Math for Quantatative Finance

[@alphafound3459]

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 (f(x)g(x))'=f'(x)g(x)+f(x)g'(x). In stochastic calculus the product rule is (f(x)g(x))'=f'(x)g(x)+f(x)g'(x) + 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.

[@thefourthbrotherkaramazov245]

Hey, how much measure theory for stochastic calculus? Is there an approach for undergrads that have analysis exposure and a good amount of probability and statistics but no measure theory? Thanks

[@alphafound3459]

@@thefourthbrotherkaramazov245 Pavel: Since mine was a masters program, I never had to have measure theory. Occasionally something in class was said to the effect "There is a theorem from measure theory which states..." Computational finance can be wide ranging in it's requirements. There are statistics/probability approaches and PDE/numerical methods approaches, and of course coding. Some programs are heavy on finance/economics and other have finance almost as an afterthought. I had some of both. You will have to read the introduction to any book to see if measure theory is required or recommended. Sometimes I think the authors are writing for someone other than the students as the equations, even after proper development have no intuition to them. One time I asked a guest professor where an unlikely equation came from, he said the equation is one that could be solved, he was making no claim that it reflected reality. There have been many books written, I do not know one that I can say, "this is the best." It might help to read an introductory econometrics book, not so much for the math, but for the context. One finance text, not very mathy but should give you the investment background is: Investment, by Bodie, Kane and Marcus. You can find it in free PDF. Best wishes.

[@ytwow1233]

@Alpha Found where have you done your MS?

[@alphafound3459]

@@ytwow1233 University of Cincinnati. Started in 1998. Finished in 2001. I was not a great student as I was distracted by the problems of life.

[@ytwow1233]

@@alphafound3459 Thank you for your answer, Sir. I hope everything went well for you. Is there any chance that you have scripts or something from your studies left that you could share?

[@shriidharkulkarni6648]

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.

[@SebaCape55]

You still have time to do so

[@timenow5312]

I'm 68, and I was taught maths at school including Logarithms, Algebra but never taught what they were used for, and never did Calculus so my Mathematical journey through life was a calculator, which was invented 2 years after I left school. The reason why I am here is, yes, I like everyone else who fears Dementia and are constantly told about Languages, Painting and Maths. On yet another journey to a local charity shop, I found kids school books dealing with basic Algebra,, I bought them, and under no pressure, am enjoying the learning and expanding my mental synapses. One day I will find out what it is used for, because haven't found out exactly yet.

[@johnnykleytonful]

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

[@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.

[@alphafound3459]

In graduate school I took a year long seminar course using the 5th edition. It can be downloaded for free. It covers much more than stochastic finance, but there is a dedicated chapter.

[@vvillegas01]

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

[@mr.erikchun5863]

Did you have to include the word, literally?

[@Efesus67]

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.

[@Efesus67]

@@gger1234 Book of proof is free online as a pdf. The other two, idk. I bought them on paperbacks, and u thought they were cheap.

[@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!

[@thefourthbrotherkaramazov245]

Hey, how much measure theory for stochastic calculus? Is there an approach for undergrads that have analysis exposure and a good amount of probability and statistics but no measure theory?

[@chunawalla]

@@thefourthbrotherkaramazov245 For someone, who has exposure to basic analysis, "Measure, Integral and Probability", by Capinski (Springer) is very accessible.

[@americanhero8606]

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).

[@benjamintreitz1647]

Casella / Berger. Wilmott. Shreve 1 & 2.

[@blazel462]

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

[@seanhunter111]

Please for goodness sake don't choose this. It really is one of the worst possible choices. I worked as a quant in the securities division at Goldman for 8 years. Instead of Hull I would go for "Introduction to the Mathematics of Financial Derivatives" by Neftci. It's targetted at a similar place to Hull but is just way way better in every possible way. I would also recommend "Concepts and Practise of Mathematical Finance" by joshi. You only need volume I. Volume 2 is all C++ code which is probably a bit dated now. Then once you've worked through Neftci if you really want to go deep on Stochastic Calculus colleagues who are good at that really like the Springer books by Shreve but I understand them to be *hard* and haven't read them myself (not at that level yet).

[@davidc4408]

​@@seanhunter111Thanks for sharing that. Do you mind sharing type of salary you can make after 8 years in a tier 1 investment bank like Goldman as a quant? Or would a hedge fund pay more?

[@seanhunter111]

@@davidc4408 Honestly my info is highly out of date. That said a hedge fund is always going to be able to pay more at the extreme upper end given some people at hedge funds have had huge one-off payouts or extreme career outliers in the billions of dollars (Jim Simons for example). I would say in either case if you’re good and/or lucky you can earn more money than anyone ever really needs.

[@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...

[@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)

[@kshitijshekhar1144]

If you're looking for Quant research roles, a PhD in any quantitative discipline like Math, CS, Econ, Even Neuroscience/Computational Biology will do. Cuz they often have training programs for recent PhD grads, where they teach you finance concepts etc. It would help if you did some research with a professor tho, in quant finance. Tbh Algebraic Toplogy is overkill for most recruiters, a PhD in mathematics in any area is usually enough.

[@nielubiegdyktospatrzyjakje3909]

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!

[@suhanikadian4229]

From where are you doing your masters ?

[@richtofen4888]

Hey, how has it been? :)

[@ryanhermanson6121]

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.

[@anthonybernardi4929]

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!

[@merkonerko2]

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.

[@matteogirelli1023]

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

[@jessewolf7649]

High level theoretical finance is also extremely “mathematical “.

[@matheusferesturcheti288]

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).

[@DimitriBianco]

Great recommendations subscriber!

[@yuvrajsingh099]

Waiting for this video Thanks for uploading.

[@albertotrelles5748]

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

[@randallmcgrath9345]

Ive seen Quant salaries between 175k to 400k a year, with data points above or below this, but the money is good. Even so, I don't trust banks very much, lol.

[@pariskastanias5691]

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!

[@vvillegas01]

Hi! I am in my undergraduate rn and want to go into quant finance so thank you for mentioning Zetamac!

[@chriz8754]

Hello, do you recommend learning mental abacus for this? Thanks for the advice!!

[@pariskastanias5691]

@@chriz8754 You can try out that technique. I recommend you experiment with different calculation techniques, because everyone is different.

[@pariskastanias5691]

@harrysnothead8939 Mainly because trading needs to be very high speed. You need to execute a good trade quickly or else someone else will, and you might not have time to use a calculator.

[@liondovelearning1391]

Lindsey is also a boys name in Northern US 90's

[@pushkarnagpure2357]

Nico van der Wijst Finance: A Quantitative Introduction

[@raosiddharth4726]

Thank you very much sir

[@DedliFlexx]

There is a typo in the title of the video: it should be "quantitative" 🙂

[@jessewolf7649]

Very rigorous: Methods of Mathematical Finance by Karatzas & Shreve published by Springer Verlag. Requires mathematical maturity. But the most complete theoretical treatment I have seen.

[@lukeatlas5337]

Oohh finally!

[@lukeatlas5337]

My comments seems to keep getting deleted: Here’s some unsolicited advice: Mathematical Finance evolved with the use of their tools. It heavily depends on which side of Mathematical Finance they will pursue. It is explained on Attilio Meucci’s ARPM Website, which differentiates the expected background. The two sides are P(buy-side) and Q(sell-side) World. The sell-side heavily uses PDEs, Stochastic Calculus, or Continuous-time martingales. This area has been steadily shrinking since banks were prohibited from proprietary trading. Only niche areas remain at specific firms. The buy-side, most of modern-day quantitative finance, focuses on portfolio and risk management to attain risk-adjusted absolute returns. It heavily uses discrete-time series analysis, multivariate statistics, and machine learning to name a few. Both sides use numerical methods; programming languages are a must regardless of the role of “Quant,” broadly categorized as a developer, trader, and researcher. There are many things to learn for a Quant someone must first identify which side of Quant Finance and what specific role. Assuming the buy-side is the first option, he must be familiar with Analysis to the level of Rudin’s Principles of Mathematical Analysis. Then, he need not fully dive into a purely Measure Theory course since its entire course is enormous material and an immense amount of time to cover. This study period is inefficient since a quant must possess more than one specific mathematical background. He only needs a measure-theoretic treatment of probability which can be explored at the level of Rudin. The suggested book for Probability would be Probability by Alan F. Karr. That’s sufficient background for Mathematics. If you need a review of the Analysis in a more detailed treatment, I recommend Analysis by Amann, Mathematical Analysis by Zorich, or by Tom Apostol as a reference guide. The next focus would be heavy statistical modeling background which I feel your coursework should cover. The primary pre-requisite is mastery over the basics of Mathematical Statistics. An excellent material to refer to is Robert V. Hogg or George Casella. The Statistics you will use are mainly applied with a heavy emphasis on time series, inference, spatio-temporal processes, and Bayesian perspective more than Frequentist. If not, I can recommend texts. The last requirement is a scientific computing language such as C++ and a strong background in Numerical Methods. The suggestion above assumes a strong background in calculus (single var, multivar, vector), linear algebra to the level of Halmos, and complex analysis to the level of Papa Rudin.

[@tabulaaaa]

Any book advice for agent based models?

[@Fru1tpunch]

Everyone at my university talks about their investments and I really didnt care about stocks until I found out about quantitative analysis. I generally think people who brag about their stocks are annoying because they know nothing about trading and just wanna sound smart lol.

[@singhravi9653]

How to draw a imaginary tangent?? Please give me answer how

[@patrickoconnor-read2323]

You are a guru for pathways into maths. Thankyou maths Yoda!

[@Ayesha_11122]

Do people have book recommendations for grad school economics degree? Or just like how to go about learning the math needed without getting completely overwhelmed. I need to be efficient because i tend to really lose myself into various areas and end up not covering everything needed.

[@d0m367]

hey, I hope this reaches you i am in 3 year of my engineering college and i wanna break into quant or risk managment or investment banking ,which course should i consider taking in my masters that would help me as my core is data science and i am not from the us

[@mid-westmusic3472]

Hey Math Sorcerer have you ever broken down what paying off a student loan looks like on paper?

[@sujalsrichandan9902]

Now I am in my second year btech cs, I want to go in quant role for that I need to know beginning to advance of probabilities and statistics. Can u make a roadmap

[@afiaantara8438]

Can anybody help me? My teacher said I need to find a theory of mathematics that has been used in finance. For my thesis

[@pushkarnagpure2357]

And the other by Stephen blyth

[@sangatimahata2031]

Can someone help me with my situations? S.1 My school doesn't teach me mathematics well my tutor teaches me slowly but because I have already finished half of my this year mathematics syllabus so I feel bored to learn it again as I have already learnt it but when I try to learn the other half then I don't understand it because it's not taught to me. Last year my father taught me half of the syllabus but this year Ihe Doesn't have time so I have to depend on my tutor but because he's slow so I can't learn the other half as he wouldn't teach us the last half before the first but I can't bear repeating the first half for the third time .. now can anyone tell me how I clear my concepts? 2: for a few months I have been suffering to decide what to read I have been liking mathematics for atleast a year then I understood the value of history and became a history nerd after that I saw geography is entirely connected with history so I became a geography nerd too. The problems started from that time I watched a youtuber and read a few books and started liking English literature , I watched Interstellar , read " a brief history of time" , kinda failed but tried to read "special and general relativity " "Einstein biography" read a bit of "modern physics " until I stopped understanding and became a fan of physics and astronomy. started hating biology . Now the main problem is I can't be a nerd in all these subjects but I do really love them . Although the time is not enough but I can't leave them now can anyone help me in managing time

[@paschalcharles6097]

There are tonnes of informations in mathematics is there any ways of managing a mathematical concepts???

[@Matlockization]

I wonder why your video's are no longer 480p ?

[@TheMathSorcerer]

I don't know. I use different cameras and setups. I need a better setup though!

[@Matlockization]

@@TheMathSorcerer For me the selection on your video is either 360p or 720p. But it indicates you have changes cameras within the last few weeks or months.

[@joshuatreetop8025]

If I ever become rich, I will send you a cordial invitation to lunch.

[@TheMathSorcerer]

❤️❤️

[@jongxina3595]

Is measure theory required for stochastic calculus? (from a pure math perspective)

[@jessewolf7649]

Yes

[@bvds2007]

unfortunately yes. however, in the real world of quant finance practitioners, no.

[@davidc4408]

Do you have a networth target

[@AbolitionFashionClub]

I'm laughing I love this

[@AbolitionFashionClub]

It's not about the work, it is about the understanding

[@AvantikaSharma-ic3wt]

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