In What Financial Derivative Is the Concept of “Squaring” or Non-Linearity Also Important?

The pricing of options heavily relies on non-linear relationships, particularly the concept of volatility, which is often expressed as the square root of time in models like Black-Scholes. The "Greeks," which measure the sensitivity of an option's price, are also non-linear.

Specifically, Gamma measures the rate of change of Delta (the first derivative), meaning Gamma is the second derivative, or the "square" of the option's price sensitivity to the underlying asset's price.