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In order to reduce signalling, traders may resort to limiting access to dark venues and imposing limits on minimum fill sizes they are willing to trade. However, doing this also restricts the liquidity available to the trader since an ever increasing quantity of orders are traded by algos in clips. An alternative is to attempt to monitor signalling in real time and dynamically make adjustments to the dark liquidity a…
We study the optimal liquidation problem in both lit and dark pools for investors facing execution uncertainty in a continuous-time setting with market impact. First, we design an optimal make--take fee policy for a large investor liquidating her position across both pools, interacting with small investors who pay trading fees. We explicitly characterize the large investor's optimal liquidation strategies in both lit…
Emphasizing the statistics of jumps crossing the strike and local time, we develop a decomposition of equity option risk premiums. Operationalizing this theoretical treatment, we equip the pricing kernel process with unspanned risks, embed (unspanned) jump risks, and allow equity return volatility to contain unspanned risks. Unspanned risks are consistent with negative risk premiums for jumps crossing the strike and …
We consider the issue of a market maker acting at the same time in the lit and dark pools of an exchange. The exchange wishes to establish a suitable make-take fees policy to attract transactions on its venues. We first solve the stochastic control problem of the market maker without the intervention of the exchange. Then we derive the equations defining the optimal contract to be set between the market maker and the…
Hawkes processes are a class of simple point processes that are self-exciting and have clustering effect, with wide applications in finance, social networks and many other fields. This paper considers a self-exciting Hawkes process where the baseline intensity is time-dependent, the exciting function is a general function and the jump sizes of the intensity process are independent and identically distributed non-nega…
This paper investigates the impact of dark pools on price discovery (the efficiency of prices on stock exchanges to aggregate information). Assets are traded in either an exchange or a dark pool, with the dark pool offering better prices but lower execution rates. Informed traders receive noisy and heterogeneous signals about an asset's fundamental. We find that informed traders use dark pools to mitigate their infor…
We consider a finite-horizon market-making problem faced by a dark pool that executes incoming buy and sell orders. The arrival flow of such orders is assumed to be random and, for each transaction, the dark pool earns a per-share commission no greater than the half bid-ask spread. Throughout the entire period, the main concern is inventory risk, which increases as the number of held positions becomes critically smal…
We consider an optimal trading problem over a finite period of time during which an investor has access to both a standard exchange and a dark pool. We take the exchange to be an order-driven market and propose a continuous-time setup for the best bid price and the market spread, both modelled by Lévy processes. Effects on the best bid price arising from the arrival of limit buy orders at more favourable prices, the …
We consider an illiquid financial market where a risk averse investor has to liquidate a portfolio within a finite time horizon [0,T] and can trade continuously at a traditional exchange (the "primary venue") and in a dark pool. At the primary venue, trading yields a linear price impact. In the dark pool, no price impact costs arise but order execution is uncertain, modeled by a multi-dimensional Poisson process. We …
For a market impact model, price manipulation and related notions play a role that is similar to the role of arbitrage in a derivatives pricing model. Here, we give a systematic investigation into such regularity issues when orders can be executed both at a traditional exchange and in a dark pool. To this end, we focus on a class of dark-pool models whose market impact at the exchange is described by an Almgren--Chri…
Agent-based models of markets readily produce emergent instabilities, but telling a genuine collective effect apart from a parameter artefact takes discipline. We apply Bouchaud's phase-diagram method to a continuous-double-auction order-book model. The method is to map the full phase diagram, test its robustness to rule changes, and rule out degenerate and numerical origins before we call any feature a tipping point…
Modern Algorithmic Trading ("Algo") allows institutional investors and traders to liquidate or establish big security positions in a fully automated or low-touch manner. Most existing academic or industrial Algos focus on how to "slice" a big parent order into smaller child orders over a given time horizon. Few models rigorously tackle the actual placement of these child orders. Instead, placement is mostly done with…
In this work we propose a framework to construct Market-Implied Sustainability (MIS) scores for individual firms by exploiting fund-level sustainability classifications and granular portfolio holdings. The central idea is that the relative over/under-representation of a stock in sustainability-oriented funds reveals a market-based assessment of its sustainability profile. We implement the methodology in the European …
We develop a dynamic trading strategy in the Linear Quadratic Regulator (LQR) framework. By including a price mean-reversion signal into the optimization program, in a trading environment where market impact is linear and stage costs are quadratic, we obtain an optimal trading curve that reacts opportunistically to price changes while retaining its ability to satisfy smooth or hard completion constraints. The optimal…
We solved a stylized fact on a long memory process of volatility cluster phenomena by using Minkowski metric for GARCH(1,1) under assumption that price and time can not be separated. We provide a Yang-Mills equation in financial market and anomaly on superspace of time series data as a consequence of the proof from the general relativity theory. We used an original idea in Minkowski spacetime embedded in Kolmogorov s…
We use a principal-agent model to analyze the structure of a book-driven dealer market when the dealer faces competition from a crossing network or dark pool. The agents are privately informed about their types (e.g. their portfolios), which is something that the dealer must take into account when engaging his counterparties. Instead of trading with the dealer, the agents may chose to trade in a crossing network. We …
We propose a design for schedule-based execution trading strategies based on uncertainty bands. This formulation: 1) simplifies strategy specification and implementation; 2) provides for flexible allocation among passive, opportunistic, aggressive, and dark pool crossing execution tactics; 3) allows for rapid enhancements as new optimization methods, scheduling techniques, alpha models, and execution tactics are deve…
We consider the stochastic control problem of a financial trader that needs to unwind a large asset portfolio within a short period of time. The trader can simultaneously submit active orders to a primary market and passive orders to a dark pool. Our framework is flexible enough to allow for price-dependent impact functions describing the trading costs in the primary market and price-dependent adverse selection costs…
Dark Pool Volume — Off-exchange trading share influencing price discovery and lit-market toxicity.
Dark Pool Routing (Quant).
Dark Spread (Commodities).
Dark Pool Crossing — Non-displayed liquidity venues reducing information leakage.
Dark Pool Fill US equities — Execution quality, book dynamics, or venue microstructure concept.
Dark Pool Fill EU equities — Execution quality, book dynamics, or venue microstructure concept.
Dark Pool Fill futures — Execution quality, book dynamics, or venue microstructure concept.
Dark Pool Fill ETF — Execution quality, book dynamics, or venue microstructure concept.
Dark Pool Fill options — Execution quality, book dynamics, or venue microstructure concept.
Dark Pool Fill FX spot — Execution quality, book dynamics, or venue microstructure concept.
Dark Pool Fill Treasury — Execution quality, book dynamics, or venue microstructure concept.
Dark Pool Fill IG credit — Execution quality, book dynamics, or venue microstructure concept.
Dark Pool Fill HY credit — Execution quality, book dynamics, or venue microstructure concept.
Dark Pool Fill crypto — Execution quality, book dynamics, or venue microstructure concept.
Dark Pool Fill risk-on Regime (Microstructure).
Dark Pool Fill risk-off Regime (Microstructure).
Dark Pool Fill tightening Regime (Microstructure).
Dark Pool Fill easing Regime (Microstructure).
Dark Pool Fill stagflation Regime (Microstructure).
Dark Pool Fill reflation Regime (Microstructure).
Dark Pool Fill disinflation Regime (Microstructure).
Dark Pool Fill liquidity-crisis Regime (Microstructure).
Dark Pool Fill carry Regime (Microstructure).
Dark Pool Fill recession Regime (Microstructure).
Dark Pool Crossing — Non-displayed liquidity venues reducing information leakage.
Dark Pool Fill carry Regime (Microstructure).
Dark Pool Fill crypto — Execution quality, book dynamics, or venue microstructure concept.
Dark Pool Fill disinflation Regime (Microstructure).
Dark Pool Fill easing Regime (Microstructure).
Dark Pool Fill ETF — Execution quality, book dynamics, or venue microstructure concept.
Dark Pool Fill EU equities — Execution quality, book dynamics, or venue microstructure concept.
Dark Pool Fill futures — Execution quality, book dynamics, or venue microstructure concept.
Dark Pool Fill FX spot — Execution quality, book dynamics, or venue microstructure concept.
Dark Pool Fill HY credit — Execution quality, book dynamics, or venue microstructure concept.
Dark Pool Fill IG credit — Execution quality, book dynamics, or venue microstructure concept.
Dark Pool Fill liquidity-crisis Regime (Microstructure).
Dark Pool Fill options — Execution quality, book dynamics, or venue microstructure concept.
Dark Pool Fill recession Regime (Microstructure).
Dark Pool Fill reflation Regime (Microstructure).
Dark Pool Fill risk-off Regime (Microstructure).
Dark Pool Fill risk-on Regime (Microstructure).
Dark Pool Fill stagflation Regime (Microstructure).
Dark Pool Fill tightening Regime (Microstructure).
Dark Pool Fill Treasury — Execution quality, book dynamics, or venue microstructure concept.
Dark Pool Fill US equities — Execution quality, book dynamics, or venue microstructure concept.
Dark Pool Routing (Quant).
Dark Pool Volume — Off-exchange trading share influencing price discovery and lit-market toxicity.
Dark Spread (Commodities).