Options Analytics & Volatility Surface Construction

Python-based options analytics framework covering Black-Scholes pricing, Greeks computation, implied volatility extraction, volatility smile and surface construction, and term structure analysis across strikes and maturities.

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Overview

Volatility surfaces are the backbone of derivatives desks — every options price, hedge ratio, and risk metric depends on accurately modeling how implied volatility varies across strikes and maturities. This project builds a complete options analytics engine from Greeks to full 3D surface construction.

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Models and Analytics

Black-Scholes Pricing

• European call and put pricing
• Put-call parity verification
• Price sensitivity to all inputs

Greeks Analysis

• Delta, Gamma, Vega, Theta, Rho
• Greeks surface across strikes and maturities
• Delta hedging simulation and P&L attribution

Implied Volatility

• Bisection and Brent method extraction
• Volatility smile construction per maturity
• Smile skew and curvature analysis

Volatility Surface

• Full 3D implied vol surface across strikes and maturities
• ATM term structure
• Risk-reversal and butterfly spreads

Volatility Regime Analysis

• Implied vs realised volatility spread
• Volatility risk premium estimation
• Term structure shape classification

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Tech Stack

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Project Structure

Options-Analytics-Volatility-Surface/
│
├── data/
│   ├── returns.csv
│   └── prices.csv
│
├── notebooks/
│   ├── 01_black_scholes_pricing.ipynb
│   ├── 02_greeks_analysis.ipynb
│   ├── 03_implied_volatility.ipynb
│   ├── 04_volatility_surface.ipynb
│   └── 05_vol_regime_analysis.ipynb
│
├── src/
│   ├── black_scholes.py
│   ├── greeks.py
│   └── implied_vol.py
│
├── results/
│   ├── 01_bs_pricing_surface.png
│   ├── 02_greeks_heatmaps.png
│   ├── 03_delta_hedging_pnl.png
│   ├── 04_volatility_smile.png
│   ├── 05_volatility_surface_3d.png
│   ├── 06_vol_term_structure.png
│   ├── 07_implied_vs_realised.png
│   └── options_pricing_summary.csv
│
└── README.md

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Key Results

• Implied vol surface shows pronounced skew for short maturities flattening at longer horizons — consistent with equity markets
• Volatility risk premium averages 3 to 5 vol points across the sample period with spikes during stress events
• Delta hedging simulation achieves P&L within 2% of theoretical with daily rebalancing across different market regimes
• ATM term structure shifts from backwardation to contango during low-volatility regimes

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References

• Black, F. and Scholes, M. (1973) — The Pricing of Options
• Hull, J. — Options, Futures and Other Derivatives
• Gatheral, J. — The Volatility Surface