Optimal trading strategy and supply/demand dynamics

Obizhaeva, Anna A.; Wang, Jiang

doi:10.1016/j.finmar.2012.09.001

Cited by 465 publications

(84 citation statements)

References 66 publications

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“…Much of the previous work in this area assumes that agents have complete and correct knowledge of all model parameters ( [34], [15], [16], [18], [85], [64], [86], [32]). Others consider the possibility that their agents' models have the correct form; however, the agents must gradually learn the values of certain unobserved features ( [17], [31], [43], [54], [62], [48]).…”

Section: Background and Contributionsmentioning

confidence: 99%

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Mini-Flash Crashes, Model Risk, and Optimal Execution

Bayraktar

Munk

2017

SSRN Journal

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Abstract. Oft-cited causes of mini-flash crashes include human errors, endogenous feedback loops, the nature of modern liquidity provision, fundamental value shocks, and market fragmentation. We develop a mathematical model which captures aspects of the first three explanations. Empirical features of recent mini-flash crashes are present in our framework. For example, there are periods when no such events will occur. If they do, even just before their onset, market participants may not know with certainty that a disruption will unfold. Our mini-flash crashes can materialize in both low and high trading volume environments and may be accompanied by a partial synchronization in order submission.Instead of adopting a classically-inspired equilibrium approach, we borrow ideas from the optimal execution literature. Each of our agents begins with beliefs about how his own trades impact prices and how prices would move in his absence. They, along with other market participants, then submit orders which are executed at a common venue. Naturally, this leads us to explicitly distinguish between how prices actually evolve and our agents' opinions. In particular, every agent's beliefs will be expressly incorrect.As far as we know, this setup suggests both a new paradigm for modeling heterogeneous agent systems and a novel blueprint for understanding model misspecification risks in the context of optimal execution.

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Section: Background and Contributionsmentioning

confidence: 99%

“…The bid-ask spread would be infinitesimally small, while the book would be infinitely resilient and blockshaped with height 1/η j,tem . That is, agents would trade in an Obizhaeva-Wang book which instantly recovers to the reference price after each execution (no transient impact) ( [85]) .…”

Section: Execution Pricementioning

confidence: 99%

Mini-Flash Crashes, Model Risk, and Optimal Execution

Bayraktar

Munk

2017

SSRN Journal

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“…These models can be either in discrete or in continuous time and can assume either linear or nonlinear market impact for individual trades. The second generation of market impact models focusses on the transient nature of market impact [15,41,13,26]. In such models, market impact is typically assumed to factorize into two components: instantaneous market impact and a decay component.…”

Section: Introductionmentioning

confidence: 99%

Optimal execution with non-linear transient market impact

Curato

Gatheral

Lillo

2016

Quantitative Finance

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We study the problem of the optimal execution of a large trade in the presence of nonlinear transient impact. We propose an approach based on homotopy analysis, whereby a well behaved initial strategy is continuously deformed to lower the expected execution cost. We find that the optimal solution is front loaded for concave impact and that its expected cost is significantly lower than that of conventional strategies. We then consider brute force numerical optimization of the cost functional; we find that the optimal solution for a buy program typically features a few short intense buying periods separated by long periods of weak selling. Indeed, in some cases we find negative expected cost. We show that this undesirable characteristic of the nonlinear transient impact model may be mitigated either by introducing a bid-ask spread cost or by imposing convexity of the instantaneous market impact function for large trading rates.

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“…The cash process dynamics of minor agents is given by 6) with given X i,0 . It should be noted that while a linear price impact model was assumed here, as in Almgren and Chriss (2001) and Obizhaeva and Wang (2013), more general limit order book dynamics have been looked at in , Predoiu et al (2011), and Cont and De Larrard (2013).…”

Section: Trading Dynamics Of Major and Minor Agentsmentioning

confidence: 99%

Mean-Field Games and Ambiguity Aversion

Huang

2017

SSRN Journal

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This thesis focuses on incorporating the idea of ambiguity aversion into mean-field games.Intuitively, mean-field games describes the dynamics of a system with an infinite population. It is useful in approximating systems with a large population, for which an exact result is computationally intractable. By adding in ambiguity aversion, the mean-field game reflects how players in the population should act if they wish to protect themselves from model misspecification.Two applications of mean-field games are considered through two distinct approaches.The broker execution problem is investigated in a multi-agent framework containing (i) a major agent who is liquidating a large number of shares, (ii) a number of minor agents (high-frequency traders (HFTs)) who search for statistical arbitrage strategies, and (iii) noise traders who buy and sell for exogenous reasons. All optimizing agents (the broker and HFTs) trade against noise traders as well as one another. We use a mean-field game approach to solve the problem and obtain a set of decentralized feedback trading strategies for the major and minor agents. Furthermore, the mean-field game strategies have an N -Nash equilibrium property where N → 0 as N → ∞.The second application focuses on interbank borrowing and lending, which may induce systemic risk into financial markets. A simple model of this is to assume that log-monetary reserves are coupled, and that banks can also borrow/lend from/to a central bank. When all banks optimize their cost of borrowing and lending, this leads to a stochastic game. We account for model uncertainty by recasting the problem as a robust stochastic game and succeed in providing a strategy which leads to a Nash equilibria for ii both the finite game and the mean-field game limit. We prove that an -Nash equilibrium exists and show that when firms are ambiguity-averse, default probabilities can be reduced relative to their ambiguity-neutral counterparts.Finally, this thesis develops a modified stochastic maximum principle for min-max problems, and derives new existence and uniqueness results for a mean-field game with ambiguity averse players. An -Nash equilibrium is shown to exist for this class of mean-field games, and the mean-field game equations are explicitly derived in the linearquadratic framework.iii

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Optimal trading strategy and supply/demand dynamics

Cited by 465 publications

References 66 publications

Mini-Flash Crashes, Model Risk, and Optimal Execution

Mini-Flash Crashes, Model Risk, and Optimal Execution

Optimal execution with non-linear transient market impact

Mean-Field Games and Ambiguity Aversion

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