The Dynamics of the Volatility Skew: A Kalman Filter Approach

Much attention has been devoted to understanding and modeling the dynamics of implied volatility curves and surfaces. This is crucial for both trading, pricing and risk management of option positions. We suggest a simple, yet flexible, model, based on a discrete and linear Kalman filter updating of the volatility skew. From a risk management perspective, we assess whether this model is capable of producing good density forecasts of daily returns on a number of option portfolios. We also compare our model to the sticky-delta and the vega-gamma alternatives. We find that it clearly outperforms both alternatives, given its ability to easily account for movements of different nature in the volatility curve.