Nonlinearity is a pervasive mathematical concept in the investment world, applied to situations where the relationship between an independent variable and a dependent variable cannot be adequately described or predicted by a linear equation. For instance, the returns of certain asset classes such as options might not be a directly proportional or linear relationship with the underlying assets, or even correlated with the basis of their underlying components. These properties are known as nonlinearity, and it is the degree of nonlinearity of an investment class that makes it much less predictable than basic asset classes and can lead to chaotic outcomes.

The financial industry has long recognized and tried to address the impact of nonlinearity on investments. For example, nonlinear models have been employed in several areas including derivatives pricing, option and warrant valuation, improving portfolio diversification strategies, and managing credit risks of banks and other financial institutions. Various complex options and derivatives such as swaps and exotic options are mostly heavily dependent on nonlinear models, as the payoff of these investments is highly sensitive to small changes in their underlying parameters.

Investors and analysts of asset classes with a high degree of nonlinearity often rely on sophisticated modeling techniques to identify and measure the potential risk or gain in a particular option or derivative. In certain cases, a mathematical technique known as Fourier analysis is used to analyze the periodic pattern in a nonlinear system, helping investors detect any possible relationships between an asset's value and the underlying events which result in these changes. This helps them anticipate any potential financial crisis or instability that might affect their investments in future.

The high degree of nonlinearity exhibited by particular investment classes requires investors to stay very well-informed and vigilant. Nonlinear investments can quickly take a nose-dive or skyrocket and investors should be familiar with smart risk management and contingency planning to avoid substantial losses. As the nature of nonlinearity makes it very difficult to predict the exact direction of a price change, modeling techniques can help provide investors with an insight into the levels of risk they may face when investing in asset classes with a high degree of nonlinearity.