2010/06/09 by Rainer Dahlhaus, Dahlhaus, Rainer, Jan C. Neddermeyer +1
Economics, Econometrics and Finance · #Financial Risk and Volatility Modeling #Stochastic processes and financial applications #Complex Systems and Time Series Analysis
paper · pdf · doi:10.48550/arxiv.1006.1860
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.