Statistical Computation

A covariance estimate used in a risk report must identify its observations and divisor. A regression must identify its response and factors. This lesson connects NumPy calculations to those statistical objects, then checks a simulated option price against a closed form with a stated tolerance.

• compute sample means and covariances with an explicit ddof choice and state what was estimated;
• fit a one-factor OLS slope (e.g. excess return on market) with a normal equation or np.linalg.lstsq;
• simulate a known model and assert the estimator or pricer lands near the closed form;
• refuse to invent econometric theory beyond what the computation requires.

1. Sample mean and covariance
2. Least squares as a linear map
3. Simulation check against a known formula
4. Portfolio variance as a quadratic form
5. What this note deliberately skips
6. Hand-off to design and delivery