Why is smile risk a bigger deal for exotic options than vanillas?

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AcadiFi · Accepted Answer

Vanillas reference a single strike, so you only need one point on the smile. Exotic payoffs reference paths, barriers, or averages that depend on vols at MULTIPLE strikes over time...

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Ignacio Thornberg at Porto Structured Notes prices a down-and-out barrier put on the FTSE 100. The barrier at 7,100 means the option value depends on the probability of hitting that level, which depends on implied vols for strikes NEAR the barrier. If the smile is steep on the downside (as equity indices typically show), barrier probability is higher than flat-vol models predict.

```mermaid
flowchart TD
  A[Exotic Payoff] --> B[Depends on Path]
  B --> C[Needs Smile Across Strikes]
  C --> D[Local Vol Model]
  C --> E[Stochastic Vol Model]
  D --> F[Consistent with Smile Today]
  E --> G[Consistent with Smile Dynamics]
```

Three smile-risk flavors matter:
1. Static smile risk — pricing at time zero requires the full smile surface
2. Dynamic smile risk — how the smile evolves as spot moves (sticky strike vs sticky delta)
3. Smile re-marking risk — the smile shape changes overnight from market moves

A flat-vol Black-Scholes price of a cliquet could be off by 15-30% compared to a smile-consistent model. For barrier options, the error can exceed 40% because the knock-out probability is highly sensitive to downside skew. Professional desks use local volatility or stochastic volatility models calibrated to the full surface rather than single-point BSM.

Why is smile risk a bigger deal for exotic options than vanillas?

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