Smart TWAP Trading in Continuous-Time Equilibria

Choi, Jin Hyuk; Larsen, Kasper; Seppi, Duane J.

doi:10.2139/ssrn.3146658

Cited by 9 publications

(12 citation statements)

References 62 publications

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“…To this end, we assume that the (representative) clients also act as price takers and trade to track an exogenous target position. For constant trading targets as in [12], this is similar to the optimal liquidation problems studied in [5,1,29] and many more recent papers. Diffusive trading targets correspond to the "high-frequency trading needs" considered in [24,31].…”

Section: Introductionsupporting

confidence: 61%

“…To wit, we consider representative dealers, who intermediate between the demands of their clients and a group of end-users. 1 The clients trade to track an exogenous, stochastically evolving target position as in [24,31,12] and are therefore willing to pay a premium for the immediacy the dealers provide. The end-users have no intrinsic trading needs, but are willing to trade the asset under consideration at its exogenous "fundamental value".…”

Section: Introductionmentioning

confidence: 99%

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Liquidity in Competitive Dealer Markets

Bank¹,

Ekren

Muhle‐Karbe

2018

SSRN Journal

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We study a continuous-time version of the intermediation model of Grossman and Miller [18]. To wit, we solve for the competitive equilibrium prices at which liquidity takers' demands are absorbed by dealers with quadratic inventory costs, who can in turn gradually transfer these positions to an end-user market. This endogenously leads to a model with transient price impact.Smooth, diffusive, and discrete trades all incur finite but nontrivial liquidity costs, and can arise naturally from the liquidity takers' optimization.Mathematics Subject Classification: (2010) 91B26, 91B24, 91B51.JEL Classification: C68, D43, G12.

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Section: Introductionsupporting

confidence: 61%

Section: Introductionmentioning

confidence: 99%

Liquidity in Competitive Dealer Markets

Bank¹,

Ekren

Muhle‐Karbe

2018

SSRN Journal

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“…Accordingly, for σ > 0, the process −β n /σ can also be interpreted as agent n's target position in the risky asset. Related models where deviations from an exogenous target are directly penalised by an exogenous deterministic weight rather than the infinitesimal variance of the corresponding asset are studied by [14,46].…”

Section: Frictionless Tradingmentioning

confidence: 99%

Equilibrium Asset Pricing with Transaction Costs

2019

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We study risk-sharing economies where heterogenous 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 generally exists provided that the agents' preferences are sufficiently similar. In a benchmark specification with linear state dynamics, the illiquidity discounts and liquidity premia observed empirically correspond to a positive relationship between transaction costs and volatility.Mathematics Subject Classification: (2010) 91G10, 91G80, 60H10.JEL Classification: C68, D52, G11, G12.between the effects of transaction costs on asset prices, expected returns, and volatilities. To wit, the "liquidity discount" of asset prices compared to their frictionless counterparts, the "liquidity premia" that distinguish their expected returns, and the adjustment of the corresponding volatilities all have the same sign in our model, determined by the difference of the agents' risk aversion parameters. In the empirically relevant case of positive illiquidity discounts and liquidity premia [3,9,44], our model predicts a positive relation between transaction costs and volatility, corroborating empirical evidence of [49,30,27], numerical results of [1,12], and findings in a risk-neutral model with asymmetric information [15]. In addition to these systematic shifts, transaction costs also endogenously lead to mean-reverting expected returns as in the reduced-form models of [33,16,40,23]: for illiquid assets, supply-demand imbalances do not offset immediately but only gradually, thereby leading to partially predictable returns.Without transaction costs, the equilibrium dynamics of the risky asset are determined by a scalar purely quadratic BSDE in our model, which leads to explicit formulas in concrete examples. With quadratic transaction costs on the agents' trading rates, we show that the corresponding equilibria are characterised by fully-coupled systems of FBSDEs. To wit, the optimal risky positions evolve forward from the given initial allocations. In contrast, the corresponding trading rates controlling these positions need to be determined from their zero terminal values -near the terminal time, trading stops since additional trades can no longer earn back the costs that would need to be paid to implement them. If a constant volatility is given exogenously as in [8], then these forward-backward dynamics suffice to pin down the equilibrium returns. In this case, the FBSDEs are linear, and therefore can be solved explicitly in terms of Riccati equations and conditional expectations of the endowment processes [24,6]. In the present context, where the volatility is determined endogenously from the terminal condition for the risky asset, the corresponding FBSDEs are coupled to an additional backward equation arising from this extra constraint. Due to the quadratic preferences and trading costs, the resulting forward-backward ...

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“…To this end, definẽ . 9 As shown in Lemma A.6,gq is in fact the solution to the first-order equation (17) in [27,Theorem 6], with q = α + 1. 10 Notice that for quadratic costs q = 2, this is the standard normal distribution.…”

Section: B Calibration Detailsmentioning

confidence: 99%

“…Indeed, if G(x) = λ|x| q /q, q ∈ (1, 2], set δ 2 = γσ 2 , 2 q−1 q = δ 2q−2 λ as well as q = α + 1 in (3.5). Then, differentiating the first-order ODE(17) in[27, Theorem 6] leads to the second-order ODE (3.5). The same link to a first-order equation is exploited in our existence proof in Appendix A.…”

mentioning

confidence: 99%

Asset Pricing with General Transaction Costs: Theory and Numerics

2019

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We study risk-sharing equilibria with general convex costs on the agents' trading rates. For an infinite-horizon model with linear state dynamics and exogenous volatilities, the equilibrium returns mean-revert around their frictionless counterparts -the deviation has Ornstein-Uhlenbeck dynamics for quadratic costs whereas it follows a doubly-reflected Brownian motion if costs are proportional. More general models with arbitrary state dynamics and endogenous volatilities lead to multidimensional systems of nonlinear, fully-coupled forward-backward SDEs. These fall outside the scope of known wellposedness results, but can be solved numerically using the simulation-based deep-learning approach of [28]. In a calibration to time series of returns, bidask spreads, and trading volume, transaction costs substantially affect equilibrium asset prices. In contrast, the effects of different cost specifications are rather similar, justifying the use of quadratic costs as a proxy for other less tractable specifications.Mathematics Subject Classification: (2010) 91G10, 91G80, 60H10.JEL Classification: C68, D52, G11, G12.

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Smart TWAP Trading in Continuous-Time Equilibria

Cited by 9 publications

References 62 publications

Liquidity in Competitive Dealer Markets

Liquidity in Competitive Dealer Markets

Equilibrium Asset Pricing with Transaction Costs

Asset Pricing with General Transaction Costs: Theory and Numerics

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