| Since the seminal work of Black & Scholes (1973) and Merton (1973) on option pricing, there has been growing interest in modeling the volatility of asset returns. The original assumption of constant volatility has been shown to be inadequate in many empirical studies. One way to model changing volatility is through the stochastic volatility (SV) model developed by Taylor (1986) and Hull & White (1987) in which the volatility follows its own random process.;The SV model can be placed in the more general framework of hidden Markov models (HMM). Parameter estimation is difficult for this class of models because of the intractability of the likelihood function. The main objective of this work is to develop an efficient estimator with a substantial reduction in computational complexity over direct maximum likelihood. It is based on two ideas to simplify the problem. The first idea is to start with a consistent and asymptotically normal estimator, so that only one Newton correction step is required for efficiency. The second idea is to replace the true likelihood with a pseudo-likelihood which is easier to calculate. The pseudo-likelihood we use assumes that the observations can be grouped into blocks with each block independent of all others. If this blocking is done properly, then it does not affect the asymptotic efficiency of the estimator. We also explore different Monte Carlo simulation techniques to carry out the Newton step. We first apply this algorithm to simulated data to compare its performance with some alternate methods, and then apply the procedure to financial data. |
