8,507 research outputs found
Liquidation In Limit Order Books With Controlled Intensity
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/108603/1/mafi529.pd
A convex duality method for optimal liquidation with participation constraints
In spite of the growing consideration for optimal execution in the financial
mathematics literature, numerical approximations of optimal trading curves are
almost never discussed. In this article, we present a numerical method to
approximate the optimal strategy of a trader willing to unwind a large
portfolio. The method we propose is very general as it can be applied to
multi-asset portfolios with any form of execution costs, including a bid-ask
spread component, even when participation constraints are imposed. Our method,
based on convex duality, only requires Hamiltonian functions to have
regularity while classical methods require additional regularity and cannot be
applied to all cases found in practice
Empirical Limitations on High Frequency Trading Profitability
Addressing the ongoing examination of high-frequency trading practices in
financial markets, we report the results of an extensive empirical study
estimating the maximum possible profitability of the most aggressive such
practices, and arrive at figures that are surprisingly modest. By "aggressive"
we mean any trading strategy exclusively employing market orders and relatively
short holding periods. Our findings highlight the tension between execution
costs and trading horizon confronted by high-frequency traders, and provide a
controlled and large-scale empirical perspective on the high-frequency debate
that has heretofore been absent. Our study employs a number of novel empirical
methods, including the simulation of an "omniscient" high-frequency trader who
can see the future and act accordingly
Algorithmic trading in a microstructural limit order book model
We propose a microstructural modeling framework for studying optimal market
making policies in a FIFO (first in first out) limit order book (LOB). In this
context, the limit orders, market orders, and cancel orders arrivals in the LOB
are modeled as Cox point processes with intensities that only depend on the
state of the LOB. These are high-dimensional models which are realistic from a
micro-structure point of view and have been recently developed in the
literature. In this context, we consider a market maker who stands ready to buy
and sell stock on a regular and continuous basis at a publicly quoted price,
and identifies the strategies that maximize her P\&L penalized by her
inventory. We apply the theory of Markov Decision Processes and dynamic
programming method to characterize analytically the solutions to our optimal
market making problem. The second part of the paper deals with the numerical
aspect of the high-dimensional trading problem. We use a control randomization
method combined with quantization method to compute the optimal strategies.
Several computational tests are performed on simulated data to illustrate the
efficiency of the computed optimal strategy. In particular, we simulated an
order book with constant/ symmet-ric/ asymmetrical/ state dependent
intensities, and compared the computed optimal strategy with naive strategies.
Some codes are available on https://github.com/comeh
Drift dependence of optimal trade execution strategies under transient price impact
We give a complete solution to the problem of minimizing the expected
liquidity costs in presence of a general drift when the underlying market
impact model has linear transient price impact with exponential resilience. It
turns out that this problem is well-posed only if the drift is absolutely
continuous. Optimal strategies often do not exist, and when they do, they
depend strongly on the derivative of the drift. Our approach uses elements from
singular stochastic control, even though the problem is essentially
non-Markovian due to the transience of price impact and the lack in Markovian
structure of the underlying price process. As a corollary, we give a complete
solution to the minimization of a certain cost-risk criterion in our setting
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
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