Bull call spread

Definition

A bull call spread (long call vertical, debit) buys a call at a lower strike and sells a call at a higher strike, same expiry. It expresses a rise to (at least) the short strike by expiration, with both maximum gain and maximum loss fixed at entry — direction with a defined budget, at the cost of capped upside.

How it works / structure

• Legs: +1 call at K1, −1 call at K2 (K2 > K1), same expiry.
• Cost: net debit D (long leg premium − short leg premium).
• Payoff at expiry: below K1 lose D; above K2 gain (K2 − K1) − D; between, gain (S − K1) − D. Breakeven K1 + D.
• Parameters (engine-executable): long-strike placement (ATM vs slightly ITM/OTM by delta), width K2 − K1, DTE, entry-price rule (max debit as % of width — debit/width is the position’s implied probability price), exit rules (mgmt-profit-target at x% of max gain, mgmt-time-based-exit before the final-week gamma zone).
• Greeks profile: net long delta, mildly long vega at entry when centered OTM; near expiry the P&L concentrates between the strikes (greek-gamma around each strike).
• Skew note: buying the lower strike and selling the higher sells the cheaper wing in equity smirks — verticals price the skew (opt-volatility-skew).

When it applies

Directional appreciation theses with a target near or beyond K2 inside the expiry window, when defined risk is preferred over stock or a naked call, and when high IV makes outright calls expensive (the short leg offsets premium richness).

Risk profile & failure modes

• Total-debit loss is the base case below K1: a modest rally that stalls under the long strike still loses 100% of the debit.
• Time is the opponent until the move happens: theta drains the position while it waits (greek-theta) unless deep ITM.
• Max value arrives late: even far above K2, the spread trades below full width until expiry approaches — early exits capture only part of the theoretical gain (a common expectation error, labeled folklore when stated otherwise).
• Pin/assignment complexity: expiring with the underlying between strikes, or early assignment on the short leg after a dividend, changes the position’s shape (ms-expiration-exercise-assignment).

Evidence & limits

Payoff mechanics are contract arithmetic (OCC/Cboe references). No credible public study establishes that debit verticals earn excess returns as a class; outcomes are driven by the directional thesis and the entry price relative to the realized distribution. The platform grades these on replay evidence per thesis.

Falsifiable-thesis examples

Illustrations only, not signals:

• “X will close at or above K2 at expiry, putting the K1/K2 call spread at full value” — falsified by a close below K2.
• “X will reach K1 + debit (breakeven) before expiry” — falsified if the price never touches breakeven in the window.

Cross-references

• The other three verticals: strategy-bear-call-spread, strategy-bull-put-spread, strategy-bear-put-spread
• Combinations built from verticals: strategy-iron-condor, strategy-iron-butterfly
• Pricing context: opt-expected-move, opt-volatility-skew
• Management: mgmt-profit-target, mgmt-time-based-exit