6,146 research outputs found
Optimal High Frequency Trading in a Pro-Rata Microstructure with Predictive Information
We propose a framework to study optimal trading policies in a one-tick
pro-rata limit order book, as typically arises in short-term interest rate
futures contracts. The high-frequency trader has the choice to trade via market
orders or limit orders, which are represented respectively by impulse controls
and regular controls. We model and discuss the consequences of the two main
features of this particular microstructure: first, the limit orders sent by the
high frequency trader are only partially executed, and therefore she has no
control on the executed quantity. For this purpose, cumulative executed volumes
are modelled by compound Poisson processes. Second, the high frequency trader
faces the overtrading risk, which is the risk of brutal variations in her
inventory. The consequences of this risk are investigated in the context of
optimal liquidation. The optimal trading problem is studied by stochastic
control and dynamic programming methods, which lead to a characterization of
the value function in terms of an integro quasi-variational inequality. We then
provide the associated numerical resolution procedure, and convergence of this
computational scheme is proved. Next, we examine several situations where we
can on one hand simplify the numerical procedure by reducing the number of
state variables, and on the other hand focus on specific cases of practical
interest. We examine both a market making problem and a best execution problem
in the case where the mid-price process is a martingale. We also detail a high
frequency trading strategy in the case where a (predictive) directional
information on the mid-price is available. Each of the resulting strategies are
illustrated by numerical tests
Numerical methods for an optimal order execution problem
This paper deals with numerical solutions to an impulse control problem
arising from optimal portfolio liquidation with bid-ask spread and market price
impact penalizing speedy execution trades. The corresponding dynamic
programming (DP) equation is a quasi-variational inequality (QVI) with solvency
constraint satisfied by the value function in the sense of constrained
viscosity solutions. By taking advantage of the lag variable tracking the time
interval between trades, we can provide an explicit backward numerical scheme
for the time discretization of the DPQVI. The convergence of this discrete-time
scheme is shown by viscosity solutions arguments. An optimal quantization
method is used for computing the (conditional) expectations arising in this
scheme. Numerical results are presented by examining the behaviour of optimal
liquidation strategies, and comparative performance analysis with respect to
some benchmark execution strategies. We also illustrate our optimal liquidation
algorithm on real data, and observe various interesting patterns of order
execution strategies. Finally, we provide some numerical tests of sensitivity
with respect to the bid/ask spread and market impact parameters
Optimal High Frequency Trading with limit and market orders
We propose a framework for studying optimal market making policies in a limit order book (LOB). The bid-ask spread of the LOB is modelled by a Markov chain with finite values, multiple of the tick size, and subordinated by the Poisson process of the tick-time clock. We consider a small agent who continuously submits limit buy/sell orders and submits market orders at discrete dates. The objective of the market maker is to maximize her expected utility from revenue over a short term horizon by a tradeoff between limit and market orders, while controlling her inventory position. This is formulated as a mixed regime switching regular/ impulse control problem that we characterize in terms of quasi-variational system by dynamic programming methods. In the case of a mean-variance criterion with martingale reference price or when the asset price follows a Levy process and with exponential utility criterion, the dynamic programming system can be reduced to a system of simple equations involving only the inventory and spread variables. Calibration procedures are derived for estimating the transition matrix and intensity parameters for the spread and for Cox processes modelling the execution of limit orders. Several computational tests are performed both on simulated and real data, and illustrate the impact and profit when considering execution priority in limit orders and market ordersMarket making; limit order book; inventory risk; point process; stochastic control
Underrepresented Adult Learners and the Enduring Pursuit of Workplace Readiness: Achieving Postponed Career Aspirations & Dreams Through Enhanced Self-Efficacy
Hands-on learning experiences support workplace readiness. This paper presents preliminary results of a study that examines impacts of a technology-based experiential learning activity on career aspirations of underrepresented adult learners
Promoting Learning and Upskilling for Success (PLUS): An Inclusive Excellence Framework to Facilitate Workplace Readiness of Underrepresented Adult Learners (UALs)
We propose Promoting Learning and Upskilling for Success, an inclusive excellence framework developed to help underrepresented adult learners gain the knowledge and competence needed for the modern workplace
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