How do Greeks behave for knock-in and knock-out barrier options?

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AcadiFi · Accepted Answer

Barrier options — up-and-out, down-and-in, and similar — have discontinuous payoff structures that create unstable Greeks near the barrier. For a down-and-out call, delta increases as spot falls toward the barrier (because any touch kills the option), then drops instantly to zero at knock-out. Gamma spikes sharply near the barrier and can exceed the gamma of comparable vanilla options by 5-10x in the final days before expiry.

Example: Fendrel Industrial up-and-out call with strike $80 and barrier $95. Near spot $93, delta may be 0.75 but gamma surges as traders anticipate the knockout. A $1 move to $94 could erase most option value, producing a ~$0.70 loss per contract despite bullish direction. Vega often flips sign near barriers — a vol increase can raise the knock-out probability and hurt the position.

```mermaid
flowchart TD
    A[Spot near barrier] --> B[Gamma spike]
    A --> C[Delta discontinuity]
    A --> D[Vega sign flip]
    B --> E[Hedging cost explodes]
    E --> F[Trader widens bid-ask]
```

Risk managers at Larkspire Exotics use barrier-shift techniques, shifting the book's internal barrier 2-5% further from the actual contractual level to avoid catastrophic P&L swings from microstructure noise. Some desks hedge with touch options or digital replications. FRM candidates should memorize that reverse knock-outs (barrier above strike for calls) are riskiest; regular knock-outs are easier to hedge. Understanding these nonlinearities is critical for structured product risk managers.

How do Greeks behave for knock-in and knock-out barrier options?

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