Estimating stochastic volatility via filtering for the micromovement of asset prices

Under the general framework of a previous paper, a unified approach via filtering is developed to estimate stochastic volatility for micromovement models. The key feature of the models is that they can be transformed as filtering problems with counting process observations. In order to obtain trade-by-trade, real-time Bayes estimates of stochastic volatility, the Markov chain approximation method is applied to the filtering equation to construct a consistent recursive algorithm, which computes the joint posterior. To illustrate the approach, a recursive algorithm is constructed in detail for a jumping stochastic volatility micromovement model. Simulation results show that the Bayes estimates for stochastic volatilities capture the movement of volatility. Trade-by-trade stochastic volatility estimates for a Microsoft transaction data set are obtained and they provide strong affirmative evidence that volatility changes even more dramatically at trade-by-trade level.