Bull Call Spread

Core Thesis

A Bull Call Spread buys upside with defined risk and controlled carry. You pay a debit for convex bullish exposure while financing part of the long call cost by selling a higher strike call.

Structure

• Long call at lower strike $K_1$.
• Short call at higher strike $K_2$.
• Same expiration; net debit $D$.

Expiration Payoff Mathematics

$$\Pi_T = \max(S_T-K_1,0) - \max(S_T-K_2,0) - D$$

• Max loss: $D$.
• Max profit: $(K_2-K_1)-D$.
• Break-even: $K_1 + D$.

Greek Profile

• Positive delta and positive gamma, but both capped as spot approaches $K_2$.
• Theta drag is smaller than a naked long call due to the short leg.
• Net vega is positive but reduced; IV shocks matter less than single-leg calls.

Strike and Tenor Design

• Set $K_1$ near where you want directional sensitivity.
• Set $K_2$ near target price where you are willing to cap gains.
• Typical tenor 20-60 DTE for swing positioning; longer tenor if thesis requires time.

Management Framework

• Take profits when most of max value is realized; late-stage gamma is not always worth holding.
• If thesis strengthens and price approaches $K_2$ early, roll short strike higher/out.
• If thesis invalidates, close early to preserve residual value.

Failure Modes

• Choosing too narrow a width and capping upside too early.
• Entering when IV is rich without sufficient expected move.
• Holding to expiration with little incremental edge while assignment frictions rise.

Practical Checklist

• Is forecast move large enough to exceed $K_1 + D$?
• Is capped upside at $K_2$ consistent with your target distribution?
• Is debit risk sized as a full-loss scenario?