AIM-IT4 / Topological-Risk-Measure-for-Equities

Topological Risk Analysis

Description

This research aims to fetch stock data for specific tickers and perform various analyses including normalization, calculation of Value-at-Risk (VaR), Conditional Value-at-Risk (CVaR), and Topological Data Analysis (TDA) using persistent homology. The program also plots the stock data and persistence diagrams for better visualization.

Dependencies

• yfinance
• numpy
• matplotlib
• gudhi
• scipy

You can install these dependencies using pip:

pip install yfinance numpy matplotlib gudhi scipy

Functions

fetch_stock_data(ticker, period="1y")

Fetches the stock data for a given ticker and period.

normalize_time_series(time_series)

Normalizes the time-series data between 0 and 1.

calculate_returns(time_series)

Calculates the daily returns of a stock based on its time series.

calculate_var_cvar(returns, confidence_level=0.95)

Calculates VaR and CVaR based on the given returns and confidence level.

compute_persistent_homology(time_series, window_size=10)

Computes persistent homology for the time series.

plot_persistence_diagrams(diagrams)

Plots the persistence diagrams.

clean_array(arr)

Cleans the array by removing NaN and infinite values.

How to Run

1. Clone this repository.
2. Run pip install -r requirements.txt to install dependencies.
3. Execute the script using python <script_name>.py.

Output

• Prints VaR and CVaR values for each stock at a 95% confidence interval.
• Plots the persistence diagrams for each stock.
• Computes and prints the Euclidean distance between the baseline and stress scenarios for each stock.

License

This project is open-source and available under the MIT License.