Three Modified Unscented Kalman Filterings For Volatility Extraction

As volatility pervades almost everywhere in financial markets,its estimation has become one of the key points in financial economics.There are many models to forecast volatility,including ARCH and GARCH model,but they are proposed for the linear model.The model about the nonlinear model is relatively much less.Considering this,we research the algorithms applied to volatility extraction in diffusion option pricing model.As soon as Kalman filter was proposed,it was loved by many experts and scholars thanks to its optimality and applied to navigation and location,aerospace and other fields widely,but very less in economic.In order to capture the volatility dynamics accurately and quickly,this paper combines UT transformation and the Minimum of skewness single sampling strategy?Super sphere single sam-pling strategy with the unscented Kalman filter(UKF)algorithm to propose two modified unscented Kalman filter algorithms for nonlinear Gaussian system,MUKF and AUKF algorithm.These algo-rithms are applied to volatility extraction in a diffusion option pricing model.Simulation study with the Heston stochastic volatility model indicate that to obtain an accurate estimation of volatility,both the stock and option prices are necessary,and the computation time of the MUKF and AUKF algorithms are less than UKF algorithm.This paper also study the volatility of volatility parameter and indicate that these algorithms can govern the variation of volatility.