Math for Quantatative Finance

In this video I answer a question I received from a viewer. They want to know about mathematics for quantitative finance. They are specifically concerned with math for real analysis and probability. Do you have any advice or opinions? If so, please leave a comment.

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[alphafound]

I have a MS in computational finance and work as an investment advisor. One of my professors used to say, "Slow down and lower your goals." There is no short cut to understanding because stochastic calculus is not obvious. For instance, in freshman calculus the product rule is In stochastic calculus the product rule is + f'(x)g'(x), so there is an extra term. This is because in continuous stochastic process, the function is continuous everywhere but smooth nowhere. In any case, it is a slow process getting used to it (it was difficult for me). Also, if you haven't had calculus based physics, it will help if you take some time to get familiar with the heat diffusion equation. It wouldn't hurt to study numerical analysis and have some familiarity in Python or Mathematica. I came into the program with a weak background, but I made it. I think it is well worth the effort.

[shriidharkulkarni]

I wish I had seen this kind of videos in my childhood and not at the age of 62. I too would have fallen in love with mathematics. Good video. Thanks for upload.

[AbselutlyNobody]

A little more advanced but still very useful would be "Stochastic differential equations" by Bernt Øksendal. A lot of research in quantitative finance is based on stochastic calculus and stochastic/random processes. So anything related to that would be useful.

[johnnykleytonful]

My major is also Economics and the sorcerer is really helping me with my math.

[AndersBjornTH]

Introductory books on stochastic calculus at various levels of rigor are extremely important. Also, options and futures related texts would be valuable as background for what comes next. Optimal control theory for corporate finance related topics would also be useful. Best of luck!

[blazel]

The Hull book, ‘Options, Futures and Other Derivatives’ is an industry standard. You will always find one on a quants desk.

[vvillegas]

youre literally one of the best people i know. thank you for making this video

[Efesus]

I recommend Probability for the Enthusiastic Beginner by David Morin; he takes the time to explain things more than I've seen in other books. And his problems (with solutions) are not just plug and chug, they really help you develop your understanding.


For mathematical maturity, i would recommend The Book of Proof. But I also like "Introductory mathematics: algebra and analysis" by Geoff Smith. He's very keen on foreseeing confusion with mathematical formalisms.

Best of luck.

[americanhero]

FYI Sheldon Ross has written two different books: (1) Intro to Probability and (2) Probability Models. The latter one is somewhat more advanced and assumes you already took a course on probability theory.

Not sure how prepared you are on the finance knowledge side, but assuming you're not well versed on the topic I suggest you start with Bodie/Kane/Marcus's Investments. Fairly comprehensive, includes a lot of mathematical explanation of important theories in finance and investing. After you read that cover to cover (highly suggested), then move on to Hull's "Options Futures and Swaps" to learn the fundamentals of derivatives (the finance kind, not the calculus kind).

[Pabloparsil]

Hi, I just wanted to mention that for a rigorous option pricing book you might want to check out Shreve. The first volume pretty much doesn't require math background, it is short, extremely well written and simple (it's all about the binomial model, which is discrete and very intuitive). The second volume is the hardcore one, where he briefly starts with sigma algebras, filtrations, Lebesgue integral...

[ryanhermanson]

Brownian Motion Calculus by Wiersema is the book I’m working through with my grad program for stochastic calculus. I’ve found it very approachable compared to some of the other books on the subject.

[matheusferesturcheti]

If you want a general book, maybe "A Primer for the Mathematics of Financial Engineering" from Dan Stefanica. If you need help with Analysis (which might begin at measure theory, not "formal calculus"), I'd check "Calculus" from Michael Spivak (since it's actually an intro to analysis) or the "Principles of Mathematical Analysis" from Rudin (not the "Real and Complex Analysis" one, which is measure theory).

[TQuantP]

This is a very interesting take, I actually have exactly the opposite problem to be honest. I graduated in math, did a master's in algebraic topology (it was mostly cohomology theory but still) and I've decided that it's too dense of an area for me with too narrow exits on the private sector to continue, thus I turned to econometrics and quantitative finance for my PhD. I find beffudling that there is no clear avenue in doing something related to quantitative finance.
In the end I decided to go to the high-frequency empirical data point of view, where the financial and economical literacy required is minimal (it's mainly statistics and data science).
If anyone knows a way that I can follow, any books to read or any guidelines at all, please commend. (I have an unlimited supply of "take and forget" books from my university's library so at the moment I just borrow whatever I find interesting and relevant but it's too time consuming with bad results, since I'm basically picking at random)

[nielubiegdyktospatrzyjakje]

Oh, this is very nice knowing, that I am not the only one pursuing the same educational path. I am after BSc in Financial Analysis (economics and finance), had a lot of statistics, forecasting, econometrics, maths for economics. In October I am starting my MSc in Financial Maths. I believe, I made the right choice!

[matteogirelli]

Finance is more "statistical" and economics is more "mathematical" . I suggest you read the syllabus of some courses in the graduate program. Also simply write to the professors of the graduate program or simply the professor of your bachelor's. They will know. Anyway, you'll find math and stats but I think you should focus on getting the probability and proof writing skills since those are harder

[anthonybernardi]

Great question! I am in a similar spot, preparing to enter Graduate School in Math. I had a class I took as a non-degree student in Probability, where we used Ross' Intro to Probability Models. Great book, but super dense at times. I used Ross' A First Course in Probability as a supplement and found that significantly easier to work through. I think using Ross' A First Course along with Wackerly and the other texts the Sorcerer mentioned should put you in a good position. Hope this helps!

[benjamintreitz]

Casella / Berger. Wilmott. Shreve 1 & 2.

[albertotrelles]

Just saw in the background a book with the title "Origametry". Maybe we can have a review? Wonder what kind of exercises that book may have

[pariskastanias]

I am really passionate about quant finance! I do have some advice, not for the degree, but for the industry:

Firstly, if you become a trader, fast mental maths is important. You want to be able to play the game Zetamac and get a score of about 60 or so.

Secondly, programming and algorithms are a bit important if you are a quantitative researcher. Nowadays, trading tends to be automated, so these skills are also valued.

Lastly, in terms of your degree and your worries regarding your proficiency in mathematics, it's ok! Just keep grinding and never give up your passion!

[merkonerko]

Wow thank you so much for creating a video response to my question, I can’t believe I missed it! Btw, I signed off the email with “Mr. Lindsay” because I’m male but I guess that wasn’t terribly clear lol.