In this paper we study the Stochastic Volatility Inspired model (SVI). Until recently, it was not possible to find sufficient conditions that would guarantee the absence of static arbitrage in this SVI model. Recently, we proposed a new numerical method based on Sequential Quadratic Programming (SQP) algorithm to resolve this problem. The main contribution in this paper is that we provide sufficient conditions that guarantee an SVI static arbitrage-free. These conditions ensure that the probability density function will remain positive.Finally, we present several computational synthetic examples with static arbitrage and we show how to fix them.Next, we use real market data coming from 23 indexes to calibrate the SVI model. The calibration method is robust and easy to implement,it guarantees calibration arbitrage free (calendar spread and butterfly arbitrage).