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. Furthermore, a new nonlinear market microstructure noise model is proposed that reproduces several 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 curve. We neither assume that the transaction times are equidistant nor do we use interpolated prices. We also make a distinction between volatility per time unit and volatility per transaction and provide estimators for both.