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on Market Microstructure |
| By: | Henry Schellhorn; Ran Zhao |
| Abstract: | We consider a dynamic market model where buyers and sellers submit limit orders. If at a given moment in time, the buyer is unable to complete his entire order due to the shortage of sell orders at the required limit price, the unmatched part of the order is recorded in the order book. Subsequently these buy unmatched orders may be matched with new incoming sell orders. The resulting demand curve constitutes the sole input to our model. The clearing price is then mechanically calculated using the market clearing condition. We model liquidity by considering the impact of a large trader on the market and on the clearing price. We assume a continuous model for the demand curve. We show that generically there exists an equivalent martingale measure for the clearing price, for all possible strategies of the large trader, if the driving noise is a Brownian sheet, while there may not be if the driving noise is multidimensional Brownian motion. Another contribution of this paper is to prove that, if there exists such an equivalent martingale measure, then, under mild conditions, there is no arbitrage. We use the Ito-Wentzell formula to obtain both results. We also characterize the dynamics of the demand curve and of the clearing price in the equivalent martingale measure. We find that the volatility of the clearing price is inversely proportional to the sum of buy and sell order flow density (evaluated at the clearing price), which confirms the intuition that volatility is inversely proportional to volume. We also demonstrate that our approach is implementable. We use real order book data and simulate option prices under a particularly simple parameterization of our model. The no-arbitrage conditions we obtain are applicable to a wide class of models, in the same way that the Heath-Jarrow-Morton conditions apply to a wide class of interest rate models. |
| Date: | 2016–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1608.05900&r=mst |
| By: | Robert P. Bartlett, III; Justin McCrary |
| Abstract: | We use new timestamp data from the two Securities Information Processors (SIPs) to examine SIP reporting latencies for quote and trade reports. Reporting latencies average 1.13 milliseconds for quotes and 22.84 milliseconds for trades. Despite these latencies, liquidity-taking orders gain on average $0.0002 per share when priced at the SIP-reported national best bid or offer (NBBO) rather than the NBBO calculated using exchanges’ direct data feeds. Trading surrounding SIP-priced trades shows little evidence that fast traders initiate these liquidity-taking orders to pick-off stale quotes. These findings contradict claims that fast traders systematically exploit traders who transact at the SIP NBBO. |
| JEL: | G10 G15 G18 G23 G28 K22 |
| Date: | 2016–08 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:22551&r=mst |
| By: | Luis Alberiko (Navarra Center for International Development); OlaOluwa S. Yaya; Olarenwaju I. Shittu |
| Abstract: | This paper is a follow up to Gil-Alana, Shittu and Yaya (2014). In that paper, fractional integration and symmetric volatility modeling were considered on monthly frequency data, while the present paper considers high frequency data on an asymmetric volatility model. The data were first identified within the respective bull and bear phases following earlier results in the previous paper. Then, fractional integration and the asymmetric volatility model of Glosten, Jaganathan and Runkle (GJR) were applied on the stock returns. Long range dependence was detected in the squared stock returns at each market phase, and they were more persistent than those obtained in the monthly frequency data. The estimates of asymmetry of the GJR model actually detected the different patterns of the bad news (bear phases) and the good news (bull phases). |
| Keywords: | Bull and bear periods; fractional integration; high frequency; stock returns; volatilty |
| JEL: | C22 G14 G15 |
| Date: | 2015–04 |
| URL: | http://d.repec.org/n?u=RePEc:nva:unnvaa:wp07-2015&r=mst |