Required math for Computational Finance? [closed]

Question

I don't have a strong mathematical background, but I would love to work on some computational finance problems. I got "An Introduction to Computational Finance Without Agonizing Pain " by Peter Forsyth, but it still was pretty hard for me to follow what he was saying.

What are the required maths prerequisites for this course?

I want to make sense of these kinds of papers.

Snub

"Computational finance" means doing finances with the computer. I suppose the OP does want to program such a system, not just use Excel to do some graphs and such. @kunjaan: Maybe rephrase to include your intent to program in this area? – Nies

Please consider contributing to the quantitative finance Stack Exchange proposal: area51.stackexchange.com/proposals/117/quantitative-finance. – Brittneybrittni

Answer 1

You want some calculus, linear algebra, probability, statistics, numerical analysis, Monte Carlo methods, partial differential equations, and stochastic calculus at a minimum. A good introduction is Paul Wilmott's Paul Wilmott Introduces Quantitative Finance. That will provides you references for the aforementioned subjects as well as drawing together the necessary ideas to have a basic understanding of quantitative finance.

Selfsustaining

Answer 2

Look at the wikipedia entry and it will tell you:

Generally, individuals who fill positions in computational finance are known as “quants”, referring to the quantitative skills necessary to perform the job. Specifically, knowledge of the C++ programming language, as well as of the mathematical subfields of stochastic calculus, multivariate calculus, linear algebra, differential equations, probability theory and statistical inference are often entry level requisites for such a position. C++ has become the dominant language for two main reasons, the computationally intensive nature of many algorithms and the focus on libraries rather than applications.

It might be interesting to look at artificial intelligence, and therefore mathematical logic as well, like neural networks, pattern matching, knowledge databases, inference, ...

Nies

Unlike the wikipedia article, most of the topics you mention are completely irrelevant to a quantitative analyst. – Gotcher

@jon Not if you work for a hedge fund. – Ultraviolet

Answer 3

I graduated with a math major. With that background the book you linked to is an introduction and it's painless. Without that background it's still an introduction and hopefully the pain isn't agonizing. (That you've survived long enough to ask a question here about it suggests that it's not.)

I read over the first 36 pages of the PDF you linked to (i.e. through chapter 4). It's highly technical and found I the following areas of math.

• First semester calculus
• Second semester calculus
• Linear algebra (just a little)
• Probability

Mostly the calculus is used to compute probability related things so if you're seroius about diving in to this stuff then I recommend that you start with algebraic probability and then work your way through the calculus.

Backscratcher

Thanks that helps. Since you are a mathematician,could you please finish the pdf and tell us the mathematics the subject touches? – Snub

@David Locke: Add PDE and stochastic calculus at a minimum. – Selfsustaining

@kunjaan: If you can figure out the PDE and stochastic calculus, that's more than enough to slog your way through the whole document. But that's no walk-in-the-park. – Selfsustaining

Answer 4

A book that I got a lot out of was Time Series Analysis. You do need a lot of "basic math" including every topic mentioned by other responses. The thing is that computational finance is relentlessly mathematical and the more math you know often the better off you will be.

Democracy

Answer 5

The skills you will need for being a real quant not just an IT programmer working in a quant company:

• Stochastic Calculus
  • Geometric Brownian Motion
  • Black-Scholes
  • Risk neutral measure
• Measure Theory
  • Sigma algebra
  • Integrals
• Probability
  • Expectations
• Econmetrics
  • Time Series (ARMA(p,q), MA(p), AR(p))
• Computational
  • Monte Carlo
  • Finite Difference Methods

Decency

Answer 6

I liked "Paul Wilmott on Quantitative Finance, 2nd. Ed". It's a three volume set, lots of good math and explanations presented in an accessible way. I put up videos of concepts from the first volume on YouTube, check them out. http://www.youtube.com/user/NathanWhitehead

Then I would recommend reading Mark Joshi's book "The Concept and Practice of Mathematical Finance" and working through all the exercises and computer projects. Lots of great stuff in there.

Capias

Answer 7

I really like reading through the syllabus for Carnegie Mellon's Professional Master's program in Computational Finance. Steven Shreve has written a good textbook in Stochastic Calculus for Finance. You can see the course descriptions in detail here

Demurral

Answer 8

First you should know probability (combinatorics,probability density function PDF, random variable), types of PDF and work your way into calculus - differential, integral and partial derivatives. They are rather simple conceptually. Matrix helps you solve simultaneous linear equations.

For non-linear models, in nature, most processes are non-linear, depending on your rigor, you can make things as complex as you want.

Confidence is very important.

Vasques