Options VaR Risk Engine

Quantitative risk analysis for an options butterfly spread. Simulates joint SPX–VIX market shocks and reports 1-day 95% Value at Risk (VaR) via Monte Carlo + Black-Scholes repricing.

Overview

A reproducible Python risk engine that simulates joint SPX–VIX scenarios via a Gaussian copula with Student-t marginals, re-prices an options butterfly spread using Black-Scholes, and estimates 1-day 95% Value at Risk (VaR) from the simulated PnL distribution.

What’s inside

• Scenario generation: Gaussian copula + Student-t marginals (SPX, VIX)
• Repricing: Black-Scholes calls for a butterfly spread
• Risk metric: 1-day 95% VaR from simulated PnL

Repo structure

• notebooks/ — analysis notebook(s)
• src/ — reusable Python modules (if extracted later)
• results/ — figures/tables (PnL distribution, VaR summary)
• assets/cover/ — project images
• docs/ — report/notes/slides

Key results

• 1-day 95% VaR (PnL): TBD
• 1-day 95% VaR (Return): TBD
• PnL distribution: see results/

Method overview (high level)

1. Data & returns

   • Download SPX and VIX daily levels
   • Compute log returns for both series

2. Dependence + scenario generation

   • Transform marginals to allow heavy tails (Student-t style)
   • Couple SPX and VIX with a dependence structure (copula / correlation)
   • Generate Monte Carlo scenarios of 1-day shocks

3. Repricing + VaR

   • Reprice each option leg under simulated spot & vol shocks
   • Aggregate to portfolio value → PnL distribution
   • Report VaR as the 5th percentile loss (95% confidence)

Notes & assumptions

• Pricing model: Black-Scholes (European call approximation)
• Risk factors: SPX level and VIX-derived volatility shock (as a proxy)
• Horizon: 1 trading day
• Metric: VaR at 95% confidence (historical calibration + Monte Carlo simulation)

Limitations

• VIX is a proxy for implied volatility; mapping to option IV is simplified.
• Black-Scholes assumes lognormal dynamics and constant volatility within each scenario.
• Single-day horizon only; extensions could include multi-day simulation and stress testing.

Project context

Started as a team project for a Quantitative Risk Management course. I later continued it independently by packaging the work into a reproducible risk engine: cleaning and organizing the codebase, standardizing inputs/parameters for reruns, and adding documentation + repo structure so the full workflow (scenario simulation → repricing → PnL/VaR reporting) is easy to reproduce for portfolio use.

Tech stack

Python · NumPy · pandas · SciPy · statsmodels · yfinance · matplotlib · seaborn

Quickstart

1) Install dependencies

pip install -r requirements.txt

2) Run the analysis

• Open the notebook in notebooks/ (recommended), or
• Run the script in src/ (if/when extracted later)

Data is pulled from public sources (via yfinance) unless otherwise noted.

License

MIT — see LICENSE.