A new statistic to capture the level dependence in stock price volatility

In this paper, we propose a new covariance estimator based on daily opening, high, low and closing prices. We prove theoretically that the new estimator is unbiased for a pure random walk and further validate it with simulation studies. However, upon examining empirically four indices namely: NIFTY, S&P500, FTSE100 and DAX over the sample period from January 1996 to March 2015, we find that the estimator is upward biased for all the indices under study. This overreaction in stock indices can be attributed to the level dependence in stock indices, something that is not captured by the random walk model. So we explore an alternative to random walk, namely: Constant Elasticity of Variance (CEV) specification. Simulation studies provide supporting evidence that the CEV specification can capture the level dependence that makes the estimator upward biased as seen in the data. Therefore, through this specification exercise, we can see that it is possible to isolate the effect of intraday level dependence in stock prices using our estimator.