AN APPLICATION OF THE METHOD OF MOMENTS TO RANGE-BASED VOLATILITY ESTIMATION USING DAILY HIGH, LOW, OPENING, AND CLOSING (HLOC) PRICES

We use the expectation of the range of an arithmetic Brownian motion and the method of moments on the daily high, low, opening, and closing prices to estimate the volatility of the stock price. This novel theoretical approach results in an estimator that is genuinely range-based on daily opening, high, low and closing data, unlike current estimators in the literature. The daily price jump at the opening is considered to be the result of the unobserved evolution of an after-hours virtual trading day. In comparison to an existing drift-independent estimator, we find that our estimator is actually more efficient when using a smaller number of data points, while for a larger number of points the efficiency of our estimator stays above 99% of the existing one. A toy example that uses this method to take advantage of mispricing opportunities in the options market illustrates potential applications of this method to algorithmic trading.