[HN Gopher] An Introduction to Stochastic Calculus (2022)
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An Introduction to Stochastic Calculus (2022)
Author : ibobev
Score : 105 points
Date : 2025-04-16 10:26 UTC (6 hours ago)
(HTM) web link (bjlkeng.io)
(TXT) w3m dump (bjlkeng.io)
| fancyfredbot wrote:
| Apparently this is the key to unlocking vast riches through a
| career as a derivatives quant. I'm told it's a requirement even
| though you don't really use it on the job. A bit like how you
| need to rebalance a binary tree to be a web developer.
|
| Anyway now it's the key to unlocking vast riches through a career
| as an AI researcher too, seems like a good skill to have.
| vcdimension wrote:
| Yes, you need a good tutor to help you navigate through such a
| complex topic.
| werdnapk wrote:
| Most web developers don't even know what a binary tree is,
| nevermind rebalancing one.
| mamonster wrote:
| It's not extremely difficult(I mean for the most important
| results like Yamada-Watanabe, Girsanov, etc) if you have a good
| grasp on measure theory. That said, without that grasp this
| topic is very hellish.
|
| The main problem for people is understanding intuitively what
| "quadratic variation" actually is and how that factors into the
| difference between a normal Riemann integral and a stochastic
| integral.
| almostgotcaught wrote:
| > not extremely difficult... if you have a good grasp on
| measure theory
|
| If this were Reddit I would paste the "You got into Harvard
| Law? - Elle Woods" meme.
|
| Ok it's not that hard - I did an independent study of
| Oksendahl in my junior year before my first measure theory
| class and understood most of it ok. But then again I didn't
| have to take exams on the material lol.
| mikrl wrote:
| Not a quant, but I have physics training and I'm very curious
| about stochastic calculus and finance.
|
| Isn't it implicit in a lot of the work? If you're modelling
| volatility you'll need the rigorous mathematics in the back of
| your mind while you do so to keep you on track.
|
| Similarly, a webdev isn't going to use fancy tree algorithms
| often... but they need to understand the DOM and its structure.
| v4nn4 wrote:
| The comment above is probably from a bot. You do need an
| extensive understanding of stochastic calculus to maintain
| quant models code, let alone explain what it does to
| regulators.
| ogogmad wrote:
| > The comment above is probably from a bot.
|
| Wtf
|
| Is this happening?
| bee_rider wrote:
| People accusing comments they don't agree with of being
| bots? Yes it has been happening for decades. Lots of
| folks are bad at arguing, so they make random accusations
| to distract from that fact.
| AnimalMuppet wrote:
| The parent comment _definitely_ violates the site
| guidelines.
| kelseyfrog wrote:
| How can you tell? They're missing the telltale sign -- the
| em dash.
| bee_rider wrote:
| I hate this em dash meme. Yes, using a totally normal bit
| of punctuation is a sure sign that something was written
| by a bot.
| EGreg wrote:
| Uh bruh. I took this class when I was 22 at NYU. Quadratic
| variation, brownian motion, and of course black-scholes etc. A
| lot of the work is based on a Japanese guy named Ito, who
| pioneered Ito integrals. And yes you need to know basic measure
| theory or probability as a prerequisite (take Math Analysis at
| least)
|
| The closest I ever got to being a quant is doing an internship
| at a hedge fund called Concordia. They were just using Excel
| and VBA for credit default swaps back in the day. I then ended
| up at Bloomberg building their front end in C++ which st that
| time was a huge compiled binary.
|
| I quickly exited that world and realized I enjoy building web
| applications. Had been doing that ever since. Guess turning
| $220 billion into $223 billion wasnt my idea of fun.
|
| What you need as the key is Python, ML, SciKit, etc.
| bormaj wrote:
| Adding to this, stochastic calculus matters more for modeling
| volatility/interest rates/derivatives. As you mention,
| Python/ML are more than suitable for many other areas within
| quant finance like optimization, algo development, signal
| research, etc.
| mdp2021 wrote:
| > _now it 's the key ... as an AI researcher_
|
| ...For the moment. We will have to return to controlled
| processes at some stage - pure stochastic (using stochastic
| processes alone) is not adequate for precise questions
| requiring correct answers.
|
| Only very little ago an LLM stated General Zhukov as German
| (probably because he had been the scourge of the German army -
| enough of a relation to make of something its substantive
| opposite in a weak mind). Imagine if we had that "method"
| applied to serous things.
| LostMyLogin wrote:
| Does anyone have a solid road map of what to learn to get to the
| point where learning stochastic calculus is possible? I have a CS
| degree that was obtained 8-10 years ago. What are the
| prerequisites?
| kachnuv_ocasek wrote:
| Same background here. I finally got into stochastic calculus
| last year thanks to a local college course (after several
| unsuccessful attempts on my own).
|
| You need at least
|
| 1. a basic grasp of classical calculus, measure theory and
| topology
|
| 2. solid understanding of probability theory
|
| 3. basics of stochastic processes
|
| I believe you should be able to dive in from there. It's good
| to have an idea where you're heading as well (mathematical
| finance and modelling and pricing derivatives? Bayesian
| inference and MCMC? statistical physics?).
| alphazard wrote:
| If you want to understand the language of stochastic calculus
| as mathematicians have formalized it, then you need all of
| their jargon. Probability, Diff Eqs, Integrals, and
| Derivatives. If you are trying to tick a box on a resume, then
| that's what you have to do. If you have a CS degree then you
| have a little slice of Probability from combinatorics and
| information theory. You'll have to build up from there.
|
| Stochastic Calculus was invented to understand stochastic
| processes analytically rather than experimentally. If you just
| want to build an intuition for stochastic processes, you should
| skip all that and start playing with Monte Carlo simulations,
| which you can do easily in Excel, Mathematica, or Python. Other
| programming languages will work too, but those technologies are
| the easiest to go from 0 to MC simulation in a short amount of
| time.
| gaze wrote:
| You should learn calculus and differential equations, and then
| some probability. At that point you should learn a bit of
| measure theory and then stochastic calculus builds on all that.
| Stochastic calculus is basically just weird calculus. It has an
| additional differential dW and the chain rule is more complex
| (for the Ito formulation. Stratonovich is different but not by
| much)
|
| From there you study the behavior of various forms of
| stochastic differential equations that are intended to model
| certain situations. Then, you make this cool connection between
| stochastic differential equations and ordinary differential
| equations that describe the evolution of the corresponding
| probability distributions. There's lots of other stuff but
| those are the hits.
| nyrikki wrote:
| From a CS background, several people I know have raved about
| the following book[1], of which will be friendly and useful for
| future needs anyway in the field. The first part of the book is
| what appears to be a pretty good refresher path.
|
| IMHO working through that book will make you practice with
| enough basic calc to make moving on to stochastic calculus
| fairly easy.
|
| [1] Performance Modeling and Design of Computer Systems:
| Queueing Theory in Action - Mor Harchol-Balter
|
| https://www.cs.cmu.edu/~harchol/PerformanceModeling/book.htm...
| abetusk wrote:
| I'm not a practitioner, so read with some skepticism, but
| here's my list:
|
| * Calculus
|
| * Real Analysis
|
| * Statistical Mechanics
|
| * Probability
|
| I'm not sure I have any good recommendations for Calculus, but
| for real analysis, I would recommend "The Way of Analysis" by
| Strichartz [0].
|
| I don't have good recommendations for books on statistical
| mechanics, as I haven't found a book that isn't entrenched in
| coming from a physics perspective and teaches the underlying
| methods and algorithms. The best I can recommend is "Complexity
| and Criticality" by Christensen and Moloney [1], but it's
| pretty far afield of statistical mechanics and the like.
| Simulating percolation, the Ising model and ricepiles uses a
| lot of the same methods as financial simulation (MCMC, etc.).
|
| For probability, I would recommend "Probability and Computing"
| by Mitzenmacher and Upfal [2], "Probability ..." by Durrett [3]
| and Feller Vol. 1 and 2 [4] [5] for reference.
|
| I also would recommend "Frequently asked questions in
| Quantitative Finance" by Wilmott [6].
|
| Also know that there's a quantitative finance SO [7] that might
| be helpful.
|
| [0] https://www.amazon.com/Analysis-Revised-Jones-Bartlett-
| Mathe...
|
| [1] https://www.amazon.com/COMPLEXITY-CRITICALITY-Imperial-
| Colle...
|
| [2] https://www.amazon.com/Probability-Computing-
| Randomization-P...
|
| [3] https://www.amazon.com/Probability-Theory-Examples-
| Durrett-H...
|
| [4] https://www.amazon.com/Introduction-Probability-Theory-
| Appli...
|
| [5] https://www.amazon.com/Introduction-Probability-Theory-
| Appli...
|
| [6] https://www.amazon.com/Frequently-Asked-Questions-
| Quantitati...
|
| [7] https://quant.stackexchange.com/
| chasely wrote:
| A few weeks ago I decided I wanted to get into this so I
| started self-studying probability theory (with measure theory)
| [0] as a bridge to start in on stochastic calculus [1]
|
| I think the hardest part of self-studying anything that has
| some formal math foundations is knowing _what_ to pay attention
| to. There's so much in just the first chapter of the
| probability book. Is having a general understanding of set
| theory enough or should I actually know how to prove a function
| is a singular function?
|
| That's why I often like to find a university course with
| lectures posted online so I can use that as a rough guideline
| for what's important, but I haven't quite found that yet for
| stochastic calculus. Would love if someone coul point me to
| one.
|
| [0]: https://www.amazon.com/dp/3030976815 [1]:
| https://www.amazon.com/dp/9811247560
| enthdegree wrote:
| Great post, "Wiener" is misspelled a few times.
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