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Risk aversion and the dynamics of optimal liquidation strategies in illiquid markets
 Finance and Stochastics
"... in illiquid markets ..."
2008: Highfrequency trading in a limit order book
 Quantitative Finance
"... We study a stock dealer’s strategy for submitting bid and ask quotes in a limit order book. The agent faces an inventory risk due to the diffusive nature of the stock’s midprice and a transactions risk due to a Poisson arrival of market buy and sell orders. After setting up the agent’s problem in a ..."
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Cited by 31 (0 self)
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We study a stock dealer’s strategy for submitting bid and ask quotes in a limit order book. The agent faces an inventory risk due to the diffusive nature of the stock’s midprice and a transactions risk due to a Poisson arrival of market buy and sell orders. After setting up the agent’s problem in a maximal expected utility framework, we derive the solution in a two step procedure. First, the dealer computes a personal indifference valuation for the stock, given his current inventory. Second, he calibrates his bid and ask quotes to the market’s limit order book. We compare this ”inventorybased ” strategy to a ”naive ” strategy that is symmetric around the midprice, by simulating stock price paths and displaying the P&L profiles of both strategies. We find that our strategy yields P&L profiles and final inventories that have significantly less variance than the benchmark strategy. 1
Random walks, liquidity molasses and critical response in financial markets, Quantitative Finance
, 2006
"... Stock prices are observed to be random walks in time despite a strong, long term memory in the signs of trades (buys or sells). Lillo and Farmer have recently suggested that these correlations are compensated by opposite long ranged fluctuations in liquidity, with an otherwise permanent market impac ..."
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Cited by 28 (4 self)
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Stock prices are observed to be random walks in time despite a strong, long term memory in the signs of trades (buys or sells). Lillo and Farmer have recently suggested that these correlations are compensated by opposite long ranged fluctuations in liquidity, with an otherwise permanent market impact, challenging the scenario proposed in Quantitative Finance 4, 176 (2004), where the impact is transient, with a powerlaw decay in time. The exponent of this decay is precisely tuned to a critical value, ensuring simultaneously that prices are diffusive on long time scales and that the response function is nearly constant. We provide new analysis of empirical data that confirm and make more precise our previous claims. We show that the powerlaw decay of the bare impact function comes both from an excess flow of limit order opposite to the market order flow, and to a systematic anticorrelation of the bidask motion between trades, two effects that create a ‘liquidity molasses ’ which dampens market volatility. 1 1
Constrained portfolio liquidation in a limit order book model
 Banach Center Publ
, 2008
"... Abstract. We consider the problem of optimally placing market orders so as to minimize the expected liquidity costs from buying a given amount of shares. The liquidity price impact of market orders is described by an extension of a model for a limit order book with resilience that was proposed by Ob ..."
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Cited by 26 (10 self)
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Abstract. We consider the problem of optimally placing market orders so as to minimize the expected liquidity costs from buying a given amount of shares. The liquidity price impact of market orders is described by an extension of a model for a limit order book with resilience that was proposed by Obizhaeva and Wang (2006). We extend their model by allowing for a timedependent resilience rate, arbitrary trading times, and general equilibrium dynamics for the unaffected bid and ask prices. Our main results solve the problem of minimizing the expected liquidity costs within a given convex set of predictable trading strategies by reducing it to a deterministic optimization problem. This deterministic problem is explicitly solved for the case in which the convex set of strategies is defined via finitely many linear constraints. A detailed study of optimal portfolio liquidation in markets with opening and closing call auctions is provided as 2000 Mathematics Subject Classification: 91B26, 91B28, 91B70, 93E20, 60G35. Key words and phrases: liquidity risk, optimal portfolio liquidation, limit order book with resilience, call auction, market impact model, constrained trading strategies, market order. Research of the first two authors was supported by Deutsche Forschungsgemeinschaft through the Research Center Matheon “Mathematics for key technologies ” (FZT 86). The paper is in final form and no version of it will be published elsewhere. [9] c ○ Instytut Matematyczny PAN, 200810 A. ALFONSI ET AL. an illustration. We also obtain closedform solutions for the unconstrained portfolio liquidation problem in our timeinhomogeneous setting and thus extend a result from our earlier paper [1]. 1. Introduction. A
A HamiltonJacobiBellman approach to optimal trade execution
, 2009
"... The optimal trade execution problem is formulated in terms of a meanvariance tradeoff, as seen at the initial time. The meanvariance problem can be embedded in a LinearQuadratic (LQ) optimal stochastic control problem, A semiLagrangian scheme is used to solve the resulting nonlinear Hamilton Ja ..."
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Cited by 17 (2 self)
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The optimal trade execution problem is formulated in terms of a meanvariance tradeoff, as seen at the initial time. The meanvariance problem can be embedded in a LinearQuadratic (LQ) optimal stochastic control problem, A semiLagrangian scheme is used to solve the resulting nonlinear Hamilton Jacobi Bellman (HJB) PDE. This method is essentially independent of the form for the price impact functions. Provided a strong comparision property holds, we prove that the numerical scheme converges to the viscosity solution of the HJB PDE. Numerical examples are presented in terms of the efficient trading frontier and the trading strategy. The numerical results indicate that in some cases there are many different trading strategies which generate almost identical efficient frontiers.
The price impact of order book events
, 2010
"... We study the price impact of order book events limit orders, market orders and cancelations using the NYSE TAQ data for 50 U.S. stocks. We show that, over short time intervals, price changes are mainly driven by the order flow imbalance, defined as the imbalance between supply and demand at the be ..."
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Cited by 15 (1 self)
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We study the price impact of order book events limit orders, market orders and cancelations using the NYSE TAQ data for 50 U.S. stocks. We show that, over short time intervals, price changes are mainly driven by the order flow imbalance, defined as the imbalance between supply and demand at the best bid and ask prices. Our study reveals a linear relation between order flow imbalance and price changes, with a slope inversely proportional to the market depth. These results are shown to be robust to seasonality effects, and stable across time scales and across stocks. We argue that this linear price impact model, together with a scaling argument, implies the empirically observed “squareroot” relation between price changes and trading volume. However, the relation between price changes and trade
Optimal Portfolio Liquidation for CARA Investors
, 2007
"... We consider the finitetime optimal portfolio liquidation problem for a von NeumannMorgenstern investor with constant absolute risk aversion (CARA). As underlying market impact model, we use the continuoustime liquidity model of Almgren and Chriss (2000). We show that the expected utility of sales ..."
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Cited by 14 (1 self)
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We consider the finitetime optimal portfolio liquidation problem for a von NeumannMorgenstern investor with constant absolute risk aversion (CARA). As underlying market impact model, we use the continuoustime liquidity model of Almgren and Chriss (2000). We show that the expected utility of sales revenues, taken over a large class of adapted strategies, is maximized by a deterministic strategy, which is explicitly given in terms of an analytic formula. The proof relies on the observation that the corresponding value function solves a degenerate HamiltonJacobiBellman equation with singular initial condition. 1
Price jump prediction in limit order book. SSRN eLibrary
, 2012
"... Copyright © 2013 Ban Zheng et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. A limit order book provides information on availabl ..."
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Cited by 7 (5 self)
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Copyright © 2013 Ban Zheng et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. A limit order book provides information on available limit order prices and their volumes. Based on these quantities, we give an empirical result on the relationship between the bidask liquidity balance and trade sign and we show that the liquidity balance on the best bid/best ask is quite informative for predicting the future market order’s direction. Moreover, we define price jump as a sell (buy) market order arrival which is executed at a price which is smaller (larger) than the best bid (best ask) price at the moment just after the precedent market order arrival. Features are then extracted related to limit order volumes, limit order price gaps, market order information and limit order event information. Logistic regression is applied to predict the price jump from the features of a limit order book. LASSO logistic regression is introduced to help us make variable selection from which we are capable to highlight the importance of different features in predicting the future price jump. In order to get rid of the intraday data seasonality, the analysis is based on two separated datasets: morning dataset and afternoon dataset. Based on an analysis on forty largest French stocks of CAC40, we find that trade sign and market order size as well as the liquidity on the best bid (best ask) are consistently informative for predicting the incoming price jump.