Hi,I'm having trouble understanding exactly why one uses these filtering methods for stochastic volatility modeling.Are they alternatives to methods such as maximum likelihood (using Powel for example) for estimating parameters, or something to be used in conjunction with these?Am I correct in interpreting (Xk | Z1:k) as:Xk = state at time k = stock price, volatility ... all other parameters at time k, given the ZksZ1:k = previous observations, meaning what, all previous Xks ? Edit:Ok, understood the underlying system, and thus what the Zks are. Still not sure about the first question though.

PF or Kalman filtering is not used to implement MLE directly but can be useful to evaluate the likelihood.To be specific, the likelihood could be decomposed into the product of a series of conditional densities and each component can be written as an integral involving the one-step predictive density. It's this predictive density that PF is used to approximatewith monte carlo methods. For SV, PF is probably the only choice since this state-space model is nonlinear, so Kalman may not help

BTW, what problem do you want to apply SV model to?

QuoteOriginally posted by: movielovePF or Kalman filtering is not used to implement MLE directly but can be useful to evaluate the likelihood.To be specific, the likelihood could be decomposed into the product of a series of conditional densities and each component can be written as an integral involving the one-step predictive density. It's this predictive density that PF is used to approximatewith monte carlo methods. For SV, PF is probably the only choice since this state-space model is nonlinear, so Kalman may not helpin SV state space context, the stochastic volatility evolution is perfectly linear; only the option pricing, if that is being concerned, is non-linear. In fact, a modified KF, such as extended or unscented KF, is better in a Gaussian SV case since they are much less expensive computationally than PF. PF is only practically preferrable when the state variable dynamics are non-Gaussian