username2130115
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I'm a sixth-form student studying further maths. i'm interested in reading some enrichment statistics to introduce me to some more advanced concepts. i'm interested in learning about statistics relevant to the finance industry and quantitative development.
other people on the internet have mentioned the following topics are of relevance: probability, probability distributions, returns, regression, asset pricing, derivatives, stochastic processes, black-scholes, algorithmic trading, stochastic calculus
what accessible textbook would you recommend to a sixth form student? what mathematical methods do i need to know to study these advanced topics successfully?
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Gregorius
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As general advice to a sixth former interested in statistics I would recommend two major themes:

First, learn about maximum likelihood estimation. This is a technique that is all-pervasive within modern statistics. Whenever you try to estimate the coefficients in a statistics model, whether it is as simple as a linear regression, or as complex as a multi-level random effects model, underlying the estimation is the method of maximum likelihood. I suggest Google/Wikipedia to get you started and the first few chapters of a book like Pawitan’s “In all Likelihood” to finish you off.

Second, learn how to use the statistical computing language “R”. One of the biggest differences between “school” statistics and statistics as it is actually used is the use of computationally intensive methods based on large scale simulation. Dalgaard’s “Introductory Statistics with R” is as good a place as any to start; though note that the “R” home page (at https://cran.r-project.org/) has plenty of user-contributed free manuals/introductions.

For you, particularly interested in finding out about the stats and probability associated with finance and quant, then I do warn you that you have to absorb quite a lot of mathematics before you even get close to Black-Scholes! So, the place to start is in learning more about probability, and stochastic processes in particular. I’d suggest Grimmett & Welsh’s “Probability: an Introduction” to get started and Brzezniak & Zastawniak’s “Basic Stochastic Processes” if you are feeling brave after that. If you have a lot of spare time Grimmett and Stirzaker’s “Probability and Random Processes” takes you as far as you can get without measure theory. If you want to have a look at the latter then Kapinski & Kopp’s “Measure Integral and Probability” is about as painless as it can get.

Also, once you’ve learned enough “R”, play around with Brownian Motion – I won’t recommend a book here, there’s plenty of material accessible through Google.

Finally, if you go into quant, then you have to know C++.
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shamika
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(Original post by Gregorius)
As general advice to a sixth former interested in statistics I would recommend two major themes:

First, learn about maximum likelihood estimation. This is a technique that is all-pervasive within modern statistics. Whenever you try to estimate the coefficients in a statistics model, whether it is as simple as a linear regression, or as complex as a multi-level random effects model, underlying the estimation is the method of maximum likelihood. I suggest Google/Wikipedia to get you started and the first few chapters of a book like Pawitan’s “In all Likelihood” to finish you off.

Second, learn how to use the statistical computing language “R”. One of the biggest differences between “school” statistics and statistics as it is actually used is the use of computationally intensive methods based on large scale simulation. Dalgaard’s “Introductory Statistics with R” is as good a place as any to start; though note that the “R” home page (at https://cran.r-project.org/) has plenty of user-contributed free manuals/introductions.

For you, particularly interested in finding out about the stats and probability associated with finance and quant, then I do warn you that you have to absorb quite a lot of mathematics before you even get close to Black-Scholes! So, the place to start is in learning more about probability, and stochastic processes in particular. I’d suggest Grimmett & Welsh’s “Probability: an Introduction” to get started and Brzezniak & Zastawniak’s “Basic Stochastic Processes” if you are feeling brave after that. If you have a lot of spare time Grimmett and Stirzaker’s “Probability and Random Processes” takes you as far as you can get without measure theory. If you want to have a look at the latter then Kapinski & Kopp’s “Measure Integral and Probability” is about as painless as it can get.

Also, once you’ve learned enough “R”, play around with Brownian Motion – I won’t recommend a book here, there’s plenty of material accessible through Google.

Finally, if you go into quant, then you have to know C++.
I think this is all great advice but in all likelihood (see what I did there? ) still too much.

Raees: try to do as much as what Gregorius suggested. Before you get to maximum likelihood estimation (MLE), you will need to learn partial differentiation (but for the most part, this'll be the same as normal differentiation in most basic instances).

As someone who works in finance (albeit insurance, not banking), I would start by learning basic probability first - things like moment generating functions, Bayes' theorem, the standard distributions (eg Bernoulli, Binomial, Geometric, Poisson, Normal, Exponential, Gamma etc.), etc.

You've got plenty of time for the rest whilst at uni
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