Nonlinear Regression Modeling
Jenny K. Chen · 2024
In the previous Chapter 3 , we explored how to transform nonlinear models into linear models in financial data, especially when they exhibit exponential forms. While linear regression and transformations like logarithms can handle many scenarios, certain financial models are inherently nonlinear due to their intricate dynamics. These models might involve interactions between variables, non-additive effects, or non-constant relationships over time. For example in option pricing, nonlinear models are essential for accurately pricing options and derivatives. Stochastic volatility models, for instance, capture the changing volatility dynamics inherent in financial markets. Similar to credit risk assessment, nonlinear techniques help assess credit risk by modeling the complex interactions between various factors influencing creditworthiness. In portfolio optimization, portfolio selection often involves nonlinear relationships between assets&s; expected returns and risks. Nonlinear models aid in finding optimal portfolios that balance these factors. Further in behavioral finance, understanding investor behavior often requires nonlinear models to capture biases, heuristics, and sentiment-driven decision-making.