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Quantitative Finance for a beginner in spot Forex?

Hi! At first I wish to say sorry for my English, I will try to be as understandable as I can. So, I've just recently become interested in the whole quantitative finance sphere, got pretty excited by it, and now I am facing the problem of selecting a sector of this sphere for learning in the first place. I am a graduate in applied mathematics, I love beautiful theoretical constructs and, honestly, attraction that I felt is of I think purely mathematical nature. I also work as a software developer. So I guess I could relatively easily learn at least some aspects of the 'quant science', in theory and practice.

A natural idea that comes into mind is that I should choose first those aspects that I could apply on practice. Now, I think I won't ever be working as a market analyst or someone like that. So becoming an individual trader is the only option. Now, trying to trade derivatives (futures/options) is, due to different technical reasons, is what I can't do (at least for some time). It's a pity, because at the first glimpse it seems to me that quantitative finance and its wonderful theory is all about derivatives, and the entire financial world is trading them day and night. OK, but there is another hobby that I got - I like playing with the spot Forex market from time to time, and I have no problems getting some money into it (and maybe a little into stocks), even for learning purposes.

So the main question is: What parts of the quantitative finance theoretical conglomerate I could apply to spot Forex trading and simple stocks trading? What should I learn first - financial econometrics? Time series analysis? Stochastic calculus? Portfolio theory and risk management? Anything else?

I'm fully aware that my understanding of what the quantitative finance is and what it is for, can be very distant from reality, so I'll appreciate any answers and any crititism. Thanks in advance!
I don't know what you mean by "playing around in the spot forex market", but this is a very hard place for a beginner to trade intelligently. Ultimately, I like to say that you strategize on fundamental analysis, trade on technical analysis, and you manage risk using quantitative analysis. A lot of people think quants predict the future, and they really don't. Especially with Forex, you have to understand the reasons for those big jumps, and that comes from global economic data and foreign policy. Forget about FX without developing that intuition first.

You might like math, but the truth is, trading and quant modeling is learning how to properly use models. The first rule is: "All models are wrong!" This is especially true with the forex market. You might want to start learning about ADRs, and Quantos, and learning how to model them stochastically. Learn Black-Scholes, but avoid relying on it in practice. Models are for modeling, and analyzing currencies are for trading. They are sometimes two completely different things! Overall, there is a lot more you need to learn before you can trade intelligently as an FX Quant. Try taking a grad level course in it.