SVI estimation of the implied volatility by Kalman filter.

Abstract: To understand and model the dynamics of the implied volatility smile is essential for trading, pricing and risk management portfolio. We suggest a  linear Kalman filter for updating of the Stochastic Volatility Inspired (SVI) model of the volatility. From a risk management perspective we generate the 1-day ahead forecast of profit and loss (P\&L) of option portfolios. We compare the estimation of the implied volatility using the SVI model with the cubic polynomial model. We find that the SVI Kalman filter has outperformed the  others.