On the quadratic variation in limit order markets

Abstract

This paper explores the quadratic variation (QV) as an alternative measure to the bid-ask spread in limit order markets when observed at high resolution. Although the spread cannot be precisely estimated because of microstructure noise, the QV of the price series, consisting of the transaction prices and midquotes (an expanded filtration of transaction prices), in limit order markets is an important property of high-frequency datasets. An empirical examination of a sample of stocks from the NASDAQ 100 is used to estimate and examine the QV. The examination is done at high resolution (subsecond timescale). The QV of our sample best fits a log-normal distribution with higher skewness. The QV of trades (29.73E–05) is distant from the QV measured with pretrade and posttrade price series, as they are characterized by a high range in QV. Similarly, the QV is generally lower with pretrades than posttrades. Using a high resolution, the revealed state of the limit order book presents a solution that reduced the impact cost of trading. The QV is higher with the limit order book (68.5E–05) than with trades. A measure called the limit-to-market order signal shows a consistent pattern of decline in stocks with increasing activity. The limit-to-market signal ranged from an average of 3.55 in the first quartile of stocks based on messages to 1.84 in the third quartile. This signal decreases because of a relatively larger decline in uncertainty in QV using the limit order book.