Cutting-Edge Project - Milliman

    

   

Workflows:

Lauchpads:

Documentation: Official resource

Overview

1. Implementation of path simulators for:
   • Interest rates models: Vasicek, Cox-Ingersoll-Ross (CIR), Hull & White
   • Equity-index models: Black-Scholes & Heston with stochastic rates
   • Use of Euler-Maruyama and Milstein numerical methods to solve SDEs dynamics
2. Analysis study
   • Via derivatives pricing (MC convergence, CI spatial distribution)
   • Quantile analysis
   • Parameters impact

Project conducted in collaboration with Milliman and University of Paris-Saclay..

Architecture

The dependency tree below shows the links between each declared class in the source code.

  graph TD;
      Model --> RatesModel
      Model --> EquityModel
      RatesModel --> Vasicek
      RatesModel --> CIR
      RatesModel --> HullWhite
      Scenario -. Components .-> HullWhite
      ZeroCouponHandler -. Components .-> HullWhite
      EquityModel --> BlackScholes
      EquityModel --> Heston

      Constants --> Utils

      Pricer --> EuropeanPricer
      Pricer --> AsianPricer

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Remark: Model, RatesModel and EquityModel are abstract classes and do not contain any implemented methods.

Getting started

0. Clone the repository:

git clone git@github.com:lcsrodriguez/CuttingEdge-Milliman.git
cd CuttingEdge-Milliman/

One can also download the repository by clicking on the green button Code > Download ZIP.

1. Verify the requirements to execute the Jupyter Notebook

python3 --version
pip3 -V
pip3 install -r requirements.txt

2. Run the Jupyter-Notebook

jupyter-notebook main.ipynb

3. Check and handle the figures stored in out/:

ls out/
cd out/

Build the documentation

1. Install these additional requirements

pip3 install mkdocs "mkdocstrings[python]" mkdocs-material

2. Convert the Jupyter Notebook file (.ipynb extension) into a Python script file (.py)

jupyter nbconvert --to script main.ipynb --output out/main
cat out/main.py

3. Perform the needed updates in the code

4. Run the following command to release the last version of the documentation

mdkocs build

References

1. Ioane MUNI-TOKE, Modèles stochastiques de taux d’intérêts, 2011
2. Lionel GABET, Frédéric ABERGEL, Ioane MUNI-TOKE, Introduction aux mathématiques financières, 2010
3. Black, Fischer, and Myron Scholes. The pricing of options and corporate liabilities., Journal of political economy 81.3 (1973): 637-654.
4. Cox, J. C., Ingersoll, J. E., and Ross, S. A. (1985). A theory of the term structure of interest rates. Econometrica 53(2), 385–407
5. Grzelak, L. A., and Oosterlee, C. W. (2011). On the Heston model with stochastic interest rates. SIAM Journal on Financial Mathematics 2(1), 255–286.

License

See LICENSE file

• Amal BACHA - Dalia BARBI - Khalil BATTIKH - Lucas RODRIGUEZ - Naïm SOUNI
• Academic works (January - May 2023)