Is the Relationship between Theta and Vega Linear or Non-Linear?
The relationship between Theta and Vega is non-linear. Both Greeks are related to the option's extrinsic value and time to expiration, but their interaction is complex.
For example, as time to expiration decreases, Theta increases exponentially, while Vega decreases. This non-linear relationship is governed by the Black-Scholes-Merton partial differential equation.
Glossar
Non-Linear Relationship
Correlation ⎊ A non-linear relationship often exists between the price of a cryptocurrency and the adoption rate of its underlying sustainable technology, where initial adoption may be slow before an inflection point is reached.
Volatility of Volatility
Concept ⎊ Volatility of Volatility, often referred to as Vomma or Volga, is a third-order derivative measure that quantifies the rate of change of an option's Vega with respect to a change in the underlying asset's implied volatility.