Volatility Convexity

The sensitivity of vega as a function of volatility to a change in volatility. It captures the deviation from a delta neutral hedge or duration-neutral hedge as volatility changes over time. Volatility convexity reflects the relationship between vega and volatility. As volatility rises excessively, all options become concave with respect to volatility because every option is capped at the price of its underlying asset. That means, an option price cannot exceed the price of its underlying (buying the asset itself instead of a call option on it would be a better strategy). At high levels of volatility, the price of the underlying and that of a call option converge.