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# Math in Trading

So I have a project in my Calculus class to learn about a type of math that we haven't covered in class or previous studies. I'm in my 3rd year of high school, so I've covered stuff like Calculus BC, Trig, Geometry, and Algebra. And the project is basically just presentation to the class of some math topic that we've researched. So since I have a big interest in the stock market, I was wondering if there were any applicactions of somewhat "difficult" math in the stock market. I mean the teacher doesn't really want applications of math; he was looking for topics rather than application. But he said that we could do applications as long as it wasn't too simple. Other people are doing things along the lines of Chaos Theory, Game Theory, what really happens when you divide by 0...etc

The first thing that popped into my head was Fibonnaci retracement. It's not really math, but it has do do with it. That's not gonna be enough to talk about for 10 minutes. Do any of you know of somewhat "advanced" applications of math in the stock market? I was thinking maybe I could do my presentation on math in techincal analysis, since there's a lot of math-related applications, like Fibonnaci retracement. Or is there something that you think is more interesting?

Thanks for the help!

Ooh.. Ive got one.. Black-Scholes model, its used to calculate the price of options for option trading.

Wikipedia it.. here is a taste:

The Black Scholes formula calculates the price of European put and call options. It can be obtained by solving the Black–Scholes stochastic differential equation for the corresponding terminal and boundary conditions.

The value of a call option for a non-dividend paying underlying stock in terms of the Black–Scholes parameters is:

$C(S,t)=N(d_{1})~S-N(d_{2})~K e^{-r(T-t)}\,$
$d_{1}=\frac{\ln(\frac{S}{K})+(r+\frac{\sigma^{2}}{2})(T-t)}{\sigma\sqrt{T-t}}$
$d_{2}=\frac{\ln(\frac{S}{K})+(r-\frac{\sigma^{2}}{2})(T-t)}{\sigma\sqrt{T-t}}$

Also,

$d_{2} = d_{1}-\sigma\sqrt{T-t}$

The price of a corresponding put option based on put-call parity is:

$\begin{array}[b]{rcl} P(S,t) &= &Ke^{-r(T-t)}-S+C(S,t)\ &= &N(-d_{2})~K e^{-r(T-t)}-N(-d_{1})~S\ \end{array}.\,$

Thanks for the suggestion StockJock-e. Seems interesting, but I decided that I'm just going with Stochastic Calculus. Thanks though!

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