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.
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.
> 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.
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.
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.
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.
Yes you need it, and no it’s not trivial. Not all quants need it on a daily basis though.
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.
The parent comment definitely violates the site guidelines.
How can you tell? They're missing the telltale sign — the em dash.
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.
You're good bro. This is the internet; we're all here to have a good time.
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.
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.
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.
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.
Oh wow, it is a convenient feature IMO.
> The comment above is probably from a bot.
Wtf
Is this happening?
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.
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 ;) .
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.
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.
It depends on where you are - many large banks have their derivatives pricing libraries written in c++ or c#.
Most web developers don't even know what a binary tree is, nevermind rebalancing one.
Yes, you need a good tutor to help you navigate through such a complex topic.
> 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.
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