I'm about to Study mathematics at undergraduate level. I'm interested
in a career in mathematics. What options are available to me. I'm
aware that there are many. My particular interests with regards to
this question are in the area of finance/banking/trading. So what sort
of things to professional mathematicions do in Finance jobs and (in
simple terms) how do they do it. I'm
English, so the job's I would be looking for will be in the London
markets.

Hi! Thanks for the question.

Our first link provides an overview of financial careers in
Mathematics for those living in the UK. It seems that in the UK,
graduates do prefer the financial industry as a place to establish
their careers.

“Over a third of mathematics graduates entering employment in 1998
went into the areas of business and finance as accountants, actuaries
and business analysts.”

“Key Facts on Careers for Mathematicians”
http://www.ima.org.uk/mathematics/keyfacts.htm


In a UK setting as well here are where math majors go for a career in
the finance sector.

“Accountancy, Chartered/Certified/Public Finance - employers of
trainee accountants rarely specify degree disciplines, but all look
for numeracy and literacy skills and the capacity to establish
interpersonal relationships rapidly. Opportunities exist in both the
private and the public sector.”

“Retail Banking and Personal Financial Services - while graduates in
mathematical sciences may apply for all the posts open to graduates of
any discipline they are also in demand for various specialist posts.
The growth in applications of information technology has led to an
increase in careers for graduates in areas covering communications,
data processing and funds transfer. There are also a few openings in
investment and statistical analysis.”

“”Insurance and Pensions - insurance companies offer many openings in
addition to actuarial work, including investment analysis, systems
technology and underwriting.”

“Management Consultancy - covers a wide range of applications and the
type of work depends on the sector in which a graduate works.
Competition for posts is fierce.”

The link where I got the following information also has tips on how
you could use your math degree to pursue careers like the ones
mentioned above.

“Your degree in Mathematics... what next?”
http://www.prospects.ac.uk/cms/ShowPage/Home_page/Options_with_different_subjects/Signpost_Sheets/p!edbbe?mode=view&type=d&id=45#Jobs%20Directly%20Related%20to%20Your
 

It seems that in the US, math graduates pursue the same types of
careers. The US Department of Labor provides an overview of careers
for mathematics majors.

“Other occupations that require extensive knowledge of mathematics or,
in some cases, a degree in mathematics include actuaries;
statisticians; computer programmers; systems analysts, computer
scientists, and database administrators; computer software engineers;
and operations research analysts. A strong background in mathematics
also facilitates employment as teachers—postsecondary, engineers,
economists and survey and market researchers, financial analysts and
personal financial advisors, and physicists and astronomers.”

“Mathematicians”
http://stats.bls.gov/oco/ocos043.htm 

A look at the different business and financial careers opened to math
majors from different US universities would give us good insights as
well.

Accountant
Banking/ Credit/ Investment Mgr
Compensation/Benefits Administrator
Risk & Insurance Specialist  
Risk Analyst
Cost Estimator/Analyst  
Economist
Employee Relations Specialist
External Auditor 
Financial Auditor
Financial Consultant 
Financial Manager 
Inventory Control Specialist  
Investment Banker 
Market Research Analyst  
Mortgage Researcher 
Treasury Management Specialist  

University of North Carolina at Wilmington
http://www.uncwil.edu/stuaff/career/Majors/math.htm


Actuary
Economic Analyst
Real Estate Appraiser
Auditor
Securities Analyst

Trinity University
http://www.trinity.edu/departments/career_services/Students%20side%20bar_files/Major%20Handouts/math.htm


Accountant Contract Administrator
Research Analyst Actuary
Cost Estimator/Analyst
Inventory Control Specialist
Risk and Insurance Specialist
Investment Banker
Risk Analyst
Market Research Analyst
Banking/Credit/Investment Manager
Economist Mortgage Researcher
Employee Relations Specialist
Compensation/Benefits Administrator
External Auditor
Financial Auditor
Treasury Management Specialist
Financial Consultant
Financial Manager
Purchasing/Contract Agent
Consumer Loan/Credit Officer

University of Wisconsin – River Falls
http://www.uwrf.edu/ccs/assets/documents/with-major-in/math.pdf


--------------------------
The next link that will be presented here are real life examples of
mathematicians in the UK that went to the financial services sector.
Just click on their names and you will get to their stories.

Math@Work: Financial Services Careers for Mathematicians
http://www.mathsatwork.com/real-lives/index.asp?industry=Financial%20Services

The Math@Work website is a UK based organization. You may contact them
by clicking on the link below.
 
Math@Work: Contact Page
http://www.mathsatwork.com/contact.html


Since UK and US mathematician careers have great similarities, it
would also be helpful to look at some stories of Americans who went
into the financial services sector.

Financial Engineer Summit Systems Inc.
http://www.ams.org/careers/jcardena.html 

Associate: Derivatives Research Department of J.P. Morgan Securities
Inc.
http://www.ams.org/careers/plewicki.html 

Investment Actuary Westfield Companies
http://www.ams.org/careers/dhall.html 

Senior Budget Analyst: Department of the Navy Bureau of Medicine and
Surgery
http://www.maa.org/careers/lsullivan.html 

Vice President: Senior Manager Technical Finance Bank of America
http://www.ams.org/careers/rlibby.html

Vice President: Mortgage Research for Salomon Brothers Inc.
http://www.ams.org/careers/ryoung.html 

Consulting Actuary: Muetterties, Bennett and Associates
http://www.ams.org/careers/rberens.html 

Consulting Actuary: Joan Ogden Actuaries
http://www.maa.org/careers/ogden.html 

Management Analytics (MA) Division: Price Waterhouse
http://www.ams.org/careers/cmartin.html

Cost Estimator: Naval Sea Systems Command
http://www.ams.org/careers/cbaker.html 


Search terms used:               
UK “financial careers” math mathematics majors  
                   
I hope these links would help you in your research. Before rating this
answer, please ask for a clarification if you have a question or if
you would need further information.
                   
Thanks for visiting us.                    
                   
Regards,                    
Easterangel-ga                    
Google Answers Researcher

---

Clarification of Answer by easterangel-ga on 30 Jul 2003 05:46 PDT

Hi again!

My fellow researcher jem-ga sent me a message since she and her
husband are in the finance industry in London. I advice that you read
her message so you can get valuable tips in pursuing your career.

--------------------
From: Jem-ga

Basically, an undergrad maths degree is fine as a starting point re:
working in finance/banking/trading in the City of London BUT it is
just that, a starting point. It doesn't particularly single you out
for any specialised roles in these areas. So, for example, someone
with an undergrad degree in maths is just as likely to be working in
areas like risk management, general trading and economic analysis as
someone with an undergrad degree in engineering or an undergrad degree
in economics.

The route for a professional mathemetician in the London markets is to
specialise, usually via a further degree like a PhD in applied
mathematics, a PhD in pure mathematics, a PhD in number theory, etc.
To be honest, the actual specialisation doesn't matter that much -
it's more the ability to be at an advanced level where such
specialisation can be applied.

It's usually at this point (i.e. after acheiving a further degree like
a PhD) that professional mathematicians get hired as "quants" - these
are people who specialise in focusing on things like quantitative
research in trading, financial modelling and the like. For example, I
have a friend who has an undergrad degree in math and a PhD in applied
Physics - he's currently working at an investment bank in London as a
quantitative analyst creating financial models for a specified set of
trading strategies.

I have another friend who has an undergrad degree in maths and a PhD
in pure maths - he's currently working at an investment bank in London
as a trader of highly specialised derivative products which base their
strategy on financial models which he conceptualises and creates.

One of the best places to go for a really good discussion on this
issue is:

http://www.wilmott.com/index.cfm 

a forum set up and solely dedicated to all things financial (e.g.
trading, banking, finance, quantitative research, etc). In particular,
there's a student forum there at:

http://www.wilmott.com/categories.cfm?catid=8 

as well as a careers forum at: 

http://www.wilmott.com/categories.cfm?catid=16 

both of which are incredibly useful for anyone thinking of getting
into this area of business. The general forum is also a very good
read, too!

Hope this helps. 

jem-ga
----------------------

I hope that my original answer together and this anecdote would be of
great help to you.

Thanks!

---

Request for Answer Clarification by cdl-ga on 30 Jul 2003 06:17 PDT

thanks for this, the information and links will be useful. I was
hoping more for a simple explanation of what financial mathemeticians
do. For instance, I'm aware mathemeticians do things to do with
trading equities. What do they do. What, and (roughly) how do they
predict things.

---

Clarification of Answer by easterangel-ga on 30 Jul 2003 06:52 PDT

Hi again and thanks for asking a clarification before making a rating.
It is evident that my answer satisfies your original question. The
additional information provided here will address your concerns as
regards to your request for clarification.

Predicting equities is one of the jobs mathematicians do but it is not
simple and ussually the explanation is complicated. The most basic I
found mentions that usually mathematical caluclations and tools such
as moving averages, on balance volume and the stochastic oscillator
are used for stock market presiction.

"Mathematicians, traders and financiers have studied stock markets
ever since they were invented several hundred years ago, but no one
has yet managed to devise a foolproof system for working out what will
happen next. But financial analysts can use historical data and
mathematical calculations, such as moving averages, on balance volume
and the stochastic oscillator, to try to predict future changes in the
stock market."

"Stock markets – putting your money where your math is"
http://www.science.org.au/nova/047/047key.htm

Statistics can also be used for prediction.

"There are three traditional ways to go about answering this question.
The first relies on statistical measures developed by market
mathematicians to project future risk from past performance."

"Whether you’re talking about beta, or standard deviation, or Sharpe
ratio, all these measures are based on stock market history. They’ll
tell you how risky the market is now -- if you’re willing to assume
that the future period you’re interested in resembles some period in
the past. Most of these measures, or at least the most commonly used
calculations for these measures, are based on the past three years of
stock market history."

"We need a new way to read this rocky market"
http://moneycentral.msn.com/content/P26872.asp?Printer=


Another way is the Portfolio Theory.
http://www.moneychimp.com/articles/risk/riskintro.htm


Aside from Portfolio Theory, a more complicated process called fractal
geometry
is being studied for stock market prediction as well.

"Fractal Geometry in the Stock Market"
http://cyber.bxscience.edu/archives/1999/mar/scitech/fractal.htm


I hope these additional links enriches my original answer.

Best Regards,
Easterangel-ga

Superb, Exactly what I wanted. thanks very much to everyone

Hi cdl-ga 

One other bit of info that I forgot to pass on to Easterangel-ga
during my initial comments:

Another career route that quite a lot of maths undergrads take after
their initial degree is an MSc in Mathematical Finance or similar. 
The London Business School, for example, offers this kind of Master's
Degree as well as a variety of others.

:) jem-ga

Hi again cdl-ga :)

Please find below a very concise example of one of the kinds of things
mathematicians do with respect to equities.  I have quoted it verbatim
from my husband (with thanks!).

<<This is in answer to the question about what and how mathematicians
predict things such as equities.
 
Markets are usually assumed to be informationally efficient. This
hypothesis, known as the Efficient Markets Hypothesis, rests on the
assumption that all available information is rapidly impounded into
the prices of securities, such as shares. The hypothesis is due to
Paul Samuelson "Proof that Properly Discounted Present Values of
Assets Vibrate Randomly".
 
1. If the EMH holds it doesn't make any sense to talk about
"predicting" asset prices, including share prices. The profit and loss
stream arising from following any investment strategy in an efficient
market is a random walk with expected value of zero (less transaction
costs). It makes more sense to think in terms of stochastic processes
with independent innovations, i.e. Markov process. One famous example
(Black and Scholes 1973) is the assumption that share prices follow a
Wiener process with constant drift and volatility:
 
dS = mu.S dt +sigma.S dW(t)
 
where dW(t) ~ N(0,1) iid
 
mu represents the future real-world drift of the share price. However,
mu is neither known nor observable. Black and Scholes showed that
under certain assumptions (relating to market completeness) it becomes
possible to demonstrate that there exists only one unique price for an
option written on the shares such that the option price prevents
arbitrage profits from being made. A great deal of the demand for
mathematicians in the finance sector over the last twenty years has
been to develop models using this kind of approach to value and hedge
derivative products, such as options, forwards, swaps, etc. You will
recognise straightaway that the required skills include knowledge of
stochastic calculus, pdes, measure theory/probability, etc
 
2. If the EMH doesn't hold perfectly, it does make sense to talk about
"predicting" asset prices. A great deal of statistical work has gone
into finding so-called "anomolies" in the EMH such that the profit and
loss of a trading strategy is statistically significantly different
from zero. There are certain well-known anomolies, such as persistance
(autocorrelated innovations), seasonal effects (rallies in January as
new money comes into the market), small companies effect (share prices
of small companies outperform compared to CAPM predictions) etc etc.
Most of these ideas are relatively unsophisticated. However, some
genuinely good mathematical research has gone into approaches such as
chaos theory, genetic algorithms, etc. See the work of J Doyne Farmer
and others for insights into recent work in this area.
 
3. The two things I have mentioned so far are the glossy and
glamourous end of mathematics in finance. Many mathematicians spend
their working days finding ways to refine existing models, to find
better ways of estimating parameters to use in other people's models
and so on. e.g. in the Wiener process above it is now common to write
sigma as a function of S and t, so that:
 
dS = mu.S dt + sigma(S,t) dW(t)
 
People spend a lot of time working out new and better ways to estimate
this sigma function (usually known as the volatility surface) from
prices of existing options. This and similar work is what occupies
mathematicians in equity departments of investment banks.
 
I hope this sheds some light on your question.>>

Happy reading!

:) jem-ga

p.s. Easterangel-ga - loved the links on Fractal Geometry and
Portfolio Theory :)

Thanks again Jem! Please say a special thank you to your husband as
well. Such a brilliant answer!

From a researcher who has taken the exact path you are planning on
taking...

(I graduated with a BA in Mathematics from University of Cambridge in
1998, spent a year doing non-quant bank work in Leeds and then the
past 4 years doing a Ph.D. in Finance in Boston)

One thing I would strongly encourage you to do is to make good use of
your summers to get as much work experience as possible. Summer
internships are very competitive and tough to find (although I'm sure
there are some people who can give you pointers on how to maximize the
chances of getting one) but they give you something that will separate
you out from the other candidates... even if you go to the Ph.D.
level, experience is key (especially in a bad market as I have found
out recently :)

I would definitely recommend the MS in Finance programs as a good
signal to the market that you are serious about doing quant work in
Finance. Ph.D's are fine and good - but they tend to up your expected
salary, and unless you can prove that you can produce at a level which
is comparable with that salary you might actually limit your options
rather than improve your visibility (Although few top institutions can
resist a Physics Ph.D. student that kicks ass at matlab and comes with
glowing recommendations from faculty :)

Also check out http://www.math-jobs.com/ to get some ideas for jobs
that the mathematically minded can get in finance.

Final advice - start networking as soon as possible. Use your
university or college's career network from day one of your
undergraduate program to find people in the industry to talk to. Find
out more about math jobs in finance from them - (a) it will help you
figure out what interests you most (b) it will help you pick suitable
elective courses (c) they may be able to help you find a hiring
manager that is looking for your skills.

Hope this provides additional help and good luck with your career.
Feel free to keep posting questions (there are plenty of researchers
who can give you advice on many aspects of the career that you are
seeking - from assistance understanding the maths in your course to
information on applying the math to finance, programming help and
lists of likely companies that will employ you when you are done).

Regards

calebu2-ga