Volatility measures how much and how often a quantity varies over time. In financial time series, large price movements make future prices harder to forecast and require visual inspection before modeling. section 7.2.3
Use volatility in two complementary ways:
- Inspect plotted closing prices to identify fluctuations, trends, support and resistance, and potential forecasting challenges. section 7.2.3
- Estimate historical volatility as the standard deviation of daily log returns, alongside the mean return used to represent trend. section 9.5.4
- Carry the estimated variability into Monte Carlo simulations so generated price paths reflect observed market uncertainty. section 9.5.2
GM historical volatility
For GM, the standard deviation of daily log returns is approximately 0.02005, while the mean log return is approximately −0.00061. The standard deviation represents moderate daily price fluctuation and supplies the simulation's volatility parameter. section 9.5.4
>>> mu = log_returns.mean() >>> print(mu) -0.000605520424324896 >>> sigma = log_returns.std() >>> print(sigma) 0.020045660849343817
Compute the mean and standard deviation of log returns in Python, exposing the parameters used to generate simulated daily returns. section 9.5.4
