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41
The Illiquidity of Corporate Bonds
, 2010
"... This paper examines the illiquidity of corporate bonds and its assetpricing implications. Using transactionlevel data from 2003 through 2009, we show that the illiquidity in corporate bonds is substantial, significantly greater than what can be explained by bidask spreads. We establish a strong li ..."
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Cited by 25 (11 self)
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This paper examines the illiquidity of corporate bonds and its assetpricing implications. Using transactionlevel data from 2003 through 2009, we show that the illiquidity in corporate bonds is substantial, significantly greater than what can be explained by bidask spreads. We establish a strong link between bond illiquidity and bond prices, both in aggregate and in the crosssection. In aggregate, changes in the market level illiquidity explain a substantial part of the time variation in yield spreads of highrated (AAA through A) bonds, overshadowing the credit risk component. In the crosssection, the bondlevel illiquidity measure explains individual bond yield spreads with large economic significance.
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 11 (3 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
OPTIMAL EXECUTION IN A GENERAL ONESIDED Limitorder Book
"... We construct an optimal execution strategy for the purchase of a large number of shares of a financial asset over a fixed interval of time. Purchases of the asset have a nonlinear impact on price, and this is moderated over time by resilience in the limitorder book that determines the price. The l ..."
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Cited by 9 (0 self)
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We construct an optimal execution strategy for the purchase of a large number of shares of a financial asset over a fixed interval of time. Purchases of the asset have a nonlinear impact on price, and this is moderated over time by resilience in the limitorder book that determines the price. The limitorder book is permitted to have arbitrary shape. The form of the optimal execution strategy is to make an initial lump purchase and then purchase continuously for some period of time during which the rate of purchase is set to match the order book resiliency. At the end of this period, another lump purchase is made, and following that there is again a period of purchasing continuously at a rate set to match the order book resiliency. At the end of this second period, there is a final lump purchase. Any of the lump purchases could be of size zero. A simple condition is provided that guarantees that the intermediate lump purchase is of size zero.
Dynamic Trading with Predictable Returns and Transaction Costs
, 2009
"... This paper derives in closed form the optimal dynamic portfolio policy when trading is costly and security returns are predictable by signals with different mean reversion speeds. The optimal updated portfolio is a linear combination of the existing portfolio, the optimal current portfolio absent tr ..."
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Cited by 8 (2 self)
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This paper derives in closed form the optimal dynamic portfolio policy when trading is costly and security returns are predictable by signals with different mean reversion speeds. The optimal updated portfolio is a linear combination of the existing portfolio, the optimal current portfolio absent trading costs, and the optimal portfolio based on future expected returns. Predictors with slower mean reversion (alpha decay) get more weight since they lead to a favorable positioning both now and in the future. We implement the optimal policy for commodity futures and show that the resulting portfolio has superior returns net of trading costs relative to more naive benchmarks. Finally, we derive natural equilibrium implications, including that demand shocks with faster mean reversion command a higher return premium.
Nodynamicarbitrage and market impact
 Social Science Research Network Working Paper Series
, 2008
"... Starting from a nodynamicarbitrage principle that imposes that trading costs should be nonnegative on average and a simple model for the evolution of market prices, we demonstrate a relationship between the shape of the market impact function describing the average response of the market price to ..."
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Cited by 7 (0 self)
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Starting from a nodynamicarbitrage principle that imposes that trading costs should be nonnegative on average and a simple model for the evolution of market prices, we demonstrate a relationship between the shape of the market impact function describing the average response of the market price to traded quantity and the function that describes the decay of market impact. In particular, we show that the widelyassumed exponential decay of market impact is compatible only with linear market impact. We derive various inequalities relating the typical shape of the observed market impact function to the decay of market impact, noting that empirically, these inequalities are typically close to being equalities. 1
A HamiltonJacobiBellman approach to optimal trade execution. Working paper
"... 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 5 (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.
Strategic Execution in the Presence of an Uninformed Arbitrageur
, 2010
"... We consider a trader who aims to liquidate a large position in the presence of an arbitrageur who hopes to profit from the trader’s activity. The arbitrageur is uncertain about the trader’s position and learns from observed price fluctuations. This is a dynamic game with asymmetric information. We p ..."
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Cited by 3 (1 self)
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We consider a trader who aims to liquidate a large position in the presence of an arbitrageur who hopes to profit from the trader’s activity. The arbitrageur is uncertain about the trader’s position and learns from observed price fluctuations. This is a dynamic game with asymmetric information. We present an algorithm for computing perfect Bayesian equilibrium behavior and conduct numerical experiments. Our results demonstrate that the trader’s strategy differs significantly from one that would be optimal in the absence of the arbitrageur. In particular, the trader must balance the conflicting desires of minimizing price impact and minimizing information that is signaled through trading. Accounting for information signaling and the presence of strategic adversaries can greatly reduce execution costs.
Optimal portfolio liquidation with execution cost and risk ∗
, 2009
"... We study the optimal portfolio liquidation problem over a finite horizon in a limit order book with bidask spread and temporary market price impact penalizing speedy execution trades. We use a continuoustime modeling framework, but in contrast with previous related papers (see e.g. [24] and [25]), ..."
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Cited by 1 (0 self)
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We study the optimal portfolio liquidation problem over a finite horizon in a limit order book with bidask spread and temporary market price impact penalizing speedy execution trades. We use a continuoustime modeling framework, but in contrast with previous related papers (see e.g. [24] and [25]), we do not assume continuoustime trading strategies. We consider instead real trading that occur in discretetime, and this is formulated as an impulse control problem under a solvency constraint, including the lag variable tracking the time interval between trades. A first important result of our paper is to show that nearly optimal execution strategies in this context lead actually to a finite number of trading times, and this holds true without assuming ad hoc any fixed transaction fee. Next, we derive the dynamic programming quasivariational inequality satisfied by the value function in the sense of constrained viscosity solutions. We also introduce a family of value functions converging to our value function, and which is characterized as the unique constrained viscosity solutions of an approximation of our dynamic programming equation. This convergence result is useful for numerical purpose, postponed in a further study.