15,200 research outputs found
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
Risk aversion and the dynamics of optimal liquidation strategies in illiquid markets
We consider the infinite-horizon optimal portfolio liquidation problem for a von Neumann-Morgenstern investor in the liquidity model of Almgren (2003). Using a stochastic control approach, we characterize the value function and the optimal strategy as classical solutions of nonlinear parabolic partial differential equations. We furthermore analyze the sensitivities of the value function and the optimal strategy with respect to the various model parameters. In particular, we find that the optimal strategy is aggressive or passive in-the-money, respectively, if and only if the utility function displays increasing or decreasing risk aversion. Surprisingly, only few further monotonicity relations exist with respect to the other parameters. We point out in particular that the speed by which the remaining asset position is sold can be decreasing in the size of the position but increasing in the liquidity price impact.Liquidity, illiquid markets, optimal liquidation strategies, dynamic trading strategies, algorithmic trading, utility maximization
VaR and Liquidity Risk.Impact on Market Behaviour and Measurement Issues.
Current trends in international banking supervision following the 1996 Amendment to the Basel Accord emphasise market risk control based upon internal Value-at-risk (VaR) models. This paper discusses the merits and drawbacks of VaR models in the light of their impact on market liquidity. After a preliminary review of basic concepts and measures regarding market risk, market friction and liquidity risk, the arguments supporting the internal models approach to supervision on market risk are discussed, in the light of the debate on the limitations and possible enhancements of VaR models. In particular, adverse systemic effects of widespread risk management practices are considered. Risk measurement models dealing with liquidity risk are then examined in detail, in order to verify their potential for application in the field. We conclude that VaR models are still far from effectively treating market and liquidity risk in their multi-faceted aspects. Regulatory guidelines are right in recognising the importance of internal risk control systems. Implementation of those guidelines might inadvertently encourage mechanic application of VaR models, with adverse systemic effects.
Liquidation in the Face of Adversity: Stealth Vs. Sunshine Trading, Predatory Trading Vs. Liquidity Provision
We consider a multi-player situation in an illiquid market in which one player tries to liquidate a large portfolio in a short time span, while some competitors know of the seller's intention and try to make a pro¯t by trading in this market over a longer time horizon. We show that the liquidity characteristics, the number of competitors in the market and their trading time horizons determine the optimal strategy for the competitors: they either provide liquidity to the seller, or they prey on her by simultaneous selling. Depending on the expected competitor behavior, it might be sensible for the seller to pre-announce a trading intention (\sunshine trading") or to keep it secret (\stealth trading").Liquidity; liquidity crisis; liquidity provision; optimal liquidation strategies; predatory trading; sunshine trading; stealth trading
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