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Vertical call-spread payoff by region

A long lower-strike call minus a short higher-strike call pays zero, then rises linearly, then reaches the strike-width cap.

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Define the compatible position

Use one long call at K1 and one short call at K2, with K1<K2, the same underlying, expiry and represented quantity. Let the positive net premium debit be d per underlying unit.

Subtract the correct holder expressions

Below K1 neither holder payoff is positive. Between strikes only the lower-strike call pays. Above K2 both pay, leaving K2−K1.

hspread=max⁡(S−K1,0)−max⁡(S−K2,0)h_{spread}=\max(S-K_1,0)-\max(S-K_2,0)

The writer leg is subtracted before the premium debit.

Attach the net premium

For a debit d between zero and the strike width, simple profit ranges from −d to (K2−K1)−d, with crossing at K1+d. Those bounds rely on the specified net debit; unsupported prices outside that interval need a separate consistency check.

Keep time and contract matching explicit

This is an expiry payoff formula. It does not determine the current option premiums, return on margin or an early-exercise path. Different expiries form another structure and cannot be summarized by this single-price terminal expression.

Further references