The Role of Additional Information in Option Pricing: Estimation Issues for the State Space Model

We consider two competing financial state space models and investigate whether additional information in the form of option price data is helpful to the estimation of either the unobservable state variable (volatility) or the unknown parameters in the model. The complete discussion of the estimation problem in the presence of additional information involves decisions about filtering methods, the quality of the new information, the correlation between state variables and out-of-sample forecast performance. It is found that the state variable estimation is more sensitive than the parameter estimation to the correlation, information quality and the assumed linearity or non-linearity of the underlying model. As a result of the investigation of these factors, the particle filter is shown to be an attractive method for computing posterior distributions for these models.