Project Overview
The Black-Scholes model assumes constant volatility, but markets price options with a volatility 'smile' — implied volatility varies systematically by strike and expiry. This workbook back-solves implied volatility from market option prices for a range of strikes (ITM/ATM/OTM) and multiple expiration dates, constructs the 3D volatility surface, and analyzes the skew pattern. The analysis has direct applications in derivatives pricing, risk management, and structured product design.
📋Problem Statement
Real options markets violate Black-Scholes's constant-volatility assumption — implied volatility varies by strike and expiry, creating the 'volatility smile.' Quantify and visualize this pattern using actual 2021 market data.
🎯Analytical Approach
Collected market prices for call and put options across multiple strikes and expiration dates. Used the Black-Scholes pricing formula in reverse — iteratively solving for the volatility input that produces the observed market price (Newton-Raphson bisection in Excel) — to extract implied volatility for each option.
💾Data Sources
2021 equity options market prices (calls and puts) across 5+ expiration dates and 7+ strikes ranging from 80% to 120% of spot price. Underlying spot price, risk-free rate, and dividend yield as of the observation date.
🔧Quantitative Methods
IV extraction: Excel Goal Seek / iterative formula to back-solve Black-Scholes for σ. Smile visualization: XY scatter plot of IV vs. moneyness (K/S) for each expiry. Term structure: IV by expiry at ATM strike. 3D surface: combined strike × maturity × IV chart showing the full surface.
✨Key Results
A clearly visualized volatility smile showing pronounced left skew (higher IV for OTM puts) consistent with equity crash risk premium. Term structure shows elevated short-term IV relative to longer-dated options, reflecting near-term uncertainty. Directly applicable to options desk pricing and hedging work.
🧠Key Learnings
The volatility smile is one of the most important empirical findings in modern finance — it shows that market participants price tail risk beyond what Black-Scholes assumes. Understanding skew is essential for anyone working in derivatives trading, structuring, or risk management.