# Gap Options: One Strike Triggers, Another Determines the Payoff

Understand the two-strike payoff of a gap option, its discontinuity at the trigger, replication intuition, contract wording, and model and counterparty risks.

Canonical: https://wiki.fcontext.com/options/gap-options/
Fact checked: 2026-07-22

> For educational purposes only; not investment advice.

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## Direct answer

A **gap option** separates the price that decides whether a payoff occurs from the strike used to calculate its amount. For a European gap Call with trigger `K1` and payoff strike `K2`, a common expiration definition is:

`payoff = (S(T) − K2) × 1[S(T) > K1]`.

A gap Put can be defined as `(K2 − S(T)) × 1[S(T) < K1]`. The indicator creates a discontinuity at `K1`: crossing the trigger can turn the entire payoff on or off. These are generally customized, embedded, or over-the-counter structures rather than ordinary standardized equity options. The confirmation—not the nickname—must define the inequality, observation, adjustment, floor, settlement, and issuer obligation.

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## Trigger strike versus payoff strike

`K1` answers **whether** the contract pays; `K2` answers **how much**. If a Call uses `K2 < K1`, activation produces an immediate positive amount of approximately `K1 − K2`, so the payoff jumps upward at the boundary. A textbook gap Call can be viewed as a vanilla Call struck at `K1` plus a cash-or-nothing Call paying `K1 − K2` when triggered. This decomposition clarifies why value depends strongly on the risk-neutral probability near `K1`.

If `K2 > K1`, the algebraic Call formula is negative for `K1 < S(T) < K2`. Some contracts permit a signed payment; others floor it at zero or define a different payoff. Never insert `max(·,0)` unless the legal terms do. Also distinguish a terminally observed gap option from a barrier product monitored continuously or on multiple dates.

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## A `$105` trigger and `$100` payoff strike

Consider a cash-settled gap Call with `K1 = $105`, `K2 = $100`, strict condition `S(T) > $105`, and multiplier `100`:

- At `S(T) = $104.99`, the trigger fails and payoff is `$0`.
- At exactly `$105.00`, payoff is `$0` under the strict `>` wording; an inclusive `≥` term would differ.
- At `S(T) = $105.01`, payoff is `($105.01 − $100) × 100 = $501`.
- At `S(T) = $120`, payoff is `($120 − $100) × 100 = $2,000`.

A `$0.02` move from `$104.99` to `$105.01` changes contract payoff by `$501`. That discontinuity creates large sensitivity to the final reference value, rounding, market disruption, and manipulation safeguards. It is not the smooth payoff of a vanilla `$100` Call.

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## Contract and valuation checklist

- Identify underlying, `K1`, `K2`, Call/Put, multiplier, expiration, exercise style, currency, and settlement.
- Copy the exact trigger inequality (`>`, `≥`, `<`, or `≤`) and any payoff floor, cap, rebate, or negative-payment provision.
- Define reference source, observation time, averaging, rounding, holiday, disruption, correction, and corporate-action rules.
- Determine whether monitoring is only at expiration or also intraday or on scheduled dates.
- Plot payoff on both sides of `K1` and `K2`; calculate the size and direction of every discontinuity.
- Test volatility, skew, jump, rate, dividend, and model assumptions; a discontinuous payoff is sensitive to probability mass near the trigger.
- Obtain independent valuation and an executable unwind quote; issuer marks may include model and distribution costs.
- Verify issuer credit, collateral, liquidity, transfer restrictions, tax, and whether OCC clearing applies.
- Do not assume a standard option hedge remains effective near the trigger or during a price gap.

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## Common misconceptions

- “Gap option means protection against overnight gaps.” The name refers to the gap between trigger and payoff strikes.
- “`K1` and `K2` are interchangeable.” They control different parts of the payoff.
- “It is just a vanilla option with another break-even.” Its payoff can jump discontinuously at the trigger.
- “The formula always floors loss at zero.” Only explicit contract language creates a floor.
- “Touching the trigger activates it.” Strict versus inclusive inequalities can change the result.
- “An option label means OCC-cleared standardized protection.” Many gap payoffs are customized issuer or bilateral obligations.

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## Related topics

- [Binary options](/options/binary-options/)
- [Barrier options](/options/barrier-options/)
- [FLEX options](/options/flex-options/)
- [Cash settlement](/options/cash-settlement/)

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## Primary sources

- [SEC: Structured Notes](https://www.sec.gov/resources-for-investors/investor-alerts-bulletins/structured-notes)
- [FINRA Regulatory Notice 12-03: Complex Products](https://www.finra.org/rules-guidance/notices/12-03)
- [OCC: Characteristics and Risks of Standardized Options](https://www.theocc.com/company-information/documents-and-archives/options-disclosure-document)