0000000000646446
AUTHOR
Gabriele La Spada
The non-random walk of stock prices: The long-term correlation between signs and sizes
We investigate the random walk of prices by developing a simple model relating the properties of the signs and absolute values of individual price changes to the diffusion rate (volatility) of prices at longer time scales. We show that this benchmark model is unable to reproduce the diffusion properties of real prices. Specifically, we find that for one hour intervals this model consistently over-predicts the volatility of real price series by about 70%, and that this effect becomes stronger as the length of the intervals increases. By selectively shuffling some components of the data while preserving others we are able to show that this discrepancy is caused by a subtle but long-range non-…
Tick Size and Price Diffusion
A tick size is the smallest increment of a security price. Tick size is typically regulated by the exchange where the security is traded and it may be modified either because the exchange enforces an overall tick size change or because the price of the security is too low or too high. There is an extensive literature, partially reviewed in Sect. 2 of the present paper, on the role of tick size in the price formation process. However, the role and the importance of tick size has not been yet fully understood, as testified, for example, by a recent document of the Committee of European Securities Regulators (CESR) [1].
The effect of round-off error on long memory processes
We study how the round-off (or discretization) error changes the statistical properties of a Gaussian long memory process. We show that the autocovariance and the spectral density of the discretized process are asymptotically rescaled by a factor smaller than one, and we compute exactly this scaling factor. Consequently, we find that the discretized process is also long memory with the same Hurst exponent as the original process. We consider the properties of two estimators of the Hurst exponent, namely the local Whittle (LW) estimator and the Detrended Fluctuation Analysis (DFA). By using analytical considerations and numerical simulations we show that, in presence of round-off error, both…