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Math IA on Finance: Stock Trading & Price Movements

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In this exploration, I want to see how mathematics is used to "predict" price movements by financial traders. This is very interesting to me as I want a career in Finance. Furthermore, I want to explore particular events such as the fall of the Lehman Brothers etc. and view correlations between stock valuation, output and market volatility. I also aim to find out what sort of correlations there are in particular stocks. I will use technical analysis (stats) on a particular stock index to find these price trends.

The majority of the maths required in financial markets & trading is probability, statistics & stochastic calculus. The Black-Scholes equation (although very complex) predicts the likelihood of an option being exercised and can be used for  market patterns. The volatility of financial markets/stocks is not constant and so there is a lot of statistics used such as standard deviation. The majority of the maths required will be done through Monte-Carlo simulations (which includes standard deviation, mean increase, skewness, kurtosis). In terms of particulars, in statistics I can use: Spearman's Rank Correlation to find relationships etc.

I will carry out this exploration through doing research on price movements. I will collect data from JP Morgan's financial statements to see how their stock in particular changes prices based on a variety of factors. Through collecting the data, I will model correlation graphs and different types of graphs. I could use financial information from the Credit Crunch to see how market volatility and other factors affect price movements, find the standard deviation and graph the price volumes.  

I am doing an internship as a trading analyst at J.P. Morgan Chase this summer. I have asked my supervisor at JP Morgan to provide me with support on my Math IA. Through professional teaching on this aspect of maths, I will be able to understand quantitative finance and its role in maths more clearly. Adding on, I am doing a summer course in Finance at HKUST which will improve my understanding of this topic even more. I want to spend the last 3 weeks of the summer applying everything I learnt about the mathematics in stock trading and come up with my IA.

Do you think this idea is good? Ideally, I want a 6 or a 7. 

 

 
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On 1/14/2018 at 3:51 PM, ManroopA said:

This is great, and I am also doing an I.A very similar to this. Please help me

 

On 1/15/2018 at 7:02 AM, jltc10004 said:

Is there any specific type of maths used for prediction of prices? I'm having a really hard time with mine

Okay guys I have finished my draft, and I think it will help you. The basic important things were the monte carlo method for me.

This reddit post has a lot of insight and really helped me. Take a look at it

https://www.reddit.com/r/investing/comments/2xcbn9/mathematics_applied_to_the_stock_market/

After this, here is my I.A and just skim through it and get an idea. To be fair this is my first draft and im not even close to finishing.

https://docs.google.com/document/d/1VHeIqjUu5Bv_gaJlD0ZzkwaSg_a05Ar_sEjkW4ujx58/edit?usp=sharing

 

Good luck!

 

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So my IA is also about predicting a stock price. I look through your draft, but does the Monte Carlo simulation have enough math for HL? I decided to try and use the Black Scholes model but I don't know how to go about it. If you don't mind sharing your IA could you please do that? and also how well it scored? 

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