Quant Project | Build a Volatility Surface in Python
Learn how to build an options volatility surface in Python with this comprehensive walkthrough.
What You'll Learn:
Implement the Black-Scholes formula
Extract implied volatility using numerical root-finding methods
Build a complete volatility surface grid from option prices
Smooth and interpolate discrete data into a continuous surface
Create interactive 3D visualizations with Plotly
Generate volatility smile and term structure plots
Validate your results with repricing checks
Why This Matters:
The volatility surface is essential for consistent option pricing and risk management. While the Black-Scholes model assumes constant volatility, in reality, implied volatility varies across strikes (the smile) and maturities (the term structure). This tutorial shows you exactly how to capture and visualize that behavior.
What We Build:
Starting with option prices organized by strike and maturity, we'll walk through the complete pipeline: implementing Black-Scholes, inverting it to extract implied vols, organizing results into a grid, smoothing with spline interpolation, and creating the key visualizations of smile and term structure.
Notebook: https://github.com/quantifyyourcareer...
Disclaimer:
The views expressed here are my own and do not reflect the opinions or endorsements of my employer or any institutions I am affiliated with.
📚 Resources: Concepts align with John C. Hull's discussions on volatility smiles and implied volatility in "Options, Futures, and Other Derivatives"
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Timestamps:
0:00 What are we building?
1:27 Why Does a Volatility Surface Exist?
3:14 What Implied Volatility Actually Means
4:53 Stepbystep process of the Project
6:56 Python Notebook walkthrough
19:47 Why This Matters in Practice & Applications
21:50 Final Recap
22:52 What Comes Next
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