Optimal trading with linear costs

Lataillade, Joachim de; Deremble, Cyril; Potters, Marc; Bouchaud, Jean‐Philippe

doi:10.21314/jois.2012.005

Cited by 36 publications

(61 citation statements)

References 10 publications

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“…Several researchers, including de Lataillade et al, [24], concentrated on the critical question on how linear transaction costs affect the profitability of mean-reverting trading strategies. An alternative treatment is given by [37], see also [9].…”

Section: Linear Transaction Costsmentioning

confidence: 99%

A Closed-Form Solution for Optimal Mean-Reverting Trading Strategies

Lipton

Prado

2020

SSRN Journal

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When prices reflect all available information, they oscillate around an equilibrium level. This oscillation is the result of the temporary market impact caused by waves of buyers and sellers. This price behavior can be approximated through an Ornstein-Uhlenbeck (OU) process.Market makers provide liquidity in an attempt to monetize this oscillation. They enter a long position when a security is priced below its estimated equilibrium level, and they enter a short position when a security is priced above its estimated equilibrium level. They hold that position until one of three outcomes occur: (1) they achieve the targeted profit; (2) they experience a maximum tolerated loss; (3) the position is held beyond a maximum tolerated horizon.All market makers are confronted with the problem of defining profit-taking and stop-out levels. More generally, all execution traders acting on behalf of a client must determine at what levels an order must be fulfilled. Those optimal levels can be determined by maximizing the trader's Sharpe ratio in the context of OU processes via Monte Carlo experiments, [35]. This paper develops an analytical framework and derives those optimal levels by using the method of heat potentials, [31,32].

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Section: Linear Transaction Costsmentioning

confidence: 99%

A Closed-Form Solution for Optimal Mean-Reverting Trading Strategies

Lipton

Prado

2020

SSRN Journal

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“…where θ := λρ √ N . The subtle point here is that the statistics of R t has to be self-consistently determined by the solution to all one asset problems, each of which is solvable -in principle -using the formalism of de Lataillade et al [dLDPB12]. Unfortunately, this task is still daunting in general.…”

Section: The Mean-field Limitmentioning

confidence: 99%

“…Trading in that case becomes discontinuous: when the signal is too small, it is better not to trade at all, see e.g. [DR90,SS94,MS11,dLDPB12]. More complicated cases, with both linear and quadratic costs, or more general cost functions, have been considered as well, see e.g.…”

Section: Introductionmentioning

confidence: 99%

“…Determining the shape of the no-trade region in the multi-asset case is a quite formidable problem, for which no analytic solution exists in the general case. The aim of the present paper is to extend the formalism of de Lataillade et al [dLDPB12] to treat the multi-asset problem with linear transaction costs, a maximum position constraint on each asset and a quadratic portfolio risk penalty. We propose a mean-field approach to the problem that we claim is exact in the limit of large portfolios, provided the number of common risk factors remains finite.…”

Section: Introductionmentioning

confidence: 99%

“…2 Background: single-asset optimal trading 2.1 Formulation of the problem In [dLDPB12], the authors consider the following one asset optimal trading problem: an investor must determine his/her signed position π t at time t, when he/she receives a signal p t that predicts the next price change r t = P t+1 − P t , with the following constraints:…”

Section: Introductionmentioning

confidence: 99%

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Optimal Multi-Asset Trading With Linear Costs: A Mean-Field Approach

2019

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Optimal multi-asset trading with Markovian predictors is well understood in the case of quadratic transaction costs, but remains intractable when these costs are L 1 . We present a mean-field approach that reduces the multi-asset problem to a single-asset problem, with an effective predictor that includes a risk averse component. We obtain a simple approximate solution in the case of Ornstein-Uhlenbeck predictors and maximum position constraints. The optimal strategy is of the "bang-bang" type similar to that obtained in [dLDPB12]. When the risk aversion parameter is small, we find that the trading threshold is an affine function of the instantaneous global position, with a slope coefficient that we compute exactly. We provide numerical simulations that support our analytical results.

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Equilibrium asset pricing with transaction costs

2021

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We study risk-sharing economies where heterogeneous agents trade subject to quadratic transaction costs. The corresponding equilibrium asset prices and trading strategies are characterised by a system of nonlinear, fully coupled forward–backward stochastic differential equations. We show that a unique solution exists provided that the agents’ preferences are sufficiently similar. In a benchmark specification with linear state dynamics, the empirically observed illiquidity discounts and liquidity premia correspond to a positive relationship between transaction costs and volatility.

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Optimal trading with linear costs

Cited by 36 publications

References 10 publications

A Closed-Form Solution for Optimal Mean-Reverting Trading Strategies

A Closed-Form Solution for Optimal Mean-Reverting Trading Strategies

Optimal Multi-Asset Trading With Linear Costs: A Mean-Field Approach

Equilibrium asset pricing with transaction costs

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