Reading the Candlesticks : An OK Estimator for Volatility

Academic research on nonparametric "spot" volatility inference often relies on high-quality transaction data that are not available to an average investor. Most investors, however, have free access to intraday candlestick charts through their online trading applications. Based on such data, we propose an Optimal candlesticK (OK) estimator for the spot volatility at a given time point. Under a standard infill asymptotic setting for Ito semimartingale price process, we show that the OK estimator is asymptotically unbiased and has minimal asymptotic variance within a class of linear estimators. In addition, its estimation error can be coupled by a Brownian functional, whose distribution is pivotal and known in finite-sample. Optimal confidence intervals can be constructed using the highest density interval of the (nonstandard) coupling distribution. Our theoretical and numerical results suggest that the proposed candlestick-based estimator is much more accurate than the conventional spot volatility estimator based on high-frequency returns. An empirical illustration is provided, which documents the intraday spot volatility dynamics of various assets during the Fed Chairman's recent congressional testimony