Gap Options: One Strike Triggers, Another Determines the Payoff
For educational purposes only; not investment advice.
Direct answer
Section titled “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.
Trigger strike versus payoff strike
Section titled “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.
A $105 trigger and $100 payoff strike
Section titled “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$0under 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.
Contract and valuation checklist
Section titled “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
K1andK2; 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.
Common misconceptions
Section titled “Common misconceptions”- “Gap option means protection against overnight gaps.” The name refers to the gap between trigger and payoff strikes.
- “
K1andK2are 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.