A volatility curve refers to a graphical representation of implied volatility across different strikes, expirations, or both. It provides insight into how implied volatility varies based on different factors like strike prices or time to maturity, helping traders and analysts understand the market’s pricing of options.
There are two main types of volatility curves:
1. Volatility Smile
• A volatility smile is a plot of implied volatility against different strike prices for a specific expiration date.
• In a volatility smile, the implied volatility is higher for deep in-the-money (ITM) and out-of-the-money (OTM) options, while ATM options have lower implied volatility. This creates a “smile-like” shape.
Causes:
• Higher demand for OTM options (e.g., hedging strategies).
• Market pricing in the possibility of extreme price movements (tail risk).
Example: If an option’s underlying price is $100, and implied volatilities are:
– $80 strike: 25%
– $100 strike: 20% (ATM)
– $120 strike: 25%
The plot of IV vs. strike prices forms a smile shape.
2. Volatility Skew (or Smirk)
• A volatility skew describes how implied volatility changes asymmetrically across strike prices. Instead of a symmetric smile, IV increases (or decreases) more for strikes on one side.
• The smirk shape often arises in equity options, where OTM puts (lower strikes) tend to have higher IV than OTM calls (higher strikes). This reflects a higher demand for downside protection.
Causes:
• Market fear of significant downside moves (e.g., due to crashes).
• Hedging demand for puts, as they serve as insurance.
Example: For a stock at $100:
– $80 strike: 30%
– $100 strike: 20%
– $120 strike: 15%
The plot forms a downward sloping skew.
3. Term Structure of Volatility Curve
• When plotting IV across different expirations, the term structure emerges. This curve shows how IV varies with time to maturity.
• Shapes:
• Upward-sloping: IV increases with longer tenors (normal in stable markets).
• Downward-sloping: Higher short-term IV due to near-term uncertainty (e.g., earnings).
Applications of Volatility Curves
1. Options Pricing:
• Option prices are based on implied volatility, so understanding the curve helps traders assess fair value.
2. Hedging:
• Volatility curves help in designing delta-neutral or vega-neutral strategies by identifying mispriced options.
3. Risk Management:
• Skew and smile analysis reveal market expectations of extreme price movements or risks.
4. Trading Strategies:
• Use volatility smiles or skews to implement volatility arbitrage (e.g., long OTM options if IV is underpriced).
In summary, volatility curves (whether smiles, skews, or term structures) reflect how the market perceives risk and uncertainty, helping traders analyze market sentiment and make informed decisions.