlo and Numerical PDE as numerical methods in the two area.Yet you need good regression skills with Econometric and Time Series, which help you estimate more reasonable input for your model, both in probability ones and in PDE ones. I

In my opinion, stochastic probability model is more widely used and it is better you learn Stochastic Process, where you digest the probability model and get a better understanding on that. If you take theoretical PDE class, you get a better understanding on solving PDE's analytically, but part of it may turn out a waste of time, since option pricing only need to solve one type of PDE - parabolic PDE.

Beyond the two, I wish you have a solid education in complex analysis and Fourier transforms. It helps you not only in some advanced models but also in solving PDE analytically.

 

[Zaubertrank]

Ok so I scrapped the 3 quarter Numerical PDE sequence for a single Numerical Methods PDE course which covers parabolic equations. The only place that stochastic calculus appears is in the description for the Mathematics of Finance course; I can study it on my own if need be, the wiki page on the ito integral certainly makes it look interesting enough. I also added in the Stochastic Processes course, I still have room for two more classes, should I still keep the SDE's course? Also, if I'm understanding you correctly you're saying that studying Time Series requires a certain familiarity with the finance and econometrics which help to motivate it? Is that a correct interpretation?

By the time I start the program I'll have a year of grad reals, a year of grad complex, and a course in applied Fourier analysis, so I feel like what is left for me to take is basically just Multivariate Analysis and Time Series Analysis

Please feel free to digress more if you would like, as I'm enjoying getting the broad view of quantitative finance.

 

[olgenue]

How about Optimization/Stochastic Optimization courses?
- For eg. Convex Analysis, stochastic optimal control theory

 

[quotes]

It is hard to tell, Zubertrank.

The courses have prerequisite conditions. For example, you cannot study 272C without studying 272A and 272B first, which means you have to learn 3 PDE classes altogether.

 

[AZPalta]

May I suggest since you are at UC San Diego that you see if you could enroll in the Economic Department's graduate Econometric courses rather than the pure math equivalents? The Econ department is very well known for their Econometrics program.