Market making and portfolio liquidation under uncertainty

Research output: Contribution to journalArticle

Standard

Market making and portfolio liquidation under uncertainty. / Aly, Sidi Mohamed; Nyström, Kaj; Zhang, Changyong.

In: International Journal of Theoretical and Applied Finance, Vol. 17, No. 5, 140034, 29.07.2014.

Research output: Contribution to journalArticle

Harvard

APA

CBE

MLA

Vancouver

Author

Aly, Sidi Mohamed ; Nyström, Kaj ; Zhang, Changyong. / Market making and portfolio liquidation under uncertainty. In: International Journal of Theoretical and Applied Finance. 2014 ; Vol. 17, No. 5.

RIS

TY - JOUR

T1 - Market making and portfolio liquidation under uncertainty

AU - Aly, Sidi Mohamed

AU - Nyström, Kaj

AU - Zhang, Changyong

PY - 2014/7/29

Y1 - 2014/7/29

N2 - Market making and optimal portfolio liquidation in the context of electronic limit order books are of considerably practical importance for high frequency (HF) market makers as well as more traditional brokerage firms supplying optimal execution services for clients. In general, the two problems are based on probabilistic models defined on certain reference probability spaces. However, due to uncertainty in model parameters or in periods of extreme market turmoil, ambiguity concerning the correct underlying probability measure may appear and an assessment of model risk, as well as the uncertainty on the choice of the model itself, becomes important, as for a market maker or a trader attempting to liquidate large positions, the uncertainty may result in unexpected consequences due to severe mispricing. This paper focuses on the market making and the optimal liquidation problems using limit orders, accounting for model risk or uncertainty. Both are formulated as stochastic optimal control problems, with the controls being the spreads, relative to a reference price, at which orders are placed. The models consider uncertainty in both the drift and volatility of the underlying reference price, for the study of the effect of the uncertainty on the behavior of the market maker, accounting also for inventory restriction, as well as on the optimal liquidation using limit orders.

AB - Market making and optimal portfolio liquidation in the context of electronic limit order books are of considerably practical importance for high frequency (HF) market makers as well as more traditional brokerage firms supplying optimal execution services for clients. In general, the two problems are based on probabilistic models defined on certain reference probability spaces. However, due to uncertainty in model parameters or in periods of extreme market turmoil, ambiguity concerning the correct underlying probability measure may appear and an assessment of model risk, as well as the uncertainty on the choice of the model itself, becomes important, as for a market maker or a trader attempting to liquidate large positions, the uncertainty may result in unexpected consequences due to severe mispricing. This paper focuses on the market making and the optimal liquidation problems using limit orders, accounting for model risk or uncertainty. Both are formulated as stochastic optimal control problems, with the controls being the spreads, relative to a reference price, at which orders are placed. The models consider uncertainty in both the drift and volatility of the underlying reference price, for the study of the effect of the uncertainty on the behavior of the market maker, accounting also for inventory restriction, as well as on the optimal liquidation using limit orders.

KW - high frequency trading

KW - market making

KW - optimal execution

KW - stochastic control

KW - Hamilton-Jacobi-Bellman equation

U2 - 10.1142/S021902491450034

DO - 10.1142/S021902491450034

M3 - Article

VL - 17

JO - International Journal of Theoretical and Applied Finance

T2 - International Journal of Theoretical and Applied Finance

JF - International Journal of Theoretical and Applied Finance

SN - 0219-0249

IS - 5

M1 - 140034

ER -