IDEAS home Printed from https://ideas.repec.org/p/zbw/sfb649/sfb649dp2011-053.html
   My bibliography  Save this paper

When to cross the spread: Curve following with singular control

Author

Listed:
  • Naujokat, Felix
  • Horst, Ulrich

Abstract

In this article the problem of curve following in an illiquid market is addressed. Using techniques of singular stochastic control, we extend the results of [NW11] to a twosided limit order market with temporary market impact and resilience, where the bid ask spread is now also controlled. We first show existence and uniqueness of an optimal control. In a second step, a suitable version of the stochastic maximum principle is derived which yields a characterisation of the optimal trading strategy in terms of a nonstandard coupled FBSDE. We show that the optimal control can be characterised via buy, sell and no-trade regions. The new feature is that we now get a nondegenerate no-trade region, which implies that market orders are only used when the spread is small. This allows to describe precisely when it is optimal to cross the bid ask spread, which is a fundamental problem of algorithmic trading. We also show that the controlled system can be described in terms of a reflected BSDE. As an application, we solve the portfolio liquidation problem with passive orders.

Suggested Citation

  • Naujokat, Felix & Horst, Ulrich, 2011. "When to cross the spread: Curve following with singular control," SFB 649 Discussion Papers 2011-053, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
  • Handle: RePEc:zbw:sfb649:sfb649dp2011-053
    as

    Download full text from publisher

    File URL: https://www.econstor.eu/bitstream/10419/56749/1/667302964.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Lin, Lu & Li, Feng & Zhu, Lixing & Härdle, Wolfgang Karl, 2010. "Mean volatility regressions," SFB 649 Discussion Papers 2011-003, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    2. Yao, Fang, 2011. "Monetary policy, trend inflation and inflation Persistence," SFB 649 Discussion Papers 2011-008, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    3. Fiocco, Raffaele & Gilli, Mario, 2011. "Bargaining and collusion in a regulatory model," SFB 649 Discussion Papers 2011-047, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    4. Klinke, Sigbert, 2011. "Developing web-based tools for the teaching of statistics: Our wikis and the German Wikipedia," SFB 649 Discussion Papers 2011-030, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    5. Wolfgang Karl Hardle and Maria Osipenko, 2012. "Spatial Risk Premium on Weather Derivatives and Hedging Weather Exposure in Electricity," The Energy Journal, International Association for Energy Economics, vol. 0(Number 2).
    6. Hofmann, Dirk & Qari, Salmai, 2011. "The law of attraction bilateral search and horizontal heterogeneity," SFB 649 Discussion Papers 2011-017, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    7. Anand, Kartik & Gai, Prasanna & Marsili, Matteo, 2011. "Rollover risk, network structure and systemic financial crises," SFB 649 Discussion Papers 2011-052, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    8. ,, 1999. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 15(5), pages 777-788, October.
    9. Till Strohsal & Enzo Weber, 2014. "Mean-variance cointegration and the expectations hypothesis," Quantitative Finance, Taylor & Francis Journals, vol. 14(11), pages 1983-1997, November.
    10. Reiß, Markus, 2011. "Asymptotic equivalence and sufficiency for volatility estimation under microstructure noise," SFB 649 Discussion Papers 2011-028, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    11. ,, 1999. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 15(1), pages 151-160, February.
    12. Mechtenberg, Lydia & Münster, Johannes, 2011. "A strategic mediator who is biased into the same direction as the expert can improve information transmission," SFB 649 Discussion Papers 2011-012, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    13. Santiago Moreno-Bromberg & Luca Taschini, 2011. "Pollution permits, Strategic Trading and Dynamic Technology Adoption," Papers 1103.2914, arXiv.org.
    14. Kappus, Johanna & Reiß, Markus, 2010. "Estimation of the characteristics of a Lévy process observed at arbitrary frequency," SFB 649 Discussion Papers 2010-015, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    15. Härdle, Wolfgang Karl & López Cabrera, Brenda & Okhrin, Ostap & Wang, Weining, 2010. "Localising temperature risk," SFB 649 Discussion Papers 2011-001, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    16. Aur'elien Alfonsi & Antje Fruth & Alexander Schied, 2007. "Optimal execution strategies in limit order books with general shape functions," Papers 0708.1756, arXiv.org, revised Feb 2010.
    17. Dietmar Fehr & Julia Schmid, 2018. "Exclusion in all‐pay auctions: An experimental investigation," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 27(2), pages 326-339, June.
    18. Michael C. Burda & Jennifer Hunt, 2011. "What Explains the German Labor Market Miracle in the Great Recession," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 42(1 (Spring), pages 273-335.
    19. Detmers, Gunda-Alexandra & Nautz, Dieter, 2011. "The information content of central bank interest rate projections: Evidence from New Zealand," SFB 649 Discussion Papers 2011-032, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    20. Duran, Esra Akdeniz & Guo, Mengmeng & Härdle, Wolfgang Karl, 2010. "A confidence corridor for expectile functions," SFB 649 Discussion Papers 2011-004, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    21. Anand, Kartik & Gai, Prasanna & Kapadia, Sujit & Brennan, Simon & Willison, Matthew, 2013. "A network model of financial system resilience," Journal of Economic Behavior & Organization, Elsevier, vol. 85(C), pages 219-235.
    22. Aurelien Alfonsi & Antje Fruth & Alexander Schied, 2010. "Optimal execution strategies in limit order books with general shape functions," Quantitative Finance, Taylor & Francis Journals, vol. 10(2), pages 143-157.
    23. Beresford, Alastair R. & Kübler, Dorothea & Preibusch, Sören, 2012. "Unwillingness to pay for privacy: A field experiment," Economics Letters, Elsevier, vol. 117(1), pages 25-27.
    24. ,, 1999. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 15(4), pages 629-637, August.
    25. Meyer-Gohde, Alexander, 2011. "Sticky information and determinacy," SFB 649 Discussion Papers 2011-006, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    26. Scheffel, Juliane, 2011. "How do unusual working schedules affect social life?," SFB 649 Discussion Papers 2011-025, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    27. Mechtenberg, Lydia & Münster, Johannes, 2012. "A strategic mediator who is biased in the same direction as the expert can improve information transmission," Economics Letters, Elsevier, vol. 117(2), pages 490-492.
    28. Bindseil, Ulrich & König, Philipp Johann, 2011. "The economics of TARGET2 balances," SFB 649 Discussion Papers 2011-035, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    29. Fang Yao, 2011. "Monetary Policy, Trend Inflation and Inflation Persistence," SFB 649 Discussion Papers SFB649DP2011-008, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    30. Wolfgang Karl Härdle & Brenda López Cabrera & Ostap Okhrin & Weining Wang, 2016. "Localizing Temperature Risk," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1491-1508, October.
    31. Song, Song & Bickel, Peter J., 2011. "Large vector auto regressions," SFB 649 Discussion Papers 2011-048, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    32. Bindseil, Ulrich & Lamoot, Jeroen, 2011. "The Basel III framework for liquidity standards and monetary policy implementation," SFB 649 Discussion Papers 2011-041, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    33. Alexander Schied & Torsten Schöneborn, 2009. "Risk aversion and the dynamics of optimal liquidation strategies in illiquid markets," Finance and Stochastics, Springer, vol. 13(2), pages 181-204, April.
    34. Gunda-Alexandra Detmers & Dieter Nautz, 2012. "The Information Content of Central Bank Interest Rate Projections: Evidence from New Zealand," The Economic Record, The Economic Society of Australia, vol. 88(282), pages 323-329, September.
    35. Biele, Guido & Rieskamp, Jörg & Krugel, Lea K. & Heekeren, Hauke R., 2011. "The neural basis of following advice," SFB 649 Discussion Papers 2011-038, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    36. Kappus, Johanna & Reiß, Markus, 2011. "Estimation of the characteristics of a Lévy process observed at arbitrary frequency," SFB 649 Discussion Papers 2011-027, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    37. Park, Soyoung Q & Kahnt, Thorsten & Rieskamp, Jörg & Heekeren, Hauke R., 2011. "Neurobiology of value integration: When value impacts valuation," SFB 649 Discussion Papers 2011-037, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    38. Liu, Rong & Yang, Lijian & Härdle, Wolfgang Karl, 2011. "Oracally efficient two-step estimation of generalized additive model," SFB 649 Discussion Papers 2011-016, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    39. Akdeniz Duran, Esra & Härdle, Wolfgang Karl & Osipenko, Maria, 2012. "Difference based ridge and Liu type estimators in semiparametric regression models," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 164-175.
    40. Stahlschmidt, Stephan & Tausendteufel, Helmut & Härdle, Wolfgang Karl, 2011. "Bayesian Networks and sex-related homicides," SFB 649 Discussion Papers 2011-045, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    41. Anand, Kartik & Gai, Prasanna & Marsili, Matteo, 2012. "Rollover risk, network structure and systemic financial crises," Journal of Economic Dynamics and Control, Elsevier, vol. 36(8), pages 1088-1100.
    42. repec:diw:diwwpp:dp1129 is not listed on IDEAS
    43. Fiocco, Raffaele & Scarpa, Carlo, 2011. "The regulation of interdependent markets," SFB 649 Discussion Papers 2011-046, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    44. Liu, Xiaoliang & Xu, Wei & Odening, Martin, 2011. "Can crop yield risk be globally diversified?," SFB 649 Discussion Papers 2011-018, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    45. M. H. A. Davis & A. R. Norman, 1990. "Portfolio Selection with Transaction Costs," Mathematics of Operations Research, INFORMS, vol. 15(4), pages 676-713, November.
    46. Raffaele Fiocco & Mario Gilli, 2012. "Bargaining and Collusion in a Regulatory Model," Chapters, in: Joseph E. Harrington Jr & Yannis Katsoulacos (ed.), Recent Advances in the Analysis of Competition Policy and Regulation, chapter 12, Edward Elgar Publishing.
    47. Rong Liu & Lijian Yang & Wolfgang K. Härdle, 2013. "Oracally Efficient Two-Step Estimation of Generalized Additive Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(502), pages 619-631, June.
    48. Zheng, Shuzhuan & Yang, Lijian & Härdle, Wolfgang Karl, 2010. "A confidence corridor for sparse longitudinal data curves," SFB 649 Discussion Papers 2011-002, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    49. Beresford, Alastair R. & Kübler, Dorothea & Preibusch, Sören, 2011. "Unwillingness to pay for privacy: A field experiment," SFB 649 Discussion Papers 2011-010, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    50. ,, 1999. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 15(3), pages 427-432, June.
    51. Reiß, Markus & Rozenholc, Yves & Cuenod, Charles A., 2011. "Pointwise adaptive estimation for quantile regression," SFB 649 Discussion Papers 2011-029, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    52. Bibinger, Markus, 2011. "Asymptotics of asynchronicity," SFB 649 Discussion Papers 2011-033, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    53. Härdle, Wolfgang Karl & Spokoiny, Vladimir & Wang, Weining, 2010. "Local quantile regression," SFB 649 Discussion Papers 2011-005, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    54. Diels, Jana Luisa & Wiebach, Nicole, 2011. "Customer reactions in Out-of-Stock situations: Do promotion-induced phantom positions alleviate the similarity substitution hypothsis?," SFB 649 Discussion Papers 2011-021, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    55. Fehr, Dietmar & Schmid, Julia, 2011. "Exclusion in the all-pay auction: An experimental investigation," SFB 649 Discussion Papers 2011-009, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    56. Bunk, Patrick, 2011. "News-driven business cycles in SVARs," SFB 649 Discussion Papers 2011-040, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    57. Scheffel, Juliane, 2011. "Identifying the effect of temporal work flexibility on parental time with children," SFB 649 Discussion Papers 2011-024, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    58. Song, Song & Bickel, Peter J., 2011. "Large vector auto regressions," SFB 649 Discussion Papers 2011-048, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    59. Meyer-Gohde, Alexander, 2011. "Monetary policy, determinacy, and the natural rate hypothesis," SFB 649 Discussion Papers 2011-049, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    60. Herrera, Rodrigo & Schipp, Bernhard, 2011. "Extreme value models in a conditional duration intensity framework," SFB 649 Discussion Papers 2011-022, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    61. Belitz, Heike & Clemens, Marius & von Hirschhausen, Christian & Schmidt-Ehmcke, Jens & Werwatz, Axel & Zloczysti, Petra, 2011. "An indicator for national systems of innovation: Methodology and application to 17 industrialized countries," SFB 649 Discussion Papers 2011-036, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. repec:hum:wpaper:sfb649dp2011-053 is not listed on IDEAS
    2. Anand, Kartik & Gai, Prasanna & Marsili, Matteo, 2012. "Rollover risk, network structure and systemic financial crises," Journal of Economic Dynamics and Control, Elsevier, vol. 36(8), pages 1088-1100.
    3. repec:hum:wpaper:sfb649dp2011-052 is not listed on IDEAS
    4. Mammen, Enno & Rothe, Christoph & Schienle, Melanie, 2016. "Semiparametric Estimation With Generated Covariates," Econometric Theory, Cambridge University Press, vol. 32(5), pages 1140-1177, October.
    5. Cheridito, Patrick & Horst, Ulrich & Kupper, Michael & Pirvu, Traian A., 2011. "Equilibrium pricing in incomplete markets under translation invariant preferences," SFB 649 Discussion Papers 2011-083, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    6. Luc Bauwens & Christian M. Hafner & Diane Pierret, 2013. "Multivariate Volatility Modeling Of Electricity Futures," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(5), pages 743-761, August.
    7. Bocart, Fabian Y.R.P. & Hafner, Christian M., 2012. "Econometric analysis of volatile art markets," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3091-3104.
    8. repec:hum:wpaper:sfb649dp2011-056 is not listed on IDEAS
    9. Chen, Ray-Bing & Chen, Ying & Härdle, Wolfgang Karl, 2011. "TVICA - time varying independent component analysis and its application to financial data," SFB 649 Discussion Papers 2011-054, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    10. repec:hum:wpaper:sfb649dp2011-064 is not listed on IDEAS
    11. repec:hum:wpaper:sfb649dp2011-054 is not listed on IDEAS
    12. Härdle, Wolfgang Karl & Osipenko, Maria, 2011. "Pricing Chinese rain: A multisite mulit-period equilibrium pricing model for rainfall derivatives," SFB 649 Discussion Papers 2011-055, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    13. Hautsch, Nikolaus & Huang, Ruihong, 2011. "Limit order flow, market impact and optimal order sizes: Evidence from NASDAQ TotalView-ITCH data," SFB 649 Discussion Papers 2011-056, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    14. Bertrand, Aurélie & Hafner, Christian M., 2011. "On heterogeneous latent class models with applications to the analysis of rating scores," SFB 649 Discussion Papers 2011-062, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    15. Aurélie Bertrand & Christian Hafner, 2014. "On heterogeneous latent class models with applications to the analysis of rating scores," Computational Statistics, Springer, vol. 29(1), pages 307-330, February.
    16. repec:hum:wpaper:sfb649dp2011-062 is not listed on IDEAS
    17. repec:hum:wpaper:sfb649dp2011-083 is not listed on IDEAS
    18. Horst, Ulrich & Kupper, Michael & Macrina, Andrea & Mainberger, Christoph, 2011. "Continuous equilibrium under base preferences and attainable initial endowments," SFB 649 Discussion Papers 2011-082, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    19. repec:hum:wpaper:sfb649dp2011-082 is not listed on IDEAS
    20. repec:hum:wpaper:sfb649dp2011-055 is not listed on IDEAS
    21. Meyer-Gohde, Alexander, 2011. "Monetary policy, determinacy, and the natural rate hypothesis," SFB 649 Discussion Papers 2011-049, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    22. repec:hum:wpaper:sfb649dp2011-049 is not listed on IDEAS
    23. repec:hum:wpaper:sfb649dp2011-058 is not listed on IDEAS
    24. Kratz, Peter & Schöneborn, Torsten, 2011. "Optimal liquidation in dark pools," SFB 649 Discussion Papers 2011-058, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    25. Schneider, Dorothee, 2011. "The labor share: A review of theory and evidence," SFB 649 Discussion Papers 2011-069, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    26. repec:hum:wpaper:sfb649dp2011-069 is not listed on IDEAS
    27. Nikolaus Hautsch & Julia Schaumburg & Melanie Schienle, 2015. "Financial Network Systemic Risk Contributions," Review of Finance, European Finance Association, vol. 19(2), pages 685-738.
    28. Raffaele Fiocco & Mario Gilli, 2012. "Bargaining and Collusion in a Regulatory Model," Chapters, in: Joseph E. Harrington Jr & Yannis Katsoulacos (ed.), Recent Advances in the Analysis of Competition Policy and Regulation, chapter 12, Edward Elgar Publishing.
    29. Heyne, Gregor & Kupper, Michael & Mainberger, Christoph, 2011. "Minimal supersolutions of BSDEs with lower semicontinuous generations," SFB 649 Discussion Papers 2011-067, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    30. Cebiroğlu, Gökhan & Horst, Ulrich, 2011. "Optimal display of Iceberg orders," SFB 649 Discussion Papers 2011-057, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    31. repec:hum:wpaper:sfb649dp2011-047 is not listed on IDEAS
    32. Tischer, Sven & Hildebrandt, Lutz, 2011. "Linking corporate reputation and shareholder value using the publication of reputation rankings," SFB 649 Discussion Papers 2011-065, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    33. repec:hum:wpaper:sfb649dp2011-065 is not listed on IDEAS
    34. repec:hum:wpaper:sfb649dp2011-057 is not listed on IDEAS
    35. repec:hum:wpaper:sfb649dp2011-067 is not listed on IDEAS
    36. repec:hum:wpaper:sfb649dp2011-084 is not listed on IDEAS
    37. repec:hum:wpaper:sfb649dp2011-085 is not listed on IDEAS
    38. Fiocco, Raffaele, 2011. "Competition and regulation in a differentiated good market," SFB 649 Discussion Papers 2011-084, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.

    More about this item

    Keywords

    stochastic maximum principle; convex analysis; fully coupled forward backward stochastic differential equations; trading in illiquid markets;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:zbw:sfb649:sfb649dp2011-053. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ZBW - Leibniz Information Centre for Economics (email available below). General contact details of provider: https://edirc.repec.org/data/sohubde.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.