# Analysis of Realized Volatility for Nikkei Stock Average on the Tokyo Stock Exchange

## TL;DR

This paper calculates and analyzes the realized volatility of the Nikkei 225 index, addressing microstructure noise and non-trading hours, and finds that standardized returns follow a Gaussian process with time-varying volatility.

## Contribution

It introduces a method to accurately estimate realized volatility by separating trading sessions and demonstrates that Nikkei 225 returns are Gaussian with time-varying volatility.

## Key findings

- Realized volatility decreases at small sampling frequencies due to microstructure noise.
- Standardized returns are consistent with a normal distribution.
- Return dynamics are well modeled by a Gaussian process with time-varying volatility.

## 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.