In recent years, there has been a growing interest in research on nonlinear phenomena in economic and financial theory. With nonlinear serial dependence playing a significant role in the returns of many financial time series, this makes security valuation and pricing very important, leading to an increase in studies of nonlinear modeling of financial products.

Practitioners in the financial industry use nonlinear models to forecast volatility, price derivatives, and compute Value at Risk (VAR). Unlike linear models, where linear algebra is used to find a solution, nonlinear models do not necessarily infer a global optimal solution. Numerical root-finding methods are usually employed to converge toward the nearest local optimal solution, which is a root.

In this chapter, we will discuss the following topics to explore some methods that will help us extract information from nonlinear models: