so Implied Volatility is computed by equalizing the value of the call option given by the black and scholes model with the one observed.
Then, by inversing $C_{BS}$, one gets "$\sigma_{IMP}$". My question would be, is $\sigma_{IMP}$ a function of the time to maturity ? Or, is it as I understood, it is "annualized". In other words, it represents
I am baffled by the definition of "Total Implied Variance" which is : $ T \sigma_{IMP}^2$ (T time to maturity). I don't see the interest one can have in multiplying $\sigma$ by the time T. The IV is a random variable that would vary with T, and assuming it is constant for all Ts is weird to me. Perhaps I have understood something wrong.