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Probability and Markets [pdf]
- kwant_kiddo 3y agoDuring my university studies, I found it surprising that although some topics from advanced courses might be applicable in certain jobs like at Jane Street, interviews often emphasised the fundamentals and understanding of basic concepts such as basic probability theory, rather than some specialised knowledge in Lie processes. If you look through this PDF it does not even cover a 1.semester course in probability theory from a bachelors degree in CS/math. I always go back to this lecture series to brush up my fundaments. https://projects.iq.harvard.edu/stat110/youtube https://projects.iq.harvard.edu/stat110/youtube
- KRAKRISMOTT 3y agoNot Lie processes (are you referring to Lévy?), but stochastic calculus in general, which requires a strong intuition for differential equations, calculus, and statistics. Quantitative finance heavily favor those with a background in the physical sciences rather than discrete math like CS.
- lying4fun 3y agoThat is curious. Could you elaborate or point me to some sources, I would like to investigate that relationship further. I remember Jim Simmons saying that the Renaissance fund employs many physicist PhDs and other kinds of scientists. I thought they were there because of their specialisation but perhaps the reason is what you explained above or both
- KRAKRISMOTT 3y agoPhysicists are popular because they deal with uncertainty and complex models across the time domain, which is another description of markets. When you zoom out far enough, a fluid dynamicist and a market making quant are not that different. If you want books about trading mathematics and interviews in general, the green book (practical guide to quant finance interviews by Zhou) is the usual go-to. Falcon's Heard On the Street is another classic. Note both of these focus on generic interviews (the quant equivalent of leetcoding) usually for recruiting fresh grads directly out of school. You can probably skip some steps if you have the work experience or know the right people at certain funds. If you want actual books on trading and modeling, that's another topic entirely. Figure out which area specifically you are interested in: https://teddit.net/r/wallstreetbets/comments/kcs4xy/what_quant_funds_actually_do_tldr_no_it_isnt https://teddit.net/r/wallstreetbets/comments/kcs4xy/what_qua... If you want an autobiography, Emanuel Derman's My Life as a Quant is well-regarded. I have never read it myself but Amazon has often recommended me The Physics of Wall Street.
- kwant_kiddo 3y agoyes I meant Lévy I don't really know what went through my head. I also have to say that you don't need to have a strong intuition for differential equations even through they are very related. Stochastic calculus can be studied entirely in its own right. And with respect to quantitative finance my experience is that while a candidate knowing about or having coursework in stochastic calculus is certainly relevant its not favourable. This also depends on the exact job right, if you have to be pricing XVa products then you better have know Girsanov, Ito and what have you =)
- scythmic_waves 3y agoI second this. The fundamentals take you far, and Joe Blitzstein has fantastic material. Slightly off topic, but how do you feel about his “story proofs”? They were the one part of his lectures that never really clicked with me, but I never talked to anyone else about it.
- tmoertel 3y agoReaders, if you want a great into to probability co-authored by Joe Blitzstein, see https://stat110.net/ https://stat110.net/.
- msie 3y agoWhy can't I download the PDF?
- whimsicalism 3y agoI enjoyed them - I think it shows how you can make a (relatively) rigorous, yet intuitive, argument that does not necessarily have all of the trappings/wall decoration of traditional proofs. The art is noticing when the story is complete vs. when it is papering over an important mathematical aspect. I took the course in person, so it might have been more understandable in that context.
- javidlakha 3y agoMe too - particularly when the story proof was more concise than the algebraic proof, or hinted at the deeper reason as to why something must be true. I remember them better too.
- manp2 3y agoI heard convex optimiztion techniques are widely used as well, is that true?
- agnosticmantis 3y agoI heard they try to hire for aptitude/talent. The sophisticated stuff they will teach you if you’re hired. This is similar to how math Olympiad students are picked, most questions involve combinatorics and Euclidean geometry instead of advanced calculus, as anyone can understand a basic counting problem, but it’d take a few semesters to define the terms in a typical calculus problem.
- paulpauper 3y agoAlthough Olympiad is only counting, there is considerable prep and practice that goes into it.
- agnosticmantis 3y agoThat’s true. I meant (almost) everyone can understand the ‘statement’ of Olympiad-level counting problems, but of course solving them is another issue.
- Utkarsh_Mood 3y agoHonestly I expected it to go over far more advanced topics than these, most of these are covered in the last year of high school over here.
- andsoitis 3y ago> Honestly I expected it to go over far more advanced topics than these, most of these are covered in the last year of high school over here. Opening sentence: The goal of this document is to present an introduction to probability and markets in what we hope is a fairly intuitive and accessible way.
- Utkarsh_Mood 3y agoright no I guess thats not what I meant to say, rather that I expected any learning material from Jane Street(which has some really rigorous interviews) to give a better heads-up to the type of thinking thats required to do well in those interviews.
- andsoitis 3y ago> type of thinking thats required to do well in those interviews They have a whole page dedicated to that: https://www.janestreet.com/join-jane-street/interviewing/ https://www.janestreet.com/join-jane-street/interviewing/ Attention to detail and clear communication, including good grammar and spelling, are probably important.
- elteto 3y agoBasic reading and comprehension is not covered in his last year of high school it seems.
- ausbah 3y agosimple things will go very far
- dwater 3y agoI teach post-grad stats classes in the US, with no real prerequisites besides a Bachelor's degree. Most but not all of my students have passed a college level stats class that covered these concepts, and maybe half of those did not retain a true understanding of these concepts by the time they got to my classroom. In my experience, math is the least like/most hated of the core subjects, and stats is one of the least liked/most feared math subjects.
- mannycalavera42 3y agofirst sentence in the doc: The goal of this document is to present an introduction to probability and markets in what we hope is a fairly intuitive and accessible way HN thread: wHeRe is compleXitY?!?
- antegamisou 3y agoFor the experts in the thread complaining about the simplicity of the excellent introductory text in the OP, here's an exciting reading for you: Statistical Consequences of Fat Tails: Real World Preasymptotics, Epistemology, and Applications by Nassim Nicholas Taleb https://www.amazon.com/Statistical-Consequences-Fat-Tails-Preasymptotics/dp/1544508050 https://www.amazon.com/Statistical-Consequences-Fat-Tails-Pr... Beware that it may be way more advanced than what you'd expect though.
- Err_Eek 3y agoPersonally -- I couldn't get past the first 2 chapters of the book. The notations it introduces are pretty unfamiliar for a newcomer and it quickly becomes really hard to follow. I genuinely would like to hear from somebody who managed to go through the entire book above, and what their main takeaways were (from the chapters that follow the two introductory ones). The non-technical introduction chapter is pretty easy to follow, and I would recommend reading it.
- lifeonlars 3y agoThe rule of thumb with mathematics books is that either you skip the first 2 chapters and read the whole thing, or you only read those 2.
- max_ 3y agoThere is a Technical Incerto reading group (this book) that you may find useful. https://www.techincertoreadingclub.com/ https://www.techincertoreadingclub.com/
- Utkarsh_Mood 3y agowould you recommend any books/resources before jumping straight to this? Thanks!
- antegamisou 3y agoAnything that would help build a strong probability theory background. Assuming you have some freshman-college math literacy, here are a few great introductory books to Probability theory: Introduction To Probability by D. Bertsekas & J. Tsitsiklis https://www.amazon.com/Introduction-Probability-2nd-Dimitri-Bertsekas/dp/188652923X https://www.amazon.com/Introduction-Probability-2nd-Dimitri-... Elementary Probability Theory: With Stochastic Processes and an Introduction to Mathematical Finance by K. L. Chung & F. AitSahlia https://www.amazon.com/Elementary-Probability-Theory-Introduction-Undergraduate/dp/038795578X https://www.amazon.com/Elementary-Probability-Theory-Introdu... An Introduction to Probability Theory and Its Applications Vol. 1 by W. Feller https://www.amazon.com/Introduction-Probability-Theory-Applications-Vol/dp/0471257087 https://www.amazon.com/Introduction-Probability-Theory-Appli... I'm sure there are some great video lectures on the subject as well, but unfortunately I can't point you to any relevant material since textbooks is what I used when I was in college. But if I had to guess, the latest relevant MIT OCW course that has video lectures available would be sufficient.
- mhh__ 3y agoFor a much better introduction to financial markets I highly recommend http://www.jdawiseman.com/books/pricing-money/Pricing_Money_JDAWiseman.html http://www.jdawiseman.com/books/pricing-money/Pricing_Money_... > The price is a review (even if only a few words) on your preferred social media, either tagged #PricingMoney or with the link jdawiseman.com/PricingMoney.html. There is no paywall, nor registration, nor even cookies, so this price cannot be enforced. Nonetheless, please be fair: please post a review or comment or acknowledgement, tagged or linked or both. Thank you.
- mhh__ 3y agoThis is racking up some upvotes so I've submitted it separately if discussion is desired and so on https://news.ycombinator.com/item?id=36358754 https://news.ycombinator.com/item?id=36358754
- spaceman_2020 3y agoWhat was the probability that one of JaneStreet’s alumni, Sam Bankman Fried, would use JaneStreet’s brand name to build up credibility and then pull off the biggest ponzi scheme in human history?
- clavalle 3y agoSlightly lower than one of MIT's alumni doing the same. It's telling that Jane Street stayed away from the whole mess despite the connection.
- spaceman_2020 3y agoThey were happy to trade crypto and provide market making facilities throughout the ordeal. They only decided to “step back” now that regulators are bringing the hammer down This wasn’t an innocent bystander firm. They were complicit, either directly or indirectly
- JumpCrisscross 3y agoBuying prospectors' pyrite for the little it’s worth is different from driving aspiring miners to mountains without food or water.
- dist-epoch 3y ago> use JaneStreet’s brand name to build up credibility How is that different from bragging that you finished MIT, Harvard, Oxford, you worked at Google or that your startup is in YC.
- spaceman_2020 3y agoWell for one, JaneStreet is an active market maker, trader, and investor in crypto, including in many projects created and/or backed by SBF
- berkle4455 3y agoThe fact that JaneStreet hired both SBF and Caroline shows their interview process has a few flaws.
- SirLJ 3y agoThe publication ends with "Interview Myths", so I think this is geared to potential job applicants at Jane Street...
- shapefrog 3y agotrading-interview.pdf
- Dudester230602 3y agoJust like everything they publish.
- dangwhy 3y ago> – You “fail” the interview if you get the wrong answer > We care about how you think about and approach tough problems, which includes how you take hints and respond to being wrong. First and second sentences need to swapped.
- zeitgeistcowboy 3y agoThe first section on randomness seems to imply that all you need to know is information. That if you knew all the data about the weather that you could predict the weather. I think it's more complicated than that. Even if you knew the position, type, and velocity of every molecule of the atmosphere at a given moment you would still need a model that explains how they interact over time in order to predict the future. So, I'm not sure that actually is a knowable unknown because that assumes there is a model that can be made in addition to the information. Maybe the weather is chaotic.
- daniel-cussen 3y ago[dead]
- jonhohle 3y agoBut is that chaos predictable? Current weather predictions are based on statistical models. Storm trackers, for example, typically have bands that expand as time gets further out. Without knowing every molecule that affects a hurricane, for example, they can predict within some confidence interval where the storm will head. The data meteorologists have is relatively coarse, and yet they can make predictions within some level of probability. That level of probability allows municipalities to issue evacuation orders early as opposed to throwing hands up and saying there is no certainty in anything, so let's just see what happens. Their discussion of die rolling doesn't say they can predict the outcome, rather that they can predict the probability of the outcome. In trading, life, and gaming that probability is one component of many that go into decision making. Knowing how much that randomness effects the outcome at what probability can be a successful strategy (but of course not guaranteed) in all of those domains.
- consilient 3y ago> Even if you knew the position, type, and velocity of every molecule of the atmosphere at a given moment you would still need a model that explains how they interact over time in order to predict the future. So, I'm not sure that actually is a knowable unknown because that assumes there is a model that can be made in addition to the information. Maybe the weather is chaotic. It is, but that doesn't mean you couldn't predict it with perfect information. A chaotic system is roughly speaking one that is - sensitive to initial conditions, in the sense that the distance between nearby trajectories in phase space grows as e^{l*t} for time t and some positive number l - mixing, meaning that given any two open sets in phase space X and Y there's at least one trajectory from a point in X to a point in Y. and so if you have any error bounds at all on your measurement of the initial state (which of course you always do) then you can't predict where it ends up in the long term. But there are plenty of chaotic systems for which exact numerical computations are quite simple. The logistic map x_{n+1} = rx_{n}*(1-x_{n}) for instance, is chaotic for many values of r.
- mastermedo 3y agoI remember going through that Pdf when I was interviewing with them. Very helpful stuff. I feel like I learned more about statistics while going through hundreds of Jane Street interview questions than I did during my university studies.
- paulpauper 3y agoThat seems easy, then why is getting a job there so hard? the pdf is undergrad level. it is covered in any elementary stat or probability book. I guess you have to do it on the fly or something. or have a good intuition for estimating probability when the formula is too cumbersome.
- paulpauper 3y agoThis seems like a sub-optimal way of finding top talent, even though the results still speak for themselves. Obviously Jane Street has had a lot of success using brain teasers to screen for talent. If i were a hedge fund recruiter, here is what I would do: Go on /r/ wallstreetbets and find guys who consistently are pulling huge $ like this guy: https://old.reddit.com/r/wallstreetbets/comments/14a9xyi/11m_electric_boogaloo/ https://old.reddit.com/r/wallstreetbets/comments/14a9xyi/11m... Send a DM job offer to all of them, 7 figures plus performance comp , or at least an interview that will be paid anyway, so as to not waste the recipient's time. Why ask brain teasers to try to find skills that correlate with trading when you can just pick out the best traders who already have demonstrable skill? that is how sports recruiting works. they find the people who can play the sport at best level.
- tux3 3y agoJane Street is a market maker. WSB is a gambling forum where people are addicted to chasing huge rewards by taking huge risks. This would be about as interesting as going to a casino and recruting people who have a big win streak at the slot machine.
- paulpauper 3y agobut there is evidence that some traders there are more skilled than others, like the guy I linked to (or someone like Warren Buffett or Jim Simons ). it's not all random like a casino. Plus, to make so much money at options trading so consistently, requires knowledge of position sizing, market intuition, pattern recognition, and other skills relevant for all aspects of trading.
- JaggerFoo 3y agoWhen was this published? There is no publication or revision dates in the pdf. Maybe 1999 when Jane Street started?
- devmunchies 3y agoWaybackMachine’s oldest snapshot for this url is Sept 2019. https://web.archive.org/web/20230000000000*/https://www.janestreet.com/static/pdfs/trading-interview.pdf https://web.archive.org/web/20230000000000*/https://www.jane...
- rawoke083600 3y agoNice and practical !