An Unscented Kalman Smoother for Volatility Extraction: Evidence from Stock Prices and Options
23 Pages Posted: 10 Mar 2013
Date Written: January 5, 2012
Abstract
A smoothing algorithm based on the unscented transformation is proposed for the non-linear 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.
Keywords: Non-linear Gaussian state-space models, Non-linear Kalman filters, Unscented Kalman smoother, Heston stochastic volatility model, Option pricing
JEL Classification: C10
Suggested Citation: Suggested Citation