Volatility Decomposition and Nonparametric Estimation of Spot Volatility of Models with Poisson Sampling under Market Microstructure Noise

The estimation of volatility for high-frequency data under market microstructure noise has been extensively studied during recent years. In this work, in contrast to the majority of previous research, we focus on the estimation of spot volatility of a time-changed price-model based on transaction times. In this model, volatility is decomposed into the product of two main curves, namely transaction-time volatility and trading intensity, both of which can be analyzed from data and contain valuable information. By inspecting these two curves individually we gain more insight into the cause and structure of volatility. The main methodological and theoretical contributions of this work are the introduction and theoretical investigation of a new volatility estimator based on this volatility decomposition. \n \nFor the estimation of transaction-time volatility under microstructure noise, we adapt a noise-robust estimator based on the pre-averaging technique to our situation in order to cope successfully with the contamination. The asymptotic properties of both estimators— the classical volatility estimator and the alternative volatility estimator (based on the decomposition)—are investigated using an infill asymptotic approach. We compare these estimators in order to see the benefit of factorizing the volatility in this transaction-time model. We find that the alternative estimator outperforms the classical one in many cases in terms of the rate of convergence. Finally, we explore the performance of our estimators in the finite-sample setting in simulations. Our real-data analysis of high-liquid assets reveals several interesting empirical phenomena: (i) the U-shape in the spot volatility over a trading day is primarily the feature of the intensity; (ii) the tick-time volatility is considerably smoother than the clock-time volatility and intensity; (iii) the impact of microstructure noise on spot volatility estimation is very small.