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We develop and estimate an econometric model of limit-order execution times using survival analysis and actual limit-order data. We estimate versions for time-to-first-fill and time-to-completion for both buy and sell limit orders, and incorporate the effects of explanatory variables such as the limit price, limit size, bid/offer spread, and market volatility. Execution times are very sensitive to the limit price, but are not sensitive to limit size. Hypothetical limit-order executions, constructed either theoretically from first-passage times or empirically from transactions data, are very poor proxies for actual limit-order executions.

One of the most important tools for trading equity securities is the limit order, which is an order to transact a prespecified number of shares at a prespecified price. Indeed, limit orders constitute a significant fraction of stock market trading activity, accounting for approximately 45% of total NYSE orders (Harris and Hasbrouck, 1996). The primary advantage of a limit order is the absence of price risk—a transaction occurs only if the limit price is attained. However, this advantage does not come without a cost: execution is not guaranteed, and the time-to-execution is a random function of many factors, such as the limit price, the number of shares, market conditions, and private information. For some trades, the uncertainty in execution time is unimportant, but for others, the opportunity cost of waiting can be significant. If immediacy is critical, the market order is the appropriate instrument to use. However, market orders can be subject to significant price risk, particularly for large orders and in volatile markets. In practice, traders submit both market and limit orders, with an eye towards balancing the risks of delaying execution against the risks associated with immediate execution.1 A prerequisite for any quantitative approach to making such tradeoffs is an econometric model of limit-order execution times and the associated execution probabilities. Limit orders play another important role in determining trading costs: they influence bid/offer quotes and, therefore, spreads. Chung et al. (1997) estimate that 21% of the quotes in their sample originate from limit orders on both the bid and offer sides without any direct participation from the specialist. Therefore, limit-order execution times affect the frequency with which quotes are updated and are likely to be a major factor in the dynamics of bid/offer spreads. Moreover, limit-order execution times have been used to measure the overall quality of equity markets (e.g., Battalio et al., 1999; SEC, 1997), hence their determinants can have important implications for the economic consequences of market fragmentation, the practice of “preferencing”, and the relative merits of specialist vs. multiple-dealer market structures. In this paper, we propose and estimate an econometric model of limit-order execution times using actual historical limit-order data. Using survival analysis, which is a well-known statistical technique for modeling failure times and other nonnegative random variables, we are able to estimate the conditional distribution of limit-order execution times as a function of economic variables such as the limit price, order size, and current market conditions. Because limit-order execution times can be interpreted quite naturally as failure times—they are nonnegative, random, and temporally ordered—survival analysis is the most appropriate method for modeling their evolution. Moreover, survival analysis can accommodate an important feature of limit-order execution times that existing models have ignored: censored observations, i.e., limit orders that expire or are canceled before they are executed. There is great temptation to ignore censored observations since they seem to provide little information about execution times. However, the fact that a limit order is canceled after, say, 30 minutes yields a piece of useful information: the limit order “survived” for at least 30 minutes. Therefore, censored observations do affect the conditional distribution of execution times despite the fact that they are not executions. Ignoring censored observations can dramatically bias the estimator of the conditional distribution of execution times. Using a sample of limit orders for the 100 largest stocks in the S&P 500 from August 1994 to August 1995, we construct models of limit-order execution times based on survival analysis and show that they fit the data remarkably well. In particular, we estimate separate models for time-to-first-fill and time-to-completion for both buy and sell limit orders, hence four models in all. Each of these four models yields a conditional distribution that closely matches the data's and passes several diagnostic tests of goodness-of-fit. The parameter estimates show that execution times can be quite sensitive to certain explanatory variables, such as market depth, the spread between the limit price and the quote midpoint, and market volatility, implying that the kind of strategic order-placement strategies described by Angel (1994), Foucault (1996), Harris (1994), Hollifield et al. (1999), Kumar and Seppi (1993), and Parlour (1998) could well be feasible in practice. Limit-order execution times can be accurately modeled, hence controlled. In Section 2 we review the literature on limit orders, and in Section 3 we discuss some of the institutional features of limit orders and describe our limit-order dataset. We present a simple but powerful application of this dataset in Section 4 in which we compare actual limit-order execution times to their hypothetical counterpart, constructed theoretically (from the first-passage times of Brownian motion) and empirically (from transactions data). We present a brief review of survival analysis in Section 5 and turn to our empirical analysis in Section 6. We conclude in Section 7.

The behavior of limit-order execution times is critical to the price-discovery process of most market microstructure models, and we have shown that it can be quantified to a large extent by an econometric model based on survival analysis and estimated with actual limit-order data using the ITG limit-order dataset. Survival analysis is designed to model lifetime data and incorporates many of the subtleties that characterize such data, such as skewness and censoring. We find that the generalized gamma model with an accelerated failure time specification fits the data remarkably well, and that execution times are quite sensitive to some explanatory variables (e.g., limit price) but not to others (e.g., limit shares). Despite the fact that we pool the limit orders of 100 stocks to estimate an aggregate model of execution times, our diagnostics show that such aggregate models fit reasonably well stock by stock. We also explore the properties of hypothetical limit-order executions, constructed theoretically from the first-passage times of geometric Brownian motion and empirically from transactions data. Although such models have a certain elegance due to their parsimony, and can be estimated using transactions data alone, they perform very poorly when confronted with actual limit-order data. Our findings support the practical feasibility of sophisticated dynamic order-submission strategies, strategies that trade off the price impact of market orders against the opportunity costs inherent in limit orders. We hope to explore such strategies in future research.