The Dynamic of the Volatility Skew: a Kalman Filter Approach

In the last few years, a lot of attention has been devoted to the issue of understanding and modeling the dynamic of implied volatility curves and surfaces, which 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, also in comparison with two alternative specifications, the sticky-delta model and the vegagamma expansion. We find that our model clearly outperforms both alternatives, given its ability to easily account for movements of different nature in the volatility curve.