Particle Filter-Based On-Line Estimation of Spot Volatility with Nonlinear Market Microstructure Noise Models

A new technique for the on-line estimation of spot volatility for high-frequency data is developed. The algorithm works directly on the transaction data and updates the volatility estimate immediately after the occurrence of a new transaction. We make a clear distinction between volatility per time unit and volatility per transaction and provide estimators for both. A new nonlinear market microstructure noise model is proposed that reproduces the major stylized facts of high-frequency data. A computationally efficient particle filter is used that allows for the approximation of the unknown efficient prices and, in combination with a recursive EM algorithm, for the estimation of the volatility curves. In addition, the estimators are improved by an on-line bias correction. We neither assume that the transaction times are equidistant nor do we use interpolated prices.