2,886 research outputs found
Optimal execution strategy with an uncertain volume target
In the seminal paper on optimal execution of portfolio transactions, Almgren
and Chriss (2001) define the optimal trading strategy to liquidate a fixed
volume of a single security under price uncertainty. Yet there exist
situations, such as in the power market, in which the volume to be traded can
only be estimated and becomes more accurate when approaching a specified
delivery time. During the course of execution, a trader should then constantly
adapt their trading strategy to meet their fluctuating volume target. In this
paper, we develop a model that accounts for volume uncertainty and we show that
a risk-averse trader has benefit in delaying their trades. More precisely, we
argue that the optimal strategy is a trade-off between early and late trades in
order to balance risk associated with both price and volume. By incorporating a
risk term related to the volume to trade, the static optimal strategies
suggested by our model avoid the explosion in the algorithmic complexity
usually associated with dynamic programming solutions, all the while yielding
competitive performance
Optimal Execution with Dynamic Order Flow Imbalance
We examine optimal execution models that take into account both market
microstructure impact and informational costs. Informational footprint is
related to order flow and is represented by the trader's influence on the flow
imbalance process, while microstructure influence is captured by instantaneous
price impact. We propose a continuous-time stochastic control problem that
balances between these two costs. Incorporating order flow imbalance leads to
the consideration of the current market state and specifically whether one's
orders lean with or against the prevailing order flow, key components often
ignored by execution models in the literature. In particular, to react to
changing order flow, we endogenize the trading horizon . After developing
the general indefinite-horizon formulation, we investigate several tractable
approximations that sequentially optimize over price impact and over . These
approximations, especially a dynamic version based on receding horizon control,
are shown to be very accurate and connect to the prevailing Almgren-Chriss
framework. We also discuss features of empirical order flow and links between
our model and "Optimal Execution Horizon" by Easley et al (Mathematical
Finance, 2013).Comment: 31 pages, 8 figure
An Optimal Execution Problem with S-shaped Market Impact Functions
In this study, we extend the optimal execution problem with convex market
impact function studied in Kato (2014) to the case where the market impact
function is S-shaped, that is, concave on and convex on
for some . We study the
corresponding Hamilton-Jacobi-Bellman equation and show that the optimal
execution speed under the S-shaped market impact is equal to zero or larger
than . Moreover, we provide some examples of the Black-Scholes
model. We show that the optimal strategy for a risk-neutral trader with small
shares is the time-weighted average price strategy whenever the market impact
function is S-shaped.Comment: 22 pages, 2 figures, forthcoming in "Communications on Stochastic
Analysis
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
Statistically validated network of portfolio overlaps and systemic risk
Common asset holding by financial institutions, namely portfolio overlap, is
nowadays regarded as an important channel for financial contagion with the
potential to trigger fire sales and thus severe losses at the systemic level.
In this paper we propose a method to assess the statistical significance of the
overlap between pairs of heterogeneously diversified portfolios, which then
allows us to build a validated network of financial institutions where links
indicate potential contagion channels due to realized portfolio overlaps. The
method is implemented on a historical database of institutional holdings
ranging from 1999 to the end of 2013, but can be in general applied to any
bipartite network where the presence of similar sets of neighbors is of
interest. We find that the proportion of validated network links (i.e., of
statistically significant overlaps) increased steadily before the 2007-2008
global financial crisis and reached a maximum when the crisis occurred. We
argue that the nature of this measure implies that systemic risk from fire
sales liquidation was maximal at that time. After a sharp drop in 2008,
systemic risk resumed its growth in 2009, with a notable acceleration in 2013,
reaching levels not seen since 2007. We finally show that market trends tend to
be amplified in the portfolios identified by the algorithm, such that it is
possible to have an informative signal about financial institutions that are
about to suffer (enjoy) the most significant losses (gains)
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