options_realtime_modeling

Numerical Solutions: Projects in Mathematical Modeling

Jaisal Friedman

Abstract

This paper explores the Black-Scholes-Merton options pricing model, derives a predictive extension model, and visualizes both models in comparison to real-time pricing options pricing. The paper also explores various methodologies of calculating historical volatility. A portfolio of 5 U.S. Market Stocks and 1 index fund was taken as example for the project. The model was limited to visual analysis from real-time simulations as further explained in the extensions

Overview

The project was written in python. The Jupyter notebook is a reference of how to interact with the option_.py and pytradier.py files. To configure the Library to run, rename the config_example.json file as config.json and enter your own details. You will need to get the required API keys, as well as install the python dependencies. A sample of the generated 3D volatility surfaces is shown below. Interactive Volatility Surfaces

Math

Please reference the paper/latex file in the GitHub for specifics on the Math behind each model.

Extensions & Contact

There's some really interesting extensions, if you'd like to discuss please feel free to reach out to me :)

Sample Renderings