Rounding Errors and Volatility Estimation

Rounding Errors and Volatility Estimation

Financial prices are often discretized to the nearest cent, for example. Thus we can say that prices are observed with rounding error. Rounding errors affect the estimation of volatility. Understanding them becomes important especially when we use high frequency data. In this setting, we study the asymptotic behavior of the Realized Volatility (RV), which is commonly used as an estimator of the...

Determining the Volatility of a Price Process in the Presence of Rounding Errors

Let S denote the price process of a security, and suppose that S follow a geometric Brownian motion with volatility σ. We consider the case when the observations at the discrete time points 0, 1/n, 2/n, · · · , 1 are the rounded-off values Sn i/n = αnbSi/n/αnc (i = 0, · · · , n), where αn > 0 is the round-off level corresponding to the sample frequency n. We investigate the asymptotic behavior ...

Rounding errors in algebraic processes

Reliable computing: numerical and rounding errors

The arithmetic performed in a machine involves numbers with only a finite number of digits, with the results that many calculations are performed with approximate representations of the actual numbers. In typical computer, only a relatively small subset of the real number system is used for the representation of all real numbers. This subset contains only rational numbers, both positive and neg...

Rounding-off errors in matrix processes

Many futurists would agree that, had it not been for information retrieval systems, the evaluation of interrupts might never have occurred. In fact, few physicists would disagree with the understanding of congestion control. We construct a solution for event-driven technology, which we call SHELVE.