Broadening a Mathematical Finance Cheat Sheet Beyond Derivatives
Summary
The document discusses how to broaden a mathematical finance reference sheet that is focused mainly on stochastic calculus and derivative pricing. The responses suggest adding topics that serve distinct parts of quantitative finance: risk management, including VaR and quantiles; portfolio allocation; and quantitative trading, including trade scheduling, smart order routing, and market microstructure. These areas draw on statistics, optimization, control, and point-process methods, so a compact sheet may need several sections or pages rather than a single page.
A further suggestion is to include numerical methods. Quantitative roles often require analyzing model and algorithm errors, implementing numerical solutions to differential equations, and controlling speed and robustness. The document offers topic-selection guidance rather than a defined curriculum or evidence about which subjects are most useful in practice. It also does not provide formulas or explanations for the proposed additions. Its central takeaway is that a useful reference should reflect the breadth of mathematical finance and the computational work involved in applying models.
Key ideas
- A sheet centered on stochastic calculus and derivatives covers only part of mathematical finance.
- Risk management topics include quantiles and value at risk.
- Quantitative trading topics include trade scheduling, routing, and market microstructure.
- Portfolio allocation can be treated as part of risk management or as a separate topic.
- Numerical methods help analyze model error and build efficient, robust implementations.
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Full text
# What should I put on a math finance cheat sheet? # What should I put on a math finance cheat sheet? What are the most useful results that I should put on a mathematical finance cheat sheet? Am I missing anything important: https://github.com/daleroberts/math-finance-cheat-sheet ## Answer by vonjd (score 5, accepted) https://quant.stackexchange.com/a/11134 There is a very famous math finance cheat sheet already (by Prof. Wystup), you can find the content here: https://mathfinance2.com/Products/CheatSheet#Content ## Answer by lehalle (score 2) https://quant.stackexchange.com/a/11158 At this stage your sheet is focus on "stochastic calculus for derivative pricing". It is just a subset of math finance. You are missing: - risk management (VaR, quantiles, etc) -- more statistics than stochastic calculus. See for instance the content of Attilio Meucci's book. - quantitative trading (optimal trade scheduling, smart order routing, microstructure) -- more control and point processes. See for instance the content of Lehalle-Laruelle's book. You may consider that portfolio allocation is a subset of the first topic and thus include it in it. Or have another section on its own that for. You may thus need at least three double pages instead of one... ## Answer by Jacob Amos (score 0) https://quant.stackexchange.com/a/11135 Depending on how long you want the cheat sheet to be, I think maybe touching on some numerical methods that are of importance would be useful. Simply because quant jobs will often require intense analysis of the error in your models and the algorithms that implement them, something along those lines I could see being useful. Additionally, many quant interviews may consist of asking for pseudocode implementations of various ideas, so when it comes to automating the process of solving a differential equation to use in a model, numerical computation becomes important. Especially for firms where speed of deployment is a concern, knowing how to control error and create streamlined and robust numerical algorithms that run quickly will be important.
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