Anyone here use stochastic calculus in their job? Would it be useful to charterholders?
For those of you who use it, how difficult is it? Can it be self-taught? What are some good books?
“Useful to charterholders” is very generic, if you’re running an options structuring desk, probably useful, if you’re running a bar on Koh Samui, probably not so much.
Sure it can be self taught, but it will help if you have a strong background in probability and measure theory. I assume you’re looking to learn it in the context of options pricing? I used the book by Alison Etheridge, which gave a nice introduction to the material and built Black-Scholes from the ground up.
Paul Wilmott Introduces Quantitative Finance is a good book for some of this stuff. It is not a book specifically about stochastic calculus, but it goes through a lot of the applications of it and might be a more applicable start than just diving into the definition/theorem/proof/theorem/proof/correlary approach that most mathematicians use.
If it’s useful, it would be in the curriculum. Apparently it isn’t.
Neither is knowing the difference between a red light and a green light, but it would still be useful for most charterholders to know.
To state (not being in the curriculum --> not useful for a charterholder to know) is ridiculous.
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Whether it’s useful depends on what your job is. My bet is that about 80% of chartholders / portfolio managers don’t use it. It’s not necessary in day-to-day operations of telling you to do x or not do y.
It’s immensly useful if you’re the kind of person who actually wants to understand financial models, how the models work and under what circumstances they will fail. As we saw with every financial crisis, the vast majority of players don’t really give a shit about any of how and why.
Whether it’s hard or not depends on your educational background. If you were they typical business student who either didn’t take “regular” calculus or an integral sign makes you queasy, you should not even attempt to tackle stochastic calculus. The Wilmott book is a gentle introduction (moreso than Etheridge) but if you don’t understand “regular” calculus there’s no chance in hell you’ll understand stochastic calculus.
In my experience, most of the people who learn advanced math (PDE’s, multivariate calculus, stochastic calculus, etc.) don’t use them in real life. I’ve talked to many a mechanical and petroleum engineer who say, “Yeah, I studied that in college. I think I’ve actually used it two or three times since I got out of school. Don’t remember any of it now.”
Of course, this would be different in academia. But if you’re in academia, you’re a PhD, and wouldn’t be asking (in an anonymous forum), “Should I teach myself stochastic calculus?”
If you price derivatives, particularly non-vanilla options, stochastic calculus is pretty essential.
The only other broad use is in more general asset pricing models (which are really models of expected returns, or alternately, what discount rate to use) if you are going to assume stochastic discount rates (I.e. that risk premiums have time varying random factors in them), but that’s a highly specialized topic that most CFA types don’t deal with (though there are a few here on this forum).
you might check out Wilmott.com’s forums, which has more quant folk than here.
Stochastic calculus is a funny one because applying the models is really easy and straightforward, but deriving them is 100 times harder. A lot of the time, the output after laborious calculus is just some normal distribution with weird parameters, and Black Scholes is just plug and chug numbers into a formula.
Sticking with the applications and learning about the starting assumptions is plenty enough. Learning the limitations of the models is the most interesting, brownian motion is a huge assumption in many models, and it might not reflect reality.
Again, it depends on what your job is. If it’s your job to price derivatives and/or come up with pricing models in general, you’re going to use this “in real life”. Even if you’re job is not to make pricing models, it’s still useful to understand how the models work and what their underlying assumptions are (*).Those who consistenly make money no matter what the market conditions understand this and apply it every day. (*) if you want to be a good money manager. Most sales guys get paid (in one form or another) no matter what, so they don’t give a shit either way.
That’s certainly the case for 80-90% of the advanced math I’ve learned; on the other hand, I’ve had to occasionally use my understanding of various “advanced” (upper level undergrad/graduate) math on various work projects, ranging from Cholesky decompositions to network optimization/graph theory to deriving multivariate probability distributions. And yeah I usually have to look up how exactly to perform certain calculations, but I still have a general understanding of the motivations and the fact I’ve already gone through the motions (albeit years ago) definitely helps. If you want to build innovative models, unfortunately there’s not a lot of low-hanging fruit left.
To answer the OP’s question–I have taken a half-algebra, half-calculus class, and I don’t remember any of the calculus.
I can do basic, high-school algebra. That is more than enough for me. I don’t feel like I need to learn anything more to do my job.