SPY Risk Modeling & Monte Carlo Simulation

This project is a simple implementation of market risk modeling using SPY (S&P 500 ETF) daily data.

The goal is to understand how different statistical assumptions affect risk estimation especially Value-at-Risk (VaR) and Expected Shortfall (ES).

Instead of building something overly complicated, this project focuses on clarity, structure, and clean implementation of core quantitative finance concepts.

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What This Project Covers

• Loading SPY historical price data
• Computing daily log returns
• Fitting Normal and Student-t distributions
• Monte Carlo simulation of returns
• Historical and Parametric VaR
• Expected Shortfall (ES)
• Basic VaR backtesting
• Kupiec test for model validation

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Why This Project?

Financial returns are not perfectly normal.
They are skewed, heavy-tailed, and occasionally extreme.

This project compares:

• Standard Normal assumptions
• Heavy-tailed Student-t assumptions

and evaluates how they impact risk measurement.

The focus is on understanding risk behavior, not just calculating numbers.

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Key Concepts Implemented

• Log returns
• Distribution fitting
• Monte Carlo simulation
• Value-at-Risk (VaR)
• Expected Shortfall (ES)
• Kupiec Proportion of Failures Test

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How to Run

1. Install dependencies:
   • python
   • numpy
   • pandas
   • scipy
   • matplotlib
   • statsmodels
   • yfinance
   • jupyterlab
   • seaborn
2. Load SPY data and compute returns
3. Fit distribution
4. Simulate returns
5. Compute risk metrics
6. Backtest VaR

The modules are designed to be imported into a notebook or a main script.

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What I Learned

• Real-world returns are heavy-tailed
• Risk models can underestimate tail risk
• Backtesting is just as important as modeling
• Clean structure matters more than clever tricks

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Author

Built as part of my quantitative finance learning journey.