├── .gitignore ├── Almgren-Chriss Optimal Execution Model.ipynb ├── LICENSE ├── README.md └── imgs ├── ccl.png ├── ccl_traj.png ├── fb_goog.png ├── fb_goog_traj.png └── thumbnail.png /.gitignore: -------------------------------------------------------------------------------- 1 | # Byte-compiled / optimized / DLL files 2 | __pycache__/ 3 | *.py[cod] 4 | *$py.class 5 | 6 | # C extensions 7 | *.so 8 | 9 | # Distribution / packaging 10 | .Python 11 | build/ 12 | develop-eggs/ 13 | dist/ 14 | downloads/ 15 | eggs/ 16 | .eggs/ 17 | lib/ 18 | lib64/ 19 | parts/ 20 | sdist/ 21 | var/ 22 | wheels/ 23 | pip-wheel-metadata/ 24 | share/python-wheels/ 25 | *.egg-info/ 26 | .installed.cfg 27 | *.egg 28 | MANIFEST 29 | 30 | # PyInstaller 31 | # Usually these files are written by a python script from a template 32 | # before PyInstaller builds the exe, so as to inject date/other infos into it. 33 | *.manifest 34 | *.spec 35 | 36 | # Installer logs 37 | pip-log.txt 38 | pip-delete-this-directory.txt 39 | 40 | # Unit test / coverage reports 41 | htmlcov/ 42 | .tox/ 43 | .nox/ 44 | .coverage 45 | .coverage.* 46 | .cache 47 | nosetests.xml 48 | coverage.xml 49 | *.cover 50 | *.py,cover 51 | .hypothesis/ 52 | .pytest_cache/ 53 | 54 | # Translations 55 | *.mo 56 | *.pot 57 | 58 | # Django stuff: 59 | *.log 60 | local_settings.py 61 | db.sqlite3 62 | db.sqlite3-journal 63 | 64 | # Flask stuff: 65 | instance/ 66 | .webassets-cache 67 | 68 | # Scrapy stuff: 69 | .scrapy 70 | 71 | # Sphinx documentation 72 | docs/_build/ 73 | 74 | # PyBuilder 75 | target/ 76 | 77 | # Jupyter Notebook 78 | .ipynb_checkpoints 79 | 80 | # IPython 81 | profile_default/ 82 | ipython_config.py 83 | 84 | # pyenv 85 | .python-version 86 | 87 | # pipenv 88 | # According to pypa/pipenv#598, it is recommended to include Pipfile.lock in version control. 89 | # However, in case of collaboration, if having platform-specific dependencies or dependencies 90 | # having no cross-platform support, pipenv may install dependencies that don't work, or not 91 | # install all needed dependencies. 92 | #Pipfile.lock 93 | 94 | # PEP 582; used by e.g. github.com/David-OConnor/pyflow 95 | __pypackages__/ 96 | 97 | # Celery stuff 98 | celerybeat-schedule 99 | celerybeat.pid 100 | 101 | # SageMath parsed files 102 | *.sage.py 103 | 104 | # Environments 105 | .env 106 | .venv 107 | env/ 108 | venv/ 109 | ENV/ 110 | env.bak/ 111 | venv.bak/ 112 | 113 | # Spyder project settings 114 | .spyderproject 115 | .spyproject 116 | 117 | # Rope project settings 118 | .ropeproject 119 | 120 | # mkdocs documentation 121 | /site 122 | 123 | # mypy 124 | .mypy_cache/ 125 | .dmypy.json 126 | dmypy.json 127 | 128 | # Pyre type checker 129 | .pyre/ 130 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | MIT License 2 | 3 | Copyright (c) 2021 Joshua Paul Jacob 4 | 5 | Permission is hereby granted, free of charge, to any person obtaining a copy 6 | of this software and associated documentation files (the "Software"), to deal 7 | in the Software without restriction, including without limitation the rights 8 | to use, copy, modify, merge, publish, distribute, sublicense, and/or sell 9 | copies of the Software, and to permit persons to whom the Software is 10 | furnished to do so, subject to the following conditions: 11 | 12 | The above copyright notice and this permission notice shall be included in all 13 | copies or substantial portions of the Software. 14 | 15 | THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR 16 | IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 17 | FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE 18 | AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER 19 | LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, 20 | OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE 21 | SOFTWARE. 22 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # Almgren-Chriss Optimal Execution Model 2 | 3 | The aim of the Almgren-Chriss optimal execution model is to minimize a combination of volatility risk and transaction costs arising from permanent and temporary market impact. In this notebook, we study the model for liquidation of large positions with real financial data. 4 | 5 | ![](https://raw.githubusercontent.com/joshuapjacob/almgren-chriss-optimal-execution/main/imgs/thumbnail.png) 6 | 7 | ## Correlated Assets 8 | We numerically illustrate the model with financial data for two correlated assets. In particular, we use the daily historical prices of Alphabet Inc. (NASDAQ:GOOG) and Meta Platforms, Inc. (NASDAQ:FB) over three months. 9 | ### Stock Prices 10 | ![](https://raw.githubusercontent.com/joshuapjacob/almgren-chriss-optimal-execution/main/imgs/fb_goog.png) 11 | ### Optimal Trading Trajectory 12 | ![](https://raw.githubusercontent.com/joshuapjacob/almgren-chriss-optimal-execution/main/imgs/fb_goog_traj.png) 13 | ## Cross-Market Manipulation 14 | We explore a particular case of trading shares of the same company on different exchanges. In particular, we explore the optimal strategy for closing a position of Carnival Corporation & plc (CCL) over 15 days. CCL is a British-American cruise operator which is currently the world's largest travel leisure company. Shares of CCL are traded on both the NYSE and the LSE. See Jupyter notebook for more details. 15 | ### Stock Prices 16 | ![](https://raw.githubusercontent.com/joshuapjacob/almgren-chriss-optimal-execution/main/imgs/ccl.png) 17 | ### Optimal Trading Trajectory 18 | ![](https://raw.githubusercontent.com/joshuapjacob/almgren-chriss-optimal-execution/main/imgs/ccl_traj.png) 19 | ## Reference 20 | [Almgren, R. and Chriss, N., 2001. Optimal execution of portfolio transactions. The Journal of Risk, 3(2), pp.5-39](https://www.smallake.kr/wp-content/uploads/2016/03/optliq.pdf) 21 | -------------------------------------------------------------------------------- /imgs/ccl.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/joshuapjacob/almgren-chriss-optimal-execution/3a71a1c37daf39eb25dc6c9b20dd21df2765d0d3/imgs/ccl.png -------------------------------------------------------------------------------- /imgs/ccl_traj.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/joshuapjacob/almgren-chriss-optimal-execution/3a71a1c37daf39eb25dc6c9b20dd21df2765d0d3/imgs/ccl_traj.png -------------------------------------------------------------------------------- /imgs/fb_goog.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/joshuapjacob/almgren-chriss-optimal-execution/3a71a1c37daf39eb25dc6c9b20dd21df2765d0d3/imgs/fb_goog.png -------------------------------------------------------------------------------- /imgs/fb_goog_traj.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/joshuapjacob/almgren-chriss-optimal-execution/3a71a1c37daf39eb25dc6c9b20dd21df2765d0d3/imgs/fb_goog_traj.png -------------------------------------------------------------------------------- /imgs/thumbnail.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/joshuapjacob/almgren-chriss-optimal-execution/3a71a1c37daf39eb25dc6c9b20dd21df2765d0d3/imgs/thumbnail.png --------------------------------------------------------------------------------