Table 3.7 summarizes the parameters and the moment conditions of our model. We estimate the model separately for each stock and report average parameter estimates by group. Table 3.8 report the average parameter estimates for the iceberg order book model by trading activity group. We provide the parameter estimates for each stock in the appendix in table 3.13.
Panel A of Table 3.8 reports the estimates for the price impact function. Overall, the parameter estimates for the price impact function are very close to the results for the price impact regression reported in table 3.5; time-horizon 30 trades.
Panel B reports the estimates for the discount or premium for marginal liquidity provision at the best and second best order book levels. Theδ1estimates are on average negative and range from 0.8 to 1.5 basis points. One interpretation of the negative estimates is that, on average, traders who determine the marginal prices at the best bid or ask level have some intrinsic reason for trading. Accepting a negative payoff of this magnitude is rational if the alternative is to pay one-half of the bid-ask spread, which ranges from 4 to 7 basis points. The estimates ofδ2are positive and range from 1.2 to 2.4 basis points implying that liquidity providers a the second best level expect to have a positive net payoff after accounting for the adverse selection cost.
The state-dependent δiown parameters (i = 1, 2) are positive for both the best and the second best levels albeit that for the second best level the estimates are typically not significantly different from zero. For the best price level, however, the negative average marginal payoffs turns in to a positive payoff when there is an iceberg order at the best price level. One interpretation is that limit orders that undercut an iceberg order earn a positive marginal payoff perhaps because the iceberg order limits the price
3. ICEBERG ORDERS AND THE COMPENSATION FOR LIQUIDITY PROVISION
close to the regression results reported above in table 3.6. The average hidden size of iceberg orders ranges from 9 to 14 times the normal market order size. There is no clear pattern across the activity groups.
Table 3.9 reports the average value for the net marginal compensation for liquidity provision by order book level and by iceberg state. The top part reports the average values for δ1 which is the baseline compensation for liquidity provision. Our results here are in line with the findings in Frey and Grammig (2006) and Sandås (2001) and suggest that the marginal orders at the best quotes are not submitted by value traders but instead by patient liquidity traders. The positive estimate forδ2may be interpreted as the cost of providing liquidity, if value traders are the marginal providers and liquid-ity supply is competitive. To identify the proportion ofδ2that reflects order processing cost versus any rents one would need some additional restriction like the one used in Biais, Bisiere, and Spatt (2002).
The marginal compensation when iceberg orders are on the own and opposite side of the order book show two main regularities. First, when iceberg orders are on the same side of the book, then the marginal compensation for liquidity provision is posi-tive both for the best and second-best quotes. Second, when iceberg orders are on the opposite side the marginal compensation for liquidity provision is negative both for the best quotes.
The positive compensation for liquidity provision at the best level when iceberg orders are present on the same side suggests that traders are not bidding aggressively enough when it is likely that their limit order compete with hidden liquidity. Similarly, at the second best quotes the results provide some support for the idea that after con-trolling for other factors traders bid less aggressively when they are likely to compete with hidden liquidity.
Conversely, when iceberg orders are on the opposite side we observe that traders are bidding too aggressively. Of course, one may also interpret this as evidence that when iceberg orders are present on the opposite side then liquidity traders tend to determine the marginal prices. Our evidence on the order flow suggests that when iceberg orders are present there is more frequent and larger market orders making trades more likely.
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not observe the true iceberg states. Instead they have to use available information to try to detect or predict the existence of iceberg orders. Even if we assume that market participants know the iceberg states, our model still captures the uncertainty of the precise size of the hidden volume. To improve from that we develop a reasonable approximation of the possible predictions used by the traders.
An Iceberg Detection Algorithm
The limit order book changes provides signals to traders about the existence of iceberg orders. When a trade occurs that involves the execution of volume in excess of the dis-played volume at given price, it is very likely that the price contains an iceberg order.
The ratio between total size to peak size in Table 3.2 implies that after the replenish-ing of one peak, additional hidden volume is to typically expected.4 This implies that one can detect iceberg orders comparing the recent history of transaction prices and volume with the transition of the visible order book.
We construct an iceberg detection algorithm that works as follows. Every time an iceberg order is replenished—new visible order volume is added—the algorithm sets an indicator for hidden volume at that price. The algorithm resets the indicator for that price to zero only when an event occurs that could not have occurred had the iceberg order remained at that price. The indicator and the volume until the next replenishment is stored specific for the price level. The indicator remains unchanged unless a potential replenishment is omitted. For the iceberg state variable we apply the prevailing indicators at the best price levels. A detailed example how the algorithm works is given in the appendix 3.A.
The algorithm will make both type I and type II errors (assuming that the null is to predict no iceberg state), but given the properties of iceberg order documented above, see, table 3.2, it is likely to provide informative signals. Table 3.10 reports the average percentages of correct and in-correct detections. False detections are in the range between a half and two percents. True iceberg states that are missed by the
3. ICEBERG ORDERS AND THE COMPENSATION FOR LIQUIDITY PROVISION
remain undiscovered, as the iceberg was not yet executed at least once. Comparing our results to De Winne and D’Hondt (2007) the algorithm displays similar size (false detection) for Euronext, but slightly less power with around 40 percent undiscovered states or somewhat more than ten percents in absolute terms.
We do not know, of course, to what extent the predictions from our algorithm closely approximates the predictions of the market participants. Conversations with market participants suggest that it is reasonable to assume that active participants are able to collect this type of information. Of course, it may well be the case that market participants apply algorithms that generate even more accurate predictions.
Robustness of Model Parameter Estimates
We re-estimate the model parameters using the same moment conditions as above, but by letting the indicators generated by the detection algorithm determine the values of the indicator variables. Table 3.6 provides a comparison of the δ estimates obtained in the baseline case—labeled ‘True’—and in the case of the detection algorithm labeled
‘Algorithm.’ Overall, the parameter estimates are fairly close. The price impact param-eters and the order flow paramparam-eters are also fairly similar suggestion that our main findings for the compensation for liquidity provision are robust to uncertainty about the iceberg orders.
3.6 Conclusions
We study the interaction between hidden and visible liquidity in a limit order market.
We show that the hidden liquidity that is supplied by iceberg orders influences that strategies followed by traders supplying visible liquidity using limit orders. We re-port evidence that iceberg orders have an economically significant impact on the order book and short term price dynamics despite representing a relatively small fraction of all submitted orders. We show that while it may be hard to predict the amount of hidden liquidity, a trader can, using the history of visible order books, successfully predict whether the book contains hidden liquidity or not. Based on these findings we develop a state-dependent model of liquidity provision in which traders who submit limit orders to the order book follow different strategies depending on whether there is hidden liquidity or not.
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iceberg order is on the same side of the book is consistent with traders placing orders less aggressively when they anticipate their order competing with hidden liquidity.
Our approach focuses on the response of traders submitting market and limit or-ders to the possibility of hidden liquidity. But indirectly the results also offer some in-sights into the motives of the traders submitting iceberg orders. The fact, that iceberg orders are partly detectable and we observe more frequent and larger market orders suggest that iceberg orders are used successfully as a tool for coordinating trading.
3. ICEBERG ORDERS AND THE COMPENSATION FOR LIQUIDITY PROVISION