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When I was an undergraduate 15 years ago I did not take any financial mathematics courses. Recently I was approached by an undergraduate, whose ultimate goal is to go into the financial sector, and he asked me about the topics in a financial mathematics course (If relevant, his current major subjects are statistics and mathematics). Though I am not familiar with his curriculum, I told him that typical topics are things like

  • Time value of money (inflation, loans, maybe insurance?)
  • Markets (Supply-Demand and related topics)
  • Financial markets (stock market, and derivatives, etc)

Although I asked him to meet a professor at his school and clarify this further, I would like to know whether I gave him a correct list of topics to research. I am aware of the possibility that there may not be a universal agreement on all the topics that should be included in such a course. But at least there must be an agreement on the essential components.
Also, I want to know the subtopics that come under "Financial markets". He was curious about this especially.

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    $\begingroup$ U. Chicago has prequisites here and the curriculum here for its MS degree in Fin. Math. I'm sure other school do, too. $\endgroup$
    – user1815
    Commented May 1 at 17:51

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The Society of Actuaries syllabi for Exam FM (Financial Mathematics = TVM, Bonds, Term Structure of Interest Rates, Duration/Convexity) and IFM (Investments and Financial Markets = Market Efficiency, Asset Pricing Models, Portfolio Theory, and Derivatives, no longer offered) provide recommended readings and a more detailed listing of topics.

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Given that he is into stats and math, he probably has a very decent math background (true math) already, compared to the average Goldman Sachs 22 year old analyst.

He doesn't have a full-on quant jock background, where they typically hire Ph.D. physics theorists, but that's pretty specialized—and I would argue overplayed online, versus number of true positions.

Your list is fine, but I would also add basic accounting. Doesn't need a full class or long textbook. I got all the basics I needed from an ~20 hour programmed instruction text. And it's not "hard". But you need to readily know what all the basic acronyms like COGS or EBIT mean (immediately and without Googling) in order to read spreadsheets, financial statements, etc. Also, just the very basic concepts of double entry bookkeeping and the three financial statements (income, balance, cash flow) of a typical firm.

Within econ, he just needs the basic concepts of microeconomics (supply, demand, monopoly, P-Q charts, elasticity). Macro is a waste of his time.

Jess, jess on time value of money. I quite like the presentation within the old EIT Reference Manual. It's sort of stripped down for engineers, but really gives the intuition.

I don't think the derivatives stuff is critical for an entry-level (out of undergrad) posting. Even if he worked on it, they would just expect him to have the basic smarts, rather than already knowing it. So you could de-emphasize that.

He should be familiar with Excel as well.

P.s. If he goes to an investment bank, they will train him. They hire non-STEM majors from the Ivies all the time. But the above will help him have an easier time.


I would say for study resources:

  • Work through a programmed accounting text, like I mentioned.

  • Read a few chapters of micro in a basic econ book (could be "Econ for managers")

  • Time value of money (read some articles or watch a few videos). Buy Valuation by Copeland (or comparable). Skim it, but no need to work the whole text. Know what CAPM, NPV, IRR, and "beta" all mean.

  • Corporate finance (buy a copy of Brealey and Myers, old/used is fine and skim it). No need to go through the whole thing, but it is an incredibly insightful book. And useful for ganglion bashing.

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The main Mathematical Finance program of which I am aware is the one at Boston University. You can find more about its academic components here. There is also a Graduate Certificate in Advanced Financial Technology, for which a brief description is here.

As to the topics of import, I suppose they can be inferred from the bullet-point list at the former link:

  • Algorithmic trading and high-frequency data
  • Big data analysis and cloud computing
  • Blockchain and cryptocurrencies
  • Credit and corporate risk management
  • Derivatives valuation
  • Expertise in R, Python, C++, Julia
  • Machine learning and financial applications
  • Portfolio theory and asset management
  • Risk management
  • Statistics and Financial Econometrics

This list is copied verbatim from the BU MSMFT Academics link; the corresponding three semesters of courses can also be found above.

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