README

Note: This repo is a work-in-progress. Upcoming, I will be working on comparing the current empirical analysis with a couple of well-known theoretical models. The current set of expiration dates allows for a really good comparison analysis.

This repository contains several Jupyter Notebooks for analyzing and visualizing options data. Below is a brief description of each notebook and relevant references to MATLAB scripts and directories:

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All data is from the Center of Research in Security Prices (CRSP) https://wrds-www.wharton.upenn.edu/pages/get-data/center-research-security-prices-crsp/

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The default ticker analyzed is the ^VIX ETF.

Due to the nature of the data, there seems to be only significant demand for OTM Call options. While there is demand for puts, it is only for a small amount in proportion to the entire dataset. Therefore, the visual analysis done in greeks.ipynb and visualise.ipynb is only representative of OTM Calls. However, the data calculated is still present for ITM/OTM Call & Puts in the .csv files.

Raw data file: UnderlyingOptionsIntervals_1800sec_2021-04-26.csv

dataclean.ipynb

The dataclean.ipynb notebook is responsible for cleaning and preprocessing the options data. It performs the following tasks:

• Reads raw options data from the raw data file.
• Filters and sorts the data based on specific criteria.
• Saves selected & filtered data to the /data directory.
• Converts data types as necessary.
• Calculates implied volatility for each option using the Black-Scholes model.
• Saves the implied volatility data for further analysis in the /implied directory.

Relevant MATLAB scripts:

• jaeckel.m: Used for specific calculations and data processing tasks within the notebook, including optimized root finding using Jaeckel's method (2006).
• newtonraphson.m: A less efficient but self-made NR iterative root finder, not optimally calibrated.

impliedvisual.ipynb

The impliedvisual.ipynb notebook is used for visualizing the options data. It includes various plots and charts to help understand the data better. Key visualizations include:

• Volatility smiles overplotted at each 30-minute interval of the day.
• Volatility smiles plotted for different taus (expirations).
• 3D surface scatter plots of the implied volatility surface.

greeks.ipynb

The greeks.ipynb notebook calculates the Greeks for options, which are essential for understanding the sensitivity of options prices to various factors. It includes the following calculations for each tau (expiration date):

• Delta: Measures the sensitivity of the option's price to changes in the price of the underlying asset.
• Gamma: Measures the rate of change of delta with respect to changes in the underlying price.
• Vega: Measures the sensitivity of the option's price to changes in the volatility of the underlying asset.
• Theta: Measures the sensitivity of the option's price to the passage of time (time decay).
• Rho: Measures the sensitivity of the option's price to changes in the risk-free interest rate.

Initialize Datasets

To initialize, please run the following notebooks in order:

1. dataclean.ipynb
2. impliedvisual.ipynb
3. greeks.ipynb

Then you may run and tweak them individually as you like.