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.
mamonster 3 hours ago [-]
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 3 hours ago [-]
> 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 3 hours ago [-]
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 3 hours ago [-]
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.
kelseyfrog 54 minutes ago [-]
How can you tell? They're missing the telltale sign — the em dash.
bee_rider 27 minutes ago [-]
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.
AnimalMuppet 2 hours ago [-]
The parent comment definitely violates the site guidelines.
ogogmad 2 hours ago [-]
> The comment above is probably from a bot.
Wtf
Is this happening?
bee_rider 27 minutes ago [-]
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.
werdnapk 4 hours ago [-]
Most web developers don't even know what a binary tree is, nevermind rebalancing one.
vcdimension 4 hours ago [-]
Yes, you need a good tutor to help you navigate through such a complex topic.
mdp2021 2 hours ago [-]
> 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.
EGreg 3 hours ago [-]
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 2 hours ago [-]
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.
enthdegree 52 minutes ago [-]
Great post, "Wiener" is misspelled a few times.
LostMyLogin 2 hours ago [-]
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 2 hours ago [-]
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?).
gaze 1 hours ago [-]
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 45 minutes ago [-]
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
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.
abetusk 37 minutes ago [-]
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.
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.
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.
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.
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.
Wtf
Is this happening?
...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.
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.
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?).
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.
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...
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.
* 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/