On-line Spot Volatility-Estimation and Decomposition with Nonlinear Market Microstructure Noise Models

A technique for 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 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. More precisely we use a model with random time change where spot volatility is decomposed into spot volatility per transaction times the trading intensity - thus highlighting the influence of trading intensity on volatility.