An unscented Kalman smoother for volatility extraction: Evidence from stock prices and options

A smoothing algorithm based on the unscented transformation is proposed for the nonlinear Gaussian system. The algorithm first implements a forward unscented Kalman filter and then evokes a separate backward smoothing pass by only making Gaussian approximations in the state but not in the observation space. The method is applied to volatility extraction in a diffusion option pricing model. Both simulation study and empirical applications with the Heston stochastic volatility model indicate that in order to accurately capture the volatility dynamics, both stock prices and options are necessary.

► An unscented smoothing algorithm is proposed for nonlinear Gaussian systems.
► First, the algorithm implements a forward unscented Kalman filter.
► Then it evokes a backward smoothing pass only in the state system.
► The method is applied to a diffusion option pricing model.
► Both stock prices and options are necessary to capture volatility dynamics.