03. Similarity of GBM to an Exponential Function
PRDTM2-787 AI Trading C4 L2 Vid3 Similarity Of GBM To An Exponential Function
Understanding Stock Price Modeling with Geometric Brownian Motion (GBM)
In this lesson, learn how the Geometric Brownian Motion (GBM) model assists in forecasting stock prices:
Stochastic Differential Equation (SDE): Used to model stock prices or a company's market capital. Alone, it's less insightful for trading, necessitating solving for probabilities and expectations.
Solution Approach: Decomposing the SDE begins with examining the variables:
- St: Stock price at time 't'.
- S0: Initial stock price.
- Exponential growth function: Reflects similar patterns in historical stock data, like Apple's from 2001 to 2021.
Continuous Compounding: Illustrates growth with a fixed interest, akin to risk-free investments with central banks.
Component Breakdown:
- Mu (µ): The momentum parameter indicative of expected stock growth.
- Sigma (σ): Volatility, representing risk and uncertainty, captured by the Brownian motion.
Forecasting: Predict stock prices using the derived formula by estimating µ. Understanding this process is integral for accurate market predictions.
Future content will dive into setting the momentum parameter, a process known as fitting the GBM model to historical data.