Simulating American and European Options with Python.

• Jerald Achaibar, Sukriti Raut, Joseph Yedinak

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The data folder contains the input and output data from the simulations.

• In the setup folder you can find the original dataset used, Namely the historical options data for $SPY, $QQQ, and $IWM; and historical risk free rates for the relevant time period.
• The output folder contains the output data from the simulations, in the output_analysis.ipynb file (below.)

In the setup folder, you can find the preliminary research that we base all of our findings on.

• The LSMC_intro.ipynb file shows what the Least Squares Monte Carlo method is, and how it can be applied to financial instruments for pricing models.

• The American_optioins.ipynb steps through the LSMC Algorithm step by step, to achieve the final result.

• The black-scholes.ipynb file dives into the derivation of the Brownian Motion, Monte Carlo Method for pricing European options and a comparison with the analytical methods of the Black Scholes model.

The model.ipynb contains the code that was used to set up and test the program that would run the simulations.

The Models.py contains our final model including the algorithm for LSMC, the Monte Carlo methods, and analytical Black Scholes that is used to run the simulations.

The output_analysis.ipynb file is used to observe and convey the results from the simulations