Polynomial Regression

Polynomial regression is a form of regression analysis where the relationship between the independent and dependent variables is modeled as an nth-degree polynomial. It is often used in finance to fit trends to noisy data or to create smooth surfaces for pricing models.

By choosing the appropriate degree, one can capture non-linear relationships that simple linear regression would miss. However, higher-degree polynomials are prone to overfitting, where the model captures noise rather than the underlying signal.

This can lead to poor predictive performance and dangerous risk assessments. In practice, practitioners often use low-degree polynomials or spline-based methods to balance flexibility and robustness.

It is a powerful tool for empirical analysis when the underlying relationship is not strictly linear.