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Market making and portfolio liquidation under uncertainty

Aly, Sidi Mohamed LU ; Nyström, Kaj and Zhang, Changyong (2014) In International Journal of Theoretical and Applied Finance 17(5).
Abstract
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... (More)
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. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
high frequency trading, market making, optimal execution, stochastic control, Hamilton-Jacobi-Bellman equation
in
International Journal of Theoretical and Applied Finance
volume
17
issue
5
pages
33 pages
publisher
World Scientific
external identifiers
  • scopus:84905251832
ISSN
1793-6322
DOI
10.1142/S021902491450034
language
English
LU publication?
yes
id
b7aac065-435d-4746-8027-10deafefc7aa
date added to LUP
2016-04-13 13:41:39
date last changed
2017-08-27 06:15:21
@article{b7aac065-435d-4746-8027-10deafefc7aa,
  abstract     = {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.},
  articleno    = {140034},
  author       = {Aly, Sidi Mohamed and Nyström, Kaj and Zhang, Changyong},
  issn         = {1793-6322},
  keyword      = {high frequency trading,market making,optimal execution,stochastic control,Hamilton-Jacobi-Bellman equation},
  language     = {eng},
  month        = {07},
  number       = {5},
  pages        = {33},
  publisher    = {World Scientific},
  series       = {International Journal of Theoretical and Applied Finance},
  title        = {Market making and portfolio liquidation under uncertainty},
  url          = {http://dx.doi.org/10.1142/S021902491450034},
  volume       = {17},
  year         = {2014},
}