Math in Quant Finance - Examples

A subscriber asked about the usefulness of finance classes for a quant and for examples on how math is actually used in quantitative finance. I'll use neural networks, time series, and the Black Scholes as examples of why knowing math is important.
Math is really the language of quantitative analysis while computer science is the language used to have a computer help us getting answers. Statistics is just the theory used to get inference about our data. When you combine math, computer science, and statistics while applying it to financial problems, we get quantitative finance.
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[@jameshozier7823]

at an office i used to work at, they would blindly use Excel's =FORECAST() function to try and obtain the future numbers to get their NPVs, and of course it was hardly ever accurate. had to figure out and explain that the function was utilizing the Holt-Winters exponential smoothing method and most likely with fixed alpha, beta, and gamma values (i couldn't obtain the source of what Excel was using, but through experimentation it seemed like it at the time). so i wrote them my own version with modified level, trend, and seasonal formulas and actual optimized alpha, beta, gamma values. this is why you are so correct about those crappy pre-packaged "models" and actually needing to understand the technicalities underneath the hood!

[@NOVAsteamed]

Great to know!

[@alex_8704]

A very insightful detailed video. Thank you so much.

[@sentralorigin]

nice real life examples. the first time i worked with NNs i thought it was completely a CS thing but the programmer i was working with didn't know how to take partial derivatives for the gradient when generating the activation function's bias node

[@amj864]

Great video as always , thank you.

[@rodrigoavila5580]

Discrete time stochastic processes also use A LOT of Matrices and Linear Algebra (and LA is much more than just matrices)

[@DimitriBianco]

This is a very good point! Often students want to focus on the advanced topics however having a solid foundation in linear algebra goes a long way in building more advanced skills and even conducting many forms of analytics.

[@andrewclark9083]

I love your videos man! I’m in my second year undergrad studying financial mathematics and I am really enjoying learning all of the calculus, algebra, programming etc and I’m hoping to do a Masters in Quantitative Finance or Financial Engineering. Your videos are really informative and also encouraging so thank you for your contribution!

[@ariqchowdhury5301]

what school offers undergrad financial mathematics?

[@MrCryingDragon]

@@ariqchowdhury5301 London School of Economics.

[@williamgriffin7852]

@@ariqchowdhury5301 ANU

[@krishnaprempasumarthy7295]

Thanks a lot for sharing this video!

[@DimitriBianco]

Thanks for being a part of the channel!

[@davideruggeri7240]

Dimitri, I really appreciate your contents! I would be very grateful to hear your opinion about AI in quantitative finance, are we going to be obsolete in the next decades?

[@millamulisha]

Tensor has special transformational properties though... Not just a matrix.

[@matchpoint2899]

Hi Dimitri, thanks for this video. I’m currently a CompSci background whilst trying to build my math knowledge. Would studying numerical methods (euler’s etc) be useful?

[@DimitriBianco]

Yes, numerical methods is one of the main courses that quant programs have.

[@bindoe4001]

Hi Dimitri, I'm current a first year college thinking about work as a financial analyst, I'm interesting in both finance, economic, and math. I don't know what undergrad should I take. Should I do an Math/stastitic undergrad, then take a finance or econ master with an CFA, or just pursuing finance? I personally like to work at a bank or wealth management, but the entry is pretty barrier in the future.

[@adlib3374]

Hello Dimitri, great video thank you for this channel, it is very informative. I want to get in contact with you and message you as I have a few questions about becoming a quant could you please direct me as to how I can do so thank you very much

[@DimitriBianco]

The best way to contact me is through LinkedIn. If you don't have an account I would encourage you to get one as they are useful for finding jobs as well. www.linkedin.com/in/dimitri-bianco/

[@limitedgain6433]

If you make more videos about ideas in programming some Algo Trading ideas, and Python, MQL4/5, you will have much more subscribers, and viewers.

[@maynard-x267]

Hi Dimitri, I'm an undergrade student in finance and I'm planning to register in a MFE program. I'm currently looking for a book to ''update'' my math skills (Calculus, Linear algebra...) and I've found : A Primer For The Mathematics Of Financial Engineering, by Dan Stefanica. Do you happen to have read this book and/or have any other suggestion?

[@DimitriBianco]

The Primer book by Stefanica is the best out there as it is specific to an MFE. As data science has picked up in popularity, you might also review linear algebra. The book, Mathematics for Economists by Simon and Blume was helpful for ODE, optimization, and some linear algebra. Just buy a used version to get it fairly cheap. (My affiliate link for the book): amzn.to/37WdzYM

[@maynard-x267]

@@DimitriBianco Thanks for your answer!

[@screweddevelopment12]

It hurt my head when I discovered that the function to standardize data can be different between libraries because some use sample variance and others use population variance.

[@DimitriBianco]

Just wait until you are using a model that makes you money and the results all of a sudden don't match because someone updated a package. This is where knowing the math structure is important instead of relying on packages.

[@armanmuslimov5988]

Hi Dimitri, great video! Practical illustrations made it a bit clearer for people like me who are not sure about the level of depth in math required to switch from traditional finance to quant. It clarifies to what extent the imposter syndrome is justified :). Having work experience of more than 10 years in traditional banking and theoretical knowledge from CFA and MBA, I got bored there and started studying Statistics and Data science online program from MITx a year ago (so that my brain is not degrading too much in banks bureaucracy). After I finish it in April of this your, planning to dive deeper into financial engineering, with guidance from your videos. You are doing a good job at guiding people who lack intellectual challenges and got bored with the bureaucracy of traditional finance! P.S. It is an awesome idea to publish the list of books on fancyquantnation because before i was making screenshots of your videos at moments when you recommended those books :)

[@DimitriBianco]

Thanks for the feedback and being a part of the channel!

[@bingoboost]

Great content, do you do private tutoring? What resources do you recommend for beginners, thanks!

[@Hmmmmmmm02]

Hey Dimitri, been watching your videos for a while now, and I’m loving them. I currently do an undergrad in Electrical and Electronic Engineering, i have taken a couple of classes so I am fairly proficient in Linear Algebra, ODEs, Differential Equations, but I am interested in the world of Quantitative Finance, as I love math, finance and programming. I do quite of programming on my course and by the side, but I worry that my math skills aren’t exactly up to standard to work in quant finance. I need to brush up on stats and PDEs, amongst other things. What good books or websites would you recommend for learning those sort of Math skills please? Thanks!

[@DimitriBianco]

Check out @PatrickJMT and @Ben Lambert on KZbin. Both have great content around math and statistics (econometrics). My website also has some recommendations on books including free materials. www.fancyquantnation.com

[@Alex95334]

​@@DimitriBianco Hey Dimitri, I'm trying to choose between taking a Pure Math or an Applied Math undergraduate degree with the objective of eventually getting into quantitative finance, which one would you recommend?

[@alejandroruiz8011]

Hey Dimitri! Great video. I am wondering, what kind of projects can I start on my own, so I can include them on my resume for a quant position?

[@DimitriBianco]

It depends how you are defining quant. For quant finance, projects on a resume aren't really valuable or common. If you are wanting to work in data science / technology, then projects can be helpful. For educational purposes, a project around creating a statistical or data science model is useful. Along the model development process you should continue to ask yourself why you are doing whatever you are doing. For example, why did you use specific variables in a model? You should have statistical and logic reasons not just short non-sense answers like, "because they were correlated." You could always use the same data and build a stats model and a data science model and see how/why one fits/predicts better than the other.

[@vwedeagboro-jimoh6556]

@@DimitriBianco since projects aren't really valuable or common, what then can one include on their resume in order to sell themselves?

[@alantang9571]

Hey Dimitri, I understand quantitative finance is a technical job. with a finance undergraduate how did you catch up in the mathematics/stats/programming considering your business degree had little of it?

[@DimitriBianco]

I had programming experience since I was about 16 but the math and stats was really hard. My first semester I was spending about 14-16 hours a day 7 days a week in class, doing homework, and reading a ton of lower level math books at the library. It was really depressing and discouraging but I ended up in a unique spot where I could transfer into the applied economics program while still being able to pick and choose financial engineering classes. Once in the new program I scaled back my studying but I continued to try and fill as many gaps as possible. I highly discourage finance students from trying to jump head first into a quant program as most won't finish. The overall goal should be focused around learning and not just getting the degree as well. If a finance student really wants to do it, I recommend studying a lot before starting a masters so that you get more out of it.

[@alantang9571]

Wow seems like you’ve had a really unique path and came a long way. Have you always done well/been interested in these courses throughout high school and college though? I ask this as a high school senior who’s currently taking Calculus 1 and while I’m not doing bad, I’ve never been the best in my math or technical courses. Despite this, I’ve recently became interested in fields like financial engineering or computer science. I sort of feel behind all the people who’ve been 100% in STEM.

[@DimitriBianco]

This is a great question. I actually hated high school and wasn't sure if I wanted to go to college or not. I really enjoyed geometry but didn't see much use for math outside of that and never planned on working as a quant. After high school I actually started on a biology degree thinking I wanted to be a plastic surgeon. After watching a few surgeries I decided I couldn't handle all the blood and the thought of cutting someone open. I was working at a startup and thought business and finance was interesting so I switched over to a finance degree. After graduation I felt like I needed a lot more math to really do finance correctly and ended up getting a Masters of Applied Economics in Financial Engineering. I actually loved college and graduate school as I felt like there was a reason to learn the material unlike high school. I thought hard about getting a PhD and staying in academia but decided to go into industry instead. Becoming a quant and creating a rewarding career is all about persistence. Most students who get a quant degree burn out before they even start their first job and just float through the rest of their careers. My career has been fun, scary, rewarding, and frustrating all at the same time but I have finally realized it's like a marathon. Some days I feel great and push harder (learning and working) while other days are challenging and you need to slow down and take a break. As long as you enjoy the process and have fun I don't think you'll regret a quant career as long as you really enjoy the analytics.

[@ronaldnyasha6167]

@@DimitriBianco hi Dimitri l have a bachelor degree in Political science, but l want to devesify and study MSc in banking and finance. Do you think its a good idea? I don't have strong mathematical background but um really keen to study MSc banking and finance.

[@shucklesors]

@@ronaldnyasha6167 just a very simple question: have you ever even heard of the concepts that were went through here? the mathematical ones. if no, have you begun to become incredibly curious about what they are or mean and went to start looking them up? if you answered no to both, then theres a high chance that you arent 'really keen to study MSc banking and finance' without knowing the mathematical rigour required behind it, even though you simply say you are. you might be more infatuated with the prestige than with the actual technical knowledge involved

[@beyzam9101]

hi, I am a software engineering bachelor degree student and I want to crash into finance (especially quantitative fin). Which major basic math&statistics should I cover? I am trying to find an answer for my question everywhere. Thank you!

[@Isaiah_McIntosh]

A masters is the minimum but a PHD is preferred at least in the US. Look at his video, the best quant finance masters, where he outlines the class content and structures he ideally would want of a program. If your background is computer science and your intended path is implementation then it's possible to only use a bachelor's but you won't be a "quant" at least how dimitri defines it.

[@beyzam9101]

@@Isaiah_McIntosh I don’t want to be a quant, more into the tech side of things. Alot of information online though makes me confuse

[@emmanuelameyaw9735]

Do you do neural network and durbin Watson with pen and paper on the job? I dont think so. You need to understand the math behind it, but I doubt people do these stuff with pen and paper.

[@DimitriBianco]

For verification of some packages for programming languages you will do a few examples by hand. You also have to know the math to argue why something is or isn't important. The math is just the logic on how it works. Without knowing the actual math you can make no argument.

[@DimitriBianco]

You are correct though in that we don't do these by hand daily. Now that being said most math done in any industry is done on a computer.

[@BreezeTalk]

This is the work done in a good stats degree

[@julianbeatty2909]

To begin study of pricing derivatives you should have the following prerequisites satisfied before you walk into the door. Calculus III (multivariable) Multivariable-calculus based statistics; typically a junior level math course.

[@11Samyo]

Hey Dimitri, I am not sure of your journey exactly, but I am just finishing my Financial Economics undergrad, and am really interested in Quant finance since doing Advanced Econometrics as one of my 3rd year modules, whereby we used statistical models to delve into the financial world. In reviewing the quants masters courses, how necessary is it to be from a mathematics background (undergrad) and how much harder will it be for someone like myself who has done Economics BSc previously?

[@DimitriBianco]

The Masters usually accept students from a variety of STEM backgrounds. As long as you can show you have taken a fair amount of math, stats, or computer science you should be okay. Many of my classmates for example had a variety of engineering degrees.

[@GeorgePampalis]

Hi Dimitri. At 20:12 you refer to a name concerning a different volatility model. Could you please comment with the name, and/or a link to his research and presentation? Thanks in advance.

[@DimitriBianco]

Linked is Jim Gatheral's 83 slide presentation. Enjoy! www.google.com/url?sa=t&source=web&rct=j&url=mfe.baruch.cuny.edu/wp-content/uploads/2018/02/RoughVolatilityColumbia2018.pdf&ved=2ahUKEwjltIzZ3u3mAhUNbq0KHc7wA_sQFjABegQIAhAB&usg=AOvVaw3GOEnI6aBTD1sw6Wa57rie

[@rodrigoavila5580]

Another example of the use of Linear Algebra is Multivariate Statistics and Multivariate Probability, Multivariate Regression Analysis, basically ANYTHING MULTIVARIATE USES A LOT OF LINEAR ALGEBRA

[@DimitriBianco]

Agreed. Math is really the language of science and the analysis of anything.

[@Mrpcsin]

Hey, thanks for these videos! BTW, a quick question, if punching in numbers into these default formulas in Excel, such as Black Scholes, without understanding and tweaking the underlying assumptions doesn't work in real life, why do so many 'mainstream non-quant MBA type' jobs exist in banking, financial services, insurance etc? In other words, are quant jobs eating into the mainstream finance job market as the years go by? I'm an ex-software engineer, will be in an MBA program in the near future, so, your insight into the industry's reality will be a major heads up! Thanks in advance.

[@DimitriBianco]

There is a non-spoken war going on between the business side and the quant side. Banking used to be all finance/business people however as the industry has evolved it has become more complicated and so different skills are needed today versus the past. Business degrees like MBAs shine in roles where people skills are needed. Examples include investment banking, sales, and general finance where Excel and team work can get the job done. Quant roles shine in areas like derivative pricing, credit pricing, and anything that can be modeled. A lot of regulations require banks to use models and not simple rules or opinions. The issue arises in areas like pricing where in the past business/finance professionals built models in Excel. Due to increased regulations as well as competition for more accurate predictions, these roles require a strong statistics and math background as well as the ability to code. Many MBA programs these days throw in a Python course or two and will tell you, "you are now qualified to do quant jobs because you can code." This is entertaining to watch from the outside but it is bad advice for MBA students. Even if they can pick up coding in one class which is unlikely, they still lack the statistical knowledge on what to actual do with the code and data. I will eventually make a video around this topic but it is important on both sides to see where your strengths are and focus on that. Quants for example usually don't work well with communication/soft skilled jobs where an MBA would do well in these roles.

[@kakr8r785]

I am a mechanical engineer with 1 year work experience i would like to know if i persue a masters in quantitative finance willl i be able to get a job after i complete???please help

[@DimitriBianco]

It depends. If you get a graduate degree in the US or another country with a lot of quant finance jobs then it can help. However many people get degrees and graduate unemployed or end up finding work in other industries. Quant finance is very competitive.

[@kakr8r785]

@@DimitriBianco ok..

[@farhadazadi]

I got pretty excited when saw the title of this video when you said "advaned mathematics ". I suppose advaned is in the eyes of beholder. The math you need for neural networks is basically high school math. As far as linear algebra, i guess matrix vector is considerd ljnear algebra, but there are a more inferesting applications like matrix decompostion, dimension reduction or eigenvalue problems. Do you think the quants in Renaissance technologies also use such basic math?

[@arjunarun9174]

Hey, do you mind revealing where you studied for your undergrad and masters?

[@DimitriBianco]

Here is a video on my background: kzbin.info/www/bejne/qHjHl4Vsa6mfasU You can also find my LinkedIn bio on the description of every video. I studied at Washington State University and the University of Michigan.

[@arjunarun9174]

Damn thst was quick, thanks for the response! I’m actually a high school senior going to study Finance from Ross at UMichigan this fall, but now that I see theee videos I realize how useless the undergrad degree kind of is. Would you think it’s worth it to switch majors to CS or CS + Maths?

[@DimitriBianco]

@@arjunarun9174 it depends on the area you want to end up in. Quantitative research is more statistics and math focused, implementation (quant dev) and hft is more CS focused, and trading is more finance focused. I prefer statistics undergrads with a solid math background as I work building models.

[@LordOfNoobstown]

isnt accounting always a good asset to have?

[@DimitriBianco]

Yes, accounting is good to know as it describes how a business is structured however it is a simple base knowledge. By that I mean, you can teach much of it fairly quickly to someone without an accounting background however other subjects like advanced forms of calculus require many prerequisites just to get the basic idea. For quant finance you would need that finance/accounting base however the strategies really become "quant" strategies when you use that data and other sources through more advanced math and stats methods.

[@a.h6483]

Sorry if this is unclear but, when moddelling, is that model produced by ACTUALLY doing the relevant maths manually (and not just when explaining the maths to colleagues like you said), or are you using a computer for the maths involved with producing the model. For example, if producing a model involves taking the derivative, are you doing that yourself on manually, or do you just let the computer do it by telling it which operations to execute? I suppose in essence what I'm asking is whether its the understanding of the math operations that is more important than being able to do those operations themselves, because in the job, the computer is actually doing the operations (not just crunching numbers, but doing the algebra/calculus/whatever else too). Thanks.

[@DimitriBianco]

The computer does the math however you have to know what math to tell the computer to do. Doing the correct calculations in the correct order is important to get a meaningful solution.

[@a.h6483]

@@DimitriBianco Ah okay, that clears things up for me, thanks a lot!

[@cardcode8345]

What is better a degree in computer science or Electrical engineering. I will end up in Rutgers, depending on the networking market, which major will help me the most.

[@DimitriBianco]

It really depends on your career goals. Both degrees as undergrad degrees will teach you math and programming to an extent. They should help you get into a quant program however I always consider what are your backup options if things don't work out. Would you rather work in CS or electrical engineering?

[@aymentoumi9629]

Is stat and applied econ. Good path for data science . Quant .......ex or I need dgree in CS or math ..

[@DimitriBianco]

It depends on where in quant finance you want to end up. I work in risk management at a bank and statistics is the main skill required. I have colleagues who have stats backgrounds and my applied econ background was stats focused. I have to code to test my statistical ideas however it is not required to be at the level of a CS major.

[@siomokof3425]

6:26

[@wuyunhua7368]

has no caption, hard for non english people to learn