Hey guys!
For my IB Extended Essay, I'm working on a comparative study on 2 methods of predicting the movement of the NextEra Energy--an electric services company--stock as listed on NYSE under NYSE:NEE. Why NEE and not something else? Well, it's a 'green stock', and it follows a very clear trend in the long-run. Actually, one can predict the trend as an exponential one. A fairly slow, but recent one.
So one method to predict the price in long-term that is very common is the Geometric Brownian Motion, which is the solution to this Stochastic Differential Equation (SDE):
Here St is the price of the stock, mu is the drift constant, which is deterministic, and gives the motion that forward drive with the dt term. Omega there is the volatility, or the standard deviation of the motion. dWt term is the infinitesimal change in what is called a standard Brownian motion, which is a random variable normally distributed with mean 0 and variance t. This term is the non-deterministic or "stochastic" part, that makes the wiggly, up-and-down fairly erratic behavior of stock prices. The SDE can be solved by Ito's Lemma. The solution to this equation is:
If you try to plot this on Desmos.com, good luck 🙃. I mean it's not possible to add a stochastic part there can you?
Anyways, one now can think of how we can model this
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