Constrained portfolio liquidation in a limit order book model

Constrained portfolio liquidation in a limit order book model by aurelien alfonsi, antje fruth and alexander schied topics. In this paper we propose a dynamic model of limit order book lob. Research of the first two authors was supported by deutsche forschungsgemeinschaft through the research center matheon mathematics for key technologies. A stochastic model for order book dynamics operations. Liquidity risk, optimal portfolio liquidation, limit order book with resilience, call auction, market impact model, constrained trading strategies, market order. Constrained portfolio liquidation in a limit order book model autorzy. Problem p1 general portfolio optimization problem objective function. Optimal placement in a limit order book uc berkeley ieor.

Optimal execution in a limit order book and an associated microstructure market impact model. Order book resilience, price manipulation, and the positive. Constrained portfolio liquidation in a limit order book model aurelien alfonsi, antje fruth, alexander schied a stochastic overlapping generation model with a continuum of agents emmanuelle augeraudveron, delphine david numerical solution of blackscholes option pricing with variable yield discrete dividend payment rafael company. Order book resilience, price manipulation, and the positive portfolio problem a alfonsi, a schied, a slynko siam journal on financial mathematics 3 1, 511533, 2012. In our model, the limit order book consists of a certain distribution of limit ask orders at prices. We use a continuoustime modeling framework, but in contrast with previous related papers see, e. Moallemi hua zheng may, 2015 abstract we model an electronic limit order book as a multiclass queueing system under. We propose a continuoustime stochastic model for the dynamics of a limit order book. Market impact models and optimal trade execution 9th winter school on mathematical finance, lunteren 2010 references a. In this article we consider a limit order book model that allows for timedependent, deterministic depth and resilience of the book and determine optimal portfolio liquidation strategies.

An investment style that does not require a fund or portfolio manager to adhere to a specific benchmark. We extend their model by allowing for a timedependent. Schied, constrained portfolio liquidation in a limit order book model, banach. The reference price and the spreads are then combined to the offers limit orders i place. We set up a stochastic control problem in which the goal is to maximize the expected revenue from liquidating the entire position held. S optimal execution strategies in limit order books with general shape functions. S optimal execution and absence of price manipulations in limit order book models. Order book resilience, price manipulation, and the. The impact of constraints on minimum variance portfolios. Optimal portfolio liquidation for cara investors munich. Optimal execution strategies in limit order books with general shape functions.

Then the bid and ask spread is calculated based on the volatity, drift, trade frequency and the inventory. Arbitrage and deflators in illiquid markets springerlink. This paper addresses portfolio liquidation using a new angle. A dynamic model of the limit order book by ioanid rosu. Alexander 2008 constrained portfolio liquidation in a limit order book model. Order book resilience, price manipulations, and the. This allows us to study the problem of minimizing the expected liquidation costs of an asset. Order book resilience, price manipulations, and the positive. After having introduced the limit order book model, we specify the traders objectives in section 2. 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. Optimal execution in a limit order book and an associated.

The main feature of our model is that the shape of the lob is determined endogenously by an expected utility function via a competitive equilibrium argument. Assuming zero resilience, the resulting equilibrium density of the lob is random, nonlinear, and time inhomogeneous. Adaptive basket liquidation, finance and stochastics 10. These orders are treated equally with other orders in terms of priority of execution. We use a continuoustime modeling framework, but in contrast with previous related papers see e. Constrained portfolio liquidation in a limit order book model with and banach center publications 83, 925, 2008. We consider a framework for solving optimal liquidation problems in limit order books. Liquidity risk, optimal portfolio liquidation, limit order book with resilience, call auction, market impact model, constrained trading. Therefore i need to model the reference price of the limit order book in the first step. This allows us to study the problem of minimizing the expected liquidation costs of an asset position under. Optimal portfolio liquidation with execution cost and risk. Banach center publications warszawa 83 925 zeitschriftenartikel. In addition to classical frictionless markets and markets with transaction costs or bidask spreads, our framework covers markets with.

Optimal basket liquidation for cara investors is deterministic. In addition to classical frictionless markets and markets with transaction costs or bidask spreads, our. Modelling approaches for optimal liquidation under a limit. Only perfectly negatively correlated assets portfolio margin constrained. In such a model, gatheral 12 shows that exponential decay of market. A dynamic model of the limit order book researchgate. Constrained portfolio liquidation in a limit order book model. Modelling approaches for optimal liquidation under a limitorder book structure. Download citation constrained portfolio liquidation in a limit order book model we consider the problem of optimally placing market orders so as to minimize the expected liquidity costs from. Order book resilience, price manipulations, and the positive portfolio. The main characteristic of this model is that it does not explicitly consider the limit order book but statistically models liquidity. The larger the number of shares he sells at this instant in time, the higher is the liquidity cost since his market order will be executed against the most favorable limit order prices in the book in a decreasing order.

This paper presents a stochastic model for discretetime trading in financial markets where trading costs are given by convex cost functions and portfolios are constrained by convex sets. Optimal trade execution and absence of price manipulations in limit. Optimal trade execution and price manipulation in order. Optimal liquidation in a leveli limit order book for large tick stocks. 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. Optimal execution cost for liquidation through a limit. Liquidity models in continuous and discrete time springerlink. Optimal execution strategies in limit order books uzh. Likewise, the constraints shifted the minimumvariance portfolios regional distributions closer to the benchmarks. Limit order information system the electronic system supplying information about securities traded on participating exchanges so that the best securities prices can be found. Due to the extreme time constraint in which a decision about market vs. The model strikes a balance between three desirable features. S constrained portfolio liquidation in a limit order book model. Limit order book models and optimal trading strategies.

A market impact model admits price manipulation if there is a round trip with negative expected liquidation costs. 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. The model in which we limit the number of different assets held will be referred as cardinality constrained portfolio optimization problem problem p2. We study the optimal portfolio liquidation problem over a nite horizon in a limit order book with bidask spread and temporary market price impact penalizing speedy execution trades. Keywords limit order book, high frequency trading, optimal placement, correlated random walk, diffusion. Unconstrained investing allows managers to pursue returns across. Liquidity risk, optimal portfolio liquidation, block trade execution, limit order book, market impact model, nonlinear price impact, order book resilience, market order 9. Limit order book a record of unexecuted limit orders maintained by the specialist. Instead of focusing only on the scheduling aspect like almgren and chriss in j. Dynamic equilibrium limit order book model and optimal. Preprint, forthcoming in banach center publications, tu berlin 2007. The above described minimizing problem is easily solvable by the nonlinear quadratic programming methods. Constrained portfolio liquidation in a limit order book model, preprint, qp lab and tu berlin.

Optimal execution cost for liquidation through a limit order. Schied, constrained portfolio liquidation in a limit order book model. Alfonsi cermics, projet mathfi ecole nationale des ponts et chauss. Our model is a generalization of obizhaeva, wang 2005. Our paper, along with 7, is an attempt to use this model to tackle the completely di. Alexander schied school of orie, cornell university. In particular, order arrivals are modeled as a point process whose intensity depends on the liquidation price. This cited by count includes citations to the following articles in scholar. Optimal trade execution and price manipulation in order books. Optimal portfolio liquidation with limit orders siam.

The model does not assume the existence of a cash accountnumeraire. Kharroubi university paris 7 and crest istanbul workshop on mathematical finance may 19, 2009 huyen pham optimal portfolio liquidation. Constrained portfolio liquidation in a limit order book model alfonsi a. In this model, the absence of price manipulation in the sense of huberman and stanzl can easily be characterized by means of bochners theorem. Constrained portfolio liquidation in a limit order book. Optimal execution with nonlinear impact functions and trading enhanced risk. Optimal slippage for liquidation through a limit order market 4 transaction and the best ask price. Schied, alexander 2008 constrained portfolio liquidation in a limit order book model.