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Professional · Lesson 6 of 6Volatility surfaces and professional practice
A volatility surface maps implied volatility across strikes and expiries. Equity indices show a downward skew (higher IV for low strikes) and a term structure that is usually upward sloping in calm markets and inverted in panics.
Models used beyond Black-Scholes include local volatility (Dupire), stochastic volatility (Heston, SABR) and jump-diffusion (Merton). Banks calibrate these to the surface to price exotic options consistently.
Risk management on trading desks uses scenario grids (spot x volatility), Value at Risk and stress tests, and limits on Greeks. The 1998 collapse of Long-Term Capital Management is a classic lesson in model risk, leverage and liquidity.
Key takeaways
- IV varies by strike (skew) and expiry (term structure).
- Heston, SABR and local-vol models fit the surface.
- LTCM shows how leverage turns model error into ruin.
Check your understanding
1. An inverted volatility term structure (short-dated IV above long-dated) usually signals...
- Calm markets
- Market stress
- Rising dividends
- Low interest rates
Show the answer
Market stress. Near-term fear pushes short-dated IV up.
2. Which is a stochastic volatility model?
- Black-Scholes
- Heston
- Gordon growth
- CAPM
Show the answer
Heston. Heston lets volatility itself move randomly.
Go deeper
- Wikipedia: Volatility smile
- YouTube videos: volatility surface skew term structure explained
- Investopedia: volatility skew
- Wikipedia: Heston model
- Wikipedia: SABR volatility model
- Wikipedia: Long-Term Capital Management
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