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 7 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 7 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 7 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.
fancyfredbot 2 hours ago [-]
Yes it's behind everything a derivatives quant would do. But I think quite a long way behind. Closed form analytic solutions using calculus only exist for relatively simple models and products. Most of the time you use it to calibrate and discretise a model and afterwards it's all Monte Carlo. What's more you can often just look that part up as models are increasingly commoditised rather than secret sauce.
v4nn4 1 minutes ago [-]
Stochastic calculus is required to derive closed formulas and approximations used to calibrate SDE models. Similarly to deep learning, the secret sauce lies in the training, less in the inference. The code used by banks is closed source, and the research papers are missing said secret sauce. Calibrating models in a production environment handling correlation, multi-curves, stochastic funding, discrete dividends, etc. is not a solved problem. Interest rate derivatives modeling heavily relies on change of measure, even when using simple models.
Agingcoder 3 hours ago [-]
Yes you need it, and no it’s not trivial. Not all quants need it on a daily basis though.
v4nn4 7 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 5 hours ago [-]
How can you tell? They're missing the telltale sign — the em dash.
v4nn4 35 minutes ago [-]
Good point. On a serious note, I probably overreacted, sorry about that. I have been working as a derivatives quant for a decade and thought the claim that stochastic calculus was not used/useful was ridiculous.
kelseyfrog 33 minutes ago [-]
You're good bro. This is the internet; we're all here to have a good time.
bee_rider 4 hours 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.
kelseyfrog 2 hours ago [-]
How so? A human is more likely to use a hyphen, an AI an em dash. Same with quotes - a human is much more likely to use ", an AI “ and ”. Typography is a differentiating signal when it's used dis-proportionally more by one group than another.
bee_rider 2 hours ago [-]
Word processors (less of an issue for Internet comments, but worth keeping in mind) but more significantly iOS (at least) and I assume Android will just swap in an em dash where needed—it is automatic.
There is probably some signal, but be a good Bayesian; we have people saying “oh, this is a bot” when there’s a huge population of mobile users with smart keyboards that are the more likely cause.
Anyway, in general I find bot-hunting annoying. Comments should be handled as comments, if someone has made a bad argument, it should be taken down as a bad argument. If it was bot-generated, it is still there to mislead people. The advantage that bots have is that they have infinite patience and nothing better in their lives to do than argue, but there have always been people like that, so hopefully readers will be able to observe that persistence!=correctness.
kelseyfrog 2 hours ago [-]
I'm using a stock Android keyboard - it doesn't. Perhaps that's were our differing perspectives originate. I'm updating away from AI, and toward iPhone users.
EDIT: I plugged in my prior, hit rate and false alarm rates from before updating and found that my P(AI|fancy-em) = 0.09. After updating my false alarm rate, P(AI|fancy-em) now = 0.016.
bee_rider 2 hours ago [-]
Oh wow, it is a convenient feature IMO.
AnimalMuppet 6 hours ago [-]
The parent comment definitely violates the site guidelines.
ogogmad 6 hours ago [-]
> The comment above is probably from a bot.
Wtf
Is this happening?
mdp2021 2 hours ago [-]
Yes, it happens that some people create bots and have them post in these pages. They (some?) do not pass the "naïve Turing Test" though: there is one that tries to speak like an "inspiring lifecoach" and has zero juice squared. Check the shadowed posts around...
And on the other side, I have been accused a few times - writing outside expected canon (of form and content) can be sufficient.
So, bragging I will say, accusations hit both tails of the juice curve ;) .
bee_rider 4 hours 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.
2 hours ago [-]
werdnapk 8 hours ago [-]
Most web developers don't even know what a binary tree is, nevermind rebalancing one.
vcdimension 8 hours ago [-]
Yes, you need a good tutor to help you navigate through such a complex topic.
mdp2021 6 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 7 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.
Agingcoder 3 hours ago [-]
It depends on where you are - many large banks have their derivatives pricing libraries written in c++ or c#.
bormaj 6 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.
whatup480 3 hours ago [-]
[dead]
LostMyLogin 6 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?
chasely 3 hours ago [-]
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.
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 5 hours ago [-]
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 5 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 5 hours 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
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.
I remember that it's "ie" not "ei" by imagining (and this is probably true) that Wiener means "someone from Vienna", and I have no problem remembering how to spell Vienna.
6 hours ago [-]
Rendered at 20:22:15 GMT+0000 (Coordinated Universal Time) with Vercel.
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.
There is probably some signal, but be a good Bayesian; we have people saying “oh, this is a bot” when there’s a huge population of mobile users with smart keyboards that are the more likely cause.
Anyway, in general I find bot-hunting annoying. Comments should be handled as comments, if someone has made a bad argument, it should be taken down as a bad argument. If it was bot-generated, it is still there to mislead people. The advantage that bots have is that they have infinite patience and nothing better in their lives to do than argue, but there have always been people like that, so hopefully readers will be able to observe that persistence!=correctness.
EDIT: I plugged in my prior, hit rate and false alarm rates from before updating and found that my P(AI|fancy-em) = 0.09. After updating my false alarm rate, P(AI|fancy-em) now = 0.016.
Wtf
Is this happening?
And on the other side, I have been accused a few times - writing outside expected canon (of form and content) can be sufficient.
So, bragging I will say, accusations hit both tails of the juice curve ;) .
...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.
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
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?).
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.
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...
* 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/