Hello all,New to the forum, and trying to make my way from physics to finance, as many others have before...I have seen this issue addressed in other threads, but I still had questions regarding the mathematical backgrounds of practicioners of quanitative finance. I hope I am not repeating an already dead issue...It seems to me, that when I see books related to stochastic calculus, they really emphasize the need to rigorously justify every single step done in the mathematics. Honestly if you talk to a lot of physicsts, finance people and engineers, I think many of them would have trouble remembering the rigorous derivation of an ORIDNARY Taylor series let alone the version used to derive Ito's Lemma in a lot of books. Yet people seem to take a different view of mathematics when the topic turns to derivatives pricing.As a physicist who always got along better with engineers , I really feel like just learning how to do stochastic calculus the way I learned Ordinary calculus. I took analysis once, and I can truly say it did not make me a better physicist. It made me appreciate the hard work mathematicians have done to put calculus on a solid foundation, but it didn't help me do any new integrals or derivatives.My questions: 1) How much, REALLY do I need to know about analysis etc. to do stochastic calculus? I have seen some nice intro books that seem to give me all I would need to know without delving into sigma algebras or whatever... 2) For those of you have a solid math background (graduate level mathematics vs. say, engineering/physics or finance curriculum) do you see your colleagues from other disciplines struggling with their work and in need of a better mathematics background? 3) FOr those of you who came from a background where you simply used math, have you found this to be a problem, or have you been able to use math the way you did in your previous career.Sorry to simplify these categories. I know we are not all just mathematicians, finance guys, engineers, and physicists, but I know we all have varying math backgrounds and this has influenced how we view problem solving. I am working from my reference frame and put myself in other people's shoes...

Quote 1) How much, REALLY do I need to know about analysis etc. to do stochastic calculus?Yeah, cause you need to be able to do proofs and show limit theorems, etc.Quote2) For those of you have a solid math background (graduate level mathematics vs. say, engineering/physics or finance curriculum) do you see your colleagues from other disciplines struggling with their work and in need of a better mathematics background?If I do, it is not because they aren't grounded enough in math. The areas you go into in industry are so specialized that this does not happen. It is like an engineer that only does antenna work, or a plasma physicist, or an optics guy. The fields are specialized. It uses its own jargon and math.3) FOr those of you who came from a background where you simply used math, have you found this to be a problem, or have you been able to use math the way you did in your previous career.Different animal. Although you would be surprised what you wind uip using to help you solve a hard problem. If you can show it is the best way, then you can use all the high faulutin math you want. It usually works out that this is not required and, rather than making the math harder, if you increase your conceptual understanding as much as possible, you find that a simple solution exists.

Your post definitely struck a chord with me -- I had similar observations coming into the business from a physics background. You bring up good points for discussion. You'll want to read what Emanuel (sp?) Derman has to say on the subject, check out http://www.ederman.com/There was a time when more sophisticated models yielded edge in the options market (US equity market at least). Now speed rules the day -- all the players are better capitalized, markets are tighters and more efficient, and everyone is seeing the same paper at almost the same time. Making money has turned into a footrace (faster execution systems, better quote feeds, other IT stuff), where it used to be a matter of building a better mousetrap (better models). So does knowing stochastic calculus have value for a quant? Absolutely. It's a tool like any other tool -- a way of approaching problems and creating models. But I don't think it's essential to be a modern-day Cauchy or Kolmogorov and be able to rigorously prove the stuff you see in a lot of fin math books. Proving theorems is a good way to keep one's mathematical chops in tune, not unlike a concert musician running scales on her instrument. But it's an otherwise pointless exercise if you want to get real work done. As Feynman said (paraphrasing here) mathematicians can prove only trivial theorems, because every theorem that is proved is trivial.When firms hire quants they're usually looking for math / physics / engineering PhD's. Why? Mainly b/c of the tacit belief that if you're a PhD in one of these subjects you're already smart enough to handle the complexities of the business in addition to already knowing the essential math for option valuation. In my opinion, quants these days should spend much more time studying and understanding the markets, and finance principles, and even information technology issues (FIX engines and trade execution, quote feeds, vendor API's, client server architecture) before studying stochastic calculus arcana. Ideally a quant is able to talk to traders and IT guys as easily as they talk to each other.To answer your questions, Riaz: Baxter & Rennie and Nefti's book cover enough stochastic calculus for a working quant ... I wouldnt put analysis into the 'essentials' category. But the content in Wilmott's quant fin books is DEFINITELY in the essentials category (and I'm not saying that just b/c this is wilmott.com).

There are two completely different skills in both math in general and stochastic partial differential equations in particular. Some people are good at actually solving the problems, others can understand them in mathematical depth. Engineering schools emphasize the former, problems sets with lots of problems due every week. Mathematics programs generally do a proof once, then go on to a harder proof.It's the first skill that is useful. Maybe one time in a hundred you get a useful insight from deeper mathematics. Usually you can just assume that all the regularity conditions apply and take the obvious solution. People who can both solve problems and think deep mathematical thoughts have an advantage, but they shouldn't be wasting their time making money.Even the first skill is rare. You can have a successful career as a quant without ever solving an equation. You can look answers up in books and use MatLab and do a lot of numerical approximations. I think one in ten quants I know could solve a novel stochastic PDE of the difficulty of Black-Scholes on an exam without reference materials or computer. Another one in ten (and generally not the same one) could prove the solution to the satisfaction of a mathematician.

"As a physicist who always got along better with engineers , I really feel like just learning how to do stochastic calculus the way I learned Ordinary calculus"In my opinion this is a great way forward, but may or may not work depending on the type of individual you are. I initially took this approach, but every once in a while I started questioning why certain things worked the way they did. I had this luxury becuase I am a student and can afford the time to experiment and investigate... but anyhow, whenever this happened I had to go back and learn/understand a little bit more analysis. Before I knew it, I had gone through more analysis than I ever wanted/intended to. But eventually I had satisfied my curiosities. There is still LOADS of rigour/analysis out there which I have never touched but I have reached the stage where I have gone back far enough to convince myself that stochastic calculus is ok. And I guess how far back you need to go depends on you individually. Regards,Sam

i am firmly in both camps on this one!It's actually solving the things that's more important than the theory. But truly understanding the theory helps you solve them as it gives you a feel for how things ought to work. I think most books go too much for side or the other. e.g. some emphasize the stochastic calculus but go out of their way to obscure the finance. These tend to be written either by pure mathematicians who want really want to do pure maths, or by business people who want to prove that they are up to scratch mathematically. On the other hand, there are plenty of books which err too far in the other direction and just present the results without giving enough of a background to understand them well enough to use them in a non-trivial fashion.

Guys,Thank you so much for the insight. I am seeing enough variation in the answers here, that I really feel like the best thing to do is for me to jump into the things in the way I feel most comfortable with. It seems like everyone here, had their particular approach to learning. I really appreciate the feedback. It's funny how things work. I think Aaron had a great point when he talked about how some people can bust out the solution to a diffeq no prob, and other guys need a library, internet, etc. lying around for everything. I suspect most of us lie somewhere in between.I definitely have a better idea of how I want to approach both stochastic calculus, and quant finance in general.Thanks,Riaz

Part of the job of being a quant is to improvise upon using popular trading models. I will be hard pressed if anyone out there is using these models verbatim to actually trade. Therefore, a theoretical underpinning will enable you to do such improvision, otherwise you'd be shooting things in the dark when things don't work as you expected. That being said, I don't think you need to be overworried too much. A lot of quants learn things on the fly. In a lot of situations, you will be forced to delve more into the theory when in practice, your model doesn't work, so the motivation will be there when the occasion arises. Learning all the mathematics that will possibly be used in practice is just too grand of a project if you want to launch your quant career right now. But certainly don't shy away from the rigor, because it is useful.

To be a working quant, you need to be able to set up models and solve models. I think there is a list of about six things about stochastic processes one would need to know and be able to derive. That's "derive" like a physicist, not "prove." My list would go something like:a) white noise and Ito processes,b) Ito's lemma,c) forward and backward Kolmogorov equation (and the Feynman Kac variant)d) Martingales and the Martingale representation theoreme) Girsanov's theorem.The problem with rigorous proofs in practice is that they are not stable against change-of-model. Most good solution techniques should be stable against change-in-model. Suppose one needs to add a memory to the stochastic driving term and work with "colored" noise instead of white noise. (For example, perhaps one discovers that on the short time scales of an automatic trading system, one needed to accout for "momentum.") Instantly one has to throw away all the rigorous proofs, even though (in the limit of weakly colored noise) the solutions are near the white noise solutions, and the solution method should be a perturbation of the original. Or suppose that we believe that the fundamental processes are not Gaussian, or that market correlations are different for large moves than they are for small moves. Thse all entail throwing out all the rigorous proofs.Alternatively, there is no way to have ANY rigorous proofs in practice because all models are approximate and, at some level wrong. Should we spend our effort making rigorous proofs on an approximate model (which will not improve the pricing and hedging), or should we spend our effort improving the model and it's solution (which will improve the pricing and hedging), or should we leave it as an exercise for the students while we go have a beer?