Abstract
We calculate realized volatility of the Nikkei Stock Average (Nikkei225) Index on the Tokyo Stock Exchange and investigate the return dynamics. To avoid the bias on the realized volatility from the non-trading hours issue we calculate realized volatility separately in the two trading sessions, i.e. morning and afternoon, of the Tokyo Stock Exchange and find that the microstructure noise decreases the realized volatility at small sampling frequency. Using realized volatility as a proxy of the integrated volatility we standardize returns in the morning and afternoon sessions and investigate the normality of the standardized returns by calculating variance, kurtosis and 6th moment. We find that variance, kurtosis and 6th moment are consistent with those of the standard normal distribution, which indicates that the return dynamics of the Nikkei Stock Average are well described by a Gaussian random process with time-varying volatility.
Highlights
Statistical properties of asset returns have been extensively studied and it is found that asset price returns show some universal properties that are not explained well in the framework of the standard Brownian motion
The return process with the mixture of distributions hypothesis (MDH) does not conflict with major properties observed in asset returns, e.g. volatility clustering, fat-tailed return distributions
Under the MDH, the asset return at discrete time t can be described by rt = σtǫt, where σt2 is a variance of the Gaussian distribution and ǫt is a standard normal random variable, and this indicates that the asset return process is viewed as a Gaussian random process with time-varying variance
Summary
Statistical properties of asset returns have been extensively studied and it is found that asset price returns show some universal properties that are not explained well in the framework of the standard Brownian motion. The return process with the MDH does not conflict with major properties observed in asset returns, e.g. volatility clustering, fat-tailed return distributions. Under the MDH, the standardized returns should behave as rt/σt ∼ ǫt, i.e. standard normal random variables This test has been conducted in the literature[8, 9, 10, 11, 12, 13, 14, 15] and it is shown that the MDH is hold for many cases. In [14], in order to avoid bias from non-trading hours the MDH is tested separately in morning and afternoon sessions for individual Japanese stocks and it is shown that after removing the finite-sample effect[17] the return dynamics becomes consistent with the MDH[15]. In this paper we focus on the realized volatility of the Nikkei Stock Average index and investigate whether the MDH can apply for the price dynamics of the Nikkei Stock Average index
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