大阪大学　数理・データ科学教育研究センター
Center for Mathematical Modeling and Data Science,Osaka University

On High Frequency Estimation of the Frictionless Price: The Use of Observed Liquidity Variables

Selma Chaker (Bank of Canada)

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大阪大学 金融・保険セミナーシリーズ 第51回(CSFI-CRESTジョイントセミナー)

On High Frequency Estimation of the Frictionless Price: The Use of Observed Liquidity Variables

Selma Chaker (Bank of Canada)

Observed high-frequency prices are always contaminated with liquidity costs or market microstructure noise. Inspired by the market microstructure literature, I explicitly model this noise and remove it from observed prices to obtain an estimate of the frictionless price. I then formally test whether the prices adjusted for the estimated liquidity costs are either totally or partially free from noise. If the liquidity costs are only partially removed, the residual noise is smaller and closer to an exogenous white noise than the original noise is. To illustrate my approach, I use the adjusted prices to improve volatility estimation in the presence of noise. If the noise is totally absorbed, I show that the sum of squared returns – which would be inconsistent for return variance when based on observed returns – becomes consistent when based on adjusted returns. This novel estimator achieves the maximum possible rate of convergence. If the noise is partially absorbed, however, I show that the two time scales volatility estimator – which would be inconsistent for return variance when based on observed returns – becomes consistent when based on adjusted returns even if the original noise is endogenous, heteroskedastic and autocorrelated.

KEY WORDS: Stochastic volatility; Hidden semimartingale model; Infill regression ; Endogenous noise; Semiparametric volatility estimation.