I am an applied math postdoc and I have been presented with the option of leaving academia to work in high frequency trading. I wanted to get a feel for the field and the theory underlying it so I scanned through several books in the library and it seems there are almost no books on the mathematical theory of this field. All the books I have looked at contain lots of explanations of the various aspects of trading such as 'market participants', 'limit order books', 'market microstructure', etc..which of course are very important to know, and some relatively basic math on things like 'statistical arbitrage strategies'. But where is the rigorous mathematical underpinning?
I would have expected to find books containing the same type of theory as in books on mathematical finance, i.e. a deep treatment of measure theory and probability theory, mathematical statistics, stochastic processes etc..
Why are these topics not covered in HFT books? Is advanced math not needed? If this is the case, what are the main skills needed for a high frequency trader?
Answer
Hah! There is no such thing as the “rigorous mathematical underpinning” of high frequency trading - because HFT, like all trading, is not primarily a mathematical endeavour.
It’s true that many people who work in HFT have a mathematical background, but that’s because the tools of applied math and statistics are useful when analysing the large amounts of data that are generated by HFT activity. So the math that is useful to know is linear algebra, statistics, time series and optimisation (to some extent it’s useful to be familiar with machine learning, which encompasses all of the above).
Don’t go into HFT thinking that you will primarily be doing advanced math. If you are lucky, you will mostly be doing data analysis. More likely, you will spend a lot of time cleaning data, writing code, and monitoring trading systems.
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