An efficient estimate and forecast of the implied volatility surface: A nonlinear Kalman filter approach

Abstract

As suggested by numerous studies, while the implied volatility surface changes over time, its shape tends to pervade. This motivates us to construct a dynamic model for implied volatility surface, which not only captures cross-sectional information of implied volatilities with different strikes and maturities, but also describes how the implied volatility surface evolves over time. In this paper, we use nonlinear parametric function to capture single implied volatility surface, and model the dynamics of implied volatility surface by modeling the dynamics of function coefficients. We introduce unscented Kalman filter to propagate the nonlinear system, which is constructed by the nonlinear parametric function and the dynamics of its coefficients. A dynamic approach is proposed to provide optimal estimation of model parameters and efficient forecast of future implied volatility surface. It shows that our model has a better description of implied volatility surface dynamics than other similar models, and can be used to do volatility surface forecast.