What causes the volatility smile and skew in options markets?
The FRM material discusses volatility smiles and skews as deviations from Black-Scholes assumptions. I understand that implied volatility varies by strike price, but why? What's the economic intuition and how does it affect risk management?
The volatility smile (and its asymmetric cousin, the volatility skew) refers to the pattern of implied volatility varying across strike prices for options with the same expiration. Black-Scholes assumes constant volatility, so this pattern reveals where the model fails.
What the Patterns Look Like
- Smile: Implied volatility is higher for both deep in-the-money and deep out-of-the-money options, forming a U-shape. Commonly seen in FX markets.
- Skew (Smirk): Implied volatility is higher for low-strike (OTM puts) than for high-strike (OTM calls). Dominant in equity index markets.
Why Does the Skew Exist in Equities?
- Crashophobia / Demand for downside protection: Fund managers buy OTM puts to hedge portfolios. This persistent demand drives up put prices, which translates to higher implied volatility at lower strikes.
- Leverage effect: When stock prices fall, the firm's leverage increases (debt/equity rises), making equities riskier. This increases realized volatility after down moves.
- Fat tails in return distributions: Real-world returns have fatter left tails than the normal distribution assumes. OTM puts need higher implied vol to compensate for the higher-than-normal probability of extreme down moves.
- Jump risk: Markets can gap down suddenly (crashes), which Black-Scholes doesn't capture. OTM put buyers demand compensation for this jump risk.
Why Does the Smile Exist in FX?
Currency markets experience large moves in both directions (a currency can surge or crash), so both OTM puts and OTM calls command higher implied volatility — creating a symmetric smile.
Risk Management Implications
| Issue | Impact |
|---|---|
| VaR underestimation | Using flat vol understates tail risk |
| Hedging errors | Delta hedges using BS delta are wrong when the smile shifts |
| Model risk | Different smile models (local vol, stochastic vol, jump-diffusion) give different prices for exotic options |
| P&L attribution | "Vega" isn't a single number — you need vega for each strike/tenor bucket |
Example: Ashford Capital prices a 3-month 90% strike put on the S&P 500. At-the-money implied vol is 18%, but the 90% strike has 24% implied vol due to skew. Pricing with 18% flat vol would undervalue the put by roughly 35%, leaving the firm critically underhedged.
For the FRM exam, be able to explain the economic causes of the smile and skew, and understand how they affect option pricing and risk measurement. Check our derivatives materials for more practice.
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