# Tag Info

Note that total implied variance defined as $$V(T,K) = T\Sigma(T,K)^2$$ should be an increasing function of $T$. Otherwise you have a calendar arbitrage (sell the call with shorter expiry and buy the cheap longer one). If you interpolate linearly your implied volatility is $$\Sigma(T,K) = w\Sigma(T_i,K) + (1-w)\Sigma(T_{i+1},K)$$ with weight \$w = ...