Volatility Estimation Using High, Low, and Close Data { a Maximum Likelihood Approach

The necessity of an accurate volatility estimate in order to price derivatives, and the time varying nature of volatility, make it imperative to obtain reliable volatility estimates using only the most recent data. More speciically, it is crucial to make use of all the available information. Many volatility estimates are based on the close prices of the instrument alone, despite the fact that high and low data are also available. It is to be expected that throwing away such high{low information will lead to a suboptimal volatility estimate when compared to an estimate that takes this extra information into account. We present a maximum likelihood approach to using the high, low and close information for obtaining volatility estimates. We present experiments to demonstrate that our estimate obtains consistently better performance than existing estimates on simulated data. In addition, we present simulations on real data, demonstrating that our method results in a more stable volatility estimate.