Strategy #0000000003 · Options and payoff structures
Bull call vertical spread
Trade a measured view with a defined cost and a defined ceiling.
Buy one option and sell another of the same type and expiry at a different strike. The short leg helps pay for the long leg, while capping both risk and reward.
Three ways in
Understand the story. Then inspect the risk.
Start with a familiar situation, check the payoff, then test how the numbers change.
The idea · in two minutes
Jack and Rose split the lift ticket: cheaper ride, fixed top floor.
Jack expects EUR/USD to rise, but thinks a moonshot is unlikely. He buys a call at 1.1500 and sells Rose another call at 1.1730. The net debit is 0.0075, or $750 per standard €100,000 notional. Rose calls it “the premium economy seat”: cheaper than buying the first call alone, but with a ceiling.
Below 1.1500, both calls expire worthless and Jack loses the $750 debit. Between 1.1500 and 1.1730, the spread gains as EUR/USD rises. Above 1.1730, the short call gives back further gains: the maximum profit is the 0.0230 strike width less the 0.0075 debit, or $1,550 per standard notional.
The vertical spread turns “I think it will rise” into “I think it will rise this far, and I will pay this much to express that view”. The ceiling is not a bug hidden in the terms; it is the bargain Jack made with Rose.
| Underlying at expiry | Underlying P/L | Options P/L | Total | What happens |
|---|---|---|---|---|
| 1.1300 | $0.0000 | −$0.0075 | −$7.50 | The maximum loss is the opening debit. |
| 1.1500 | $0.0000 | −$0.0075 | −$7.50 | No move means the debit is lost. |
| 1.1600 | +$0.0100 | −$0.0075 | +$2.50 | The spread gains between the two strikes. |
| 1.1800 | +$0.0230 | −$0.0075 | +$15.50 | Above the short strike, profit is capped. |
Illustrative figures only. They exclude fees, tax, financing and other costs unless stated. They are not live prices or a recommendation.
The mechanics · payoff and exposure
For a bull call spread, expiry payoff is the call-spread intrinsic value less the debit. Break-even is the long strike plus debit; maximum profit is spread width less debit.
K₁ is the lower, long-call strike; K₂ is the higher, short-call strike; D is the net debit paid.
Greeks: the directional intuition
- Delta
- Measures first-order sensitivity to the underlying price.
- Gamma
- Measures how quickly delta changes as the underlying moves.
- Theta
- Captures the effect of time passing, all else equal.
- Vega
- Measures sensitivity to implied volatility.
For a bull call spread, expiry payoff is the call-spread intrinsic value less the debit. Break-even is the long strike plus debit; maximum profit is spread width less debit.
Practical context · published observations
Bull call spread · mean P/L per debit: read the record with its caveats.
The chart uses the published figures or explicitly labelled study inputs below. A historical index or model replay is not the same as an investor’s realised account return.
This is a modelled replay using stated assumptions, not observed option fills. Source ↗ · Methodology ↗
What if the underlying expires here?
Adjust the inputs to see a theoretical expiry payoff. The starting values are teaching assumptions, not live quotes.
Calculation model: This simplified expiry model excludes early close-out value, assignment timing, funding, tax, dividends and transaction costs.
Variants · same family, different risk levers
Five close relatives change direction, premium flow or strike design.
Bull and bear call/put spreads share defined-risk shapes. Arbitrage constraints are a price-checking framework, not the same directional trade.
| Related strategy | Relationship | What changes | New cost or risk |
|---|---|---|---|
| Bull put spread | Same direction · credit structure | Sell a higher-strike put and buy a lower-strike put to express a bullish view for a net credit. | For a common out-of-the-money spread, credit is smaller than width. Maximum loss is width less credit; a high win rate does not guarantee positive expectancy. |
| Bear call spread | Opposite direction · credit structure | Sell a lower-strike call and buy a higher-strike call, expecting the underlying to stay below the short strike. | The credit is earned against a finite but potentially large spread-width risk; a sharp rise can approach maximum loss quickly. |
| Bear put spread | Opposite direction · debit structure | Buy a higher-strike put and sell a lower-strike put to express a measured bearish view for a debit. | Loss is limited to the premium and profit to the strike width; a fall below the lower strike adds no further gain. |
| Vertical-spread design | Strike-design research | Study how width, moneyness and delta choices change spread cost and payoff. | A wider spread can add upside but usually costs more and ties up more capital; a paper’s setting is not a universal optimum. |
| Static arbitrage from spread violations | Related research · price constraints | Check same-expiry option prices against strike monotonicity and convexity, then identify or repair violations. | This is about price-surface quality, not an ordinary bull call trade; an apparent violation may not be executable. |
The source groups five related entries together. The bull call spread is this page’s baseline; the others are parallel structures or adjacent research.
Read beyond the summary
References
Primary sources and research used to describe the strategy and its limits.
- 01Cboe, “Common Options Trading Strategies” — bull call / bear put spread payoff and examples.official
- 02Options Clearing Corporation, Characteristics and Risks of Standardized Options.official
- 03Board of Governors of the Federal Reserve System, U.S. Dollars to Euro Spot Exchange Rate [DEXUSEU], via FRED.data
- 04Chaput & Ederington (2003), “Option Spread and Combination Trading,” Journal of Derivatives.research
- 05Chaput & Ederington (2005), “Vertical Spread Design,” The Journal of Derivatives.research
- 06Cohen, Reisinger & Wang (2020), “Detecting and Repairing Arbitrage in Traded Option Prices,” Applied Mathematical Finance.research
- 07Kakushadze & Serur (2018), 151 Trading Strategies, §§2.6–2.9. Author version.source