Question for Acrary: Financial Mathematics

[granville]

I'm posting this question rather than PM'ing as I assume others might be interested in the topic and answer: Also, I'd like to open this up to anyone who might have advice or input.

Acrary, I've noticed that you have a strong math background and have developed techniques for trading - many of which I've never heard of prior coming to ET and reading your posts.

I'm considering enrolling in a graduate degree in financial mathematics. I see that NYU, Chicago, Stanford and others have programs. However, the coursework seems to be derivatives focused and I wonder if such ideas as drag, money management, the edge test and others are formally taught anywhere (other than by you on ET)?

Are you familiar with any of these programs? What areas of mathematics would you suggest anyone here on ET study?

All the best,
Adam

 

[Equalizer]

Quote from granville:

I'm posting this question rather than PM'ing as I assume others might be interested in the topic and answer: Also, I'd like to open this up to anyone who might have advice or input.

OK, since you are talking about a grad degree in Fin Maths, I am assuming that you already have been taught Calculus, and some Linear Algebra.

For what you are discussing, that should suffice. What is taught in FinMath programs is Stochastic Calculus, for which you would require at the very minimum an understanding of Real Analysis, Partial Differential Equations and some point-set topology wouldn't go astray either. You could 'wing-it' without these, but there will be serious gaps in your knowledge if you try to understand the literature in the field.

Of course, you'll also learn numerical methods, monte-carlo, etc, etc (you might go into specifics depending on the course i.e. antithetic variables, Sobol sequences...), not to mention pricing exotics, GARCH models, Levy processes, etc. All very useful if you wish to become a Quant.

However, like I stated above, a basic understanding of Calculus and Linear Algebra should be enough.

What is IMHO invaluable for system development, is a good understanding of Statistics and Statistical Inference.

In my experience, Engineers tend to be a little better prepared in Statistics, whereas it appears to be a weak point in teaching for most other Quantitative disciplines - unless of course you studied Statistics.

Yes, its boring to study (I'm sure you'd rather be trading and partying ), but it is very useful.

Just my $0.02.

 

[nbates]

Equalizer, nice synopsis!

My epxericence is that stockastics, black sholes, montecarlo, and statistical analysis in general are great exercises.

IMO, if you need to solve a real-world problem then physics may be the best course of study. Perhaps for example, there's relevant similarity among financial markets and Magnetic Resonance Mathematical Analysis or spin Hilbert space isotropic systems and elements.

But then again...who knows!

 

[pepper_john]

For directional bets, college math should be enough.

For more complicated trading (fixed income arbitrage, derivative), more advanced stuff are required.

 

[acrary]

All of the stuff you talk about were the result of writing down questions and working for a long time on coming up with the answers. They were inspired by the interview in The New Market Wizards with Monroe Trout (87% winning months, 60%+ annualized return, less than 8% max dd, edges - i.e. trading results better than random, diversification of trading methods in type and time).

I'm no math whiz. I struggle like everyone else. The areas I found useful are statistics, probability, and game theory.

One textbook I have that I found useful is Probability and Statistics for Engineers and Scientists ISBN 0-13-041529-4

I'll try and do a better job of explaining the details of what I've done in my thread to make it easier to understand.

 

[granville]

Thanks everyone for your replies. I'm finding this to be a good community.

Yes, I have a math & physics background and have been asking myself a lot of questions that I don't have the answers for yet- and which seem to have an answer in a solid mathematical approach. (questions regarding placements of stops and the million and 1 other things that go into a trading system )

Equalizer: That's a full list of topics, do you use any of those methods in your trading or research? How did you learn it- self taught, engineering etc? I'm trying to figure out if I should do a pure math program, fin math or computational finance program.

nbates: Could you please explain a little bit more how these apply? I know someone who actually uses weather models to predict the first few minutes of the currency market (early morning hours). He wasn't able to go into detail about any of it, but gosh, just thinking about applications for these ideas is in the very least fun!

Acrary: Somehow I just figured you would find this post....and it worked An odd coincidence, a housemate saw me working on some of this stuff and he mentioned "I've got a book for you..." - the very same book you suggested. Have you ever thought of taking your notes and research and writing a book? Again, the things you've mentioned on posts do not seem to be taught anywhere else that I've looked.

Thanks everyone!
Adam

 

[Equalizer]

Adam, it all can help but don't go overboard with it for trading, please see PM.

Alan's post is spot on.

 

[prt_systems]

Quote from granville:

....
Yes, I have a math & physics background and have been asking myself a lot of questions that I don't have the answers for yet- and which seem to have an answer in a solid mathematical approach. (questions regarding placements of stops and the million and 1 other things that go into a trading system )

.../B]

If you have a good degree in mathematics and / or physics then you should have all the knowledge you need for trading. The more esoteric ideas - some of the stated quant methods - as basically rehashes of ideas you will have seen in theoretical physics, or if your background is more strictly in mathematics, then the material is just applications of techniques to which you have already been expsosed - especially if you have done any graduate work in these areas.

The theoretical similarities between financial markets and other phenommena are interesting but translating these into models that make money are IMHO much less technical than people would make you believe. Dont overcomplicate things - to start with. You can refine your models as you go along.

 

[TheStudent]

Just my 2 cents.

I've found that in directional trading you are usually trying to ask the market a question, and mathematics is helpful in framing the question in the right way so you can understand the answer.

So, knowing a lot about math and little about markets doesn't usually work, because you don't know what questions to ask in the first place.

 

[market_hacker]

Quote from acrary:

The areas I found useful are statistics, probability, and game theory.

I would be interested to hear how you have applied game theory to trading if you are willing to share. (i'm already sold on probability and statistics)

I've read only one book and while it was interesting I found it difficult to apply in a useful way to my trading.

If you have a preferred reference for me to read that would be great too.

thanks