Vertical Spread Construction From Two Options

What Makes a Spread Vertical?

An option spread combines positions in options so that the total result depends on the payoffs of multiple legs. A vertical spread consists of positions in two options on the same underlying asset, with the same expiration date and option type, but different strike prices. The positions have opposite signs: one option is held long and the other is held short. Unless stated otherwise, the examples here use equal quantities of the two options.

“Vertical” refers to changing the strike while keeping the expiration fixed. In this tutorial, the task is to construct the two legs and calculate their combined payoff at expiration. The payoff is not the same as the investment’s profit: it excludes any premiums paid or received when the options were entered.

Definition: A one-to-one vertical spread uses one long and one short option of the same type, on the same underlying asset, with the same expiration date and different strikes. Its expiration payoff is the sum of the expiration payoffs of the two option positions, using a negative sign for a short position.

Let $S_T$ be the underlying asset’s price at expiration $T$, and let $K$ be an option’s strike. For one unit of the underlying, a call’s expiration payoff is $\max(S_T-K,0)$, and a put’s expiration payoff is $\max(K-S_T,0)$. These are intrinsic payoffs at expiration, before accounting for the option’s initial premium.

The calculations below assume both options are held to the same expiration, have identical contract multipliers, and refer to the same underlying. No probability distribution for $S_T$ is needed: each payoff is conditional on the stated expiration price. Interest rates and mortality are not used in these terminal-payoff calculations; no mortality assumption applies.

Writing the Two Legs as a Position

Use a positive sign for a long option and a negative sign for a short option. For calls with strikes $K_L$ and $K_H$, where $K_L<K_H$, the long-lower-strike, short-higher-strike position has payoff

\max(S_T-K_L,0)-\max(S_T-K_H,0).

Reversing the positions reverses the sign of the combined payoff. The strike order does not determine which option is long: always record the position in each leg explicitly.

For puts, the payoff from a long higher-strike put and a short lower-strike put, with $K_L<K_H$, is

\max(K_H-S_T,0)-\max(K_L-S_T,0).

Again, reversing the legs changes the sign. These formulas follow from adding the payoff of each option separately. They are not formulas for net profit because the initial option premiums have not been included.

Why the Combined Formula Works

The addition rule is a consequence of how separate contracts settle. If one long option pays $A$ at expiration and one short option requires a payment of $B$, the position’s net expiration payoff is $A-B$. There is no need to infer a new payoff rule for the spread; calculate each leg and add the signed amounts.

For example, consider a long call at $K_L$ and a short call at $K_H$, with $K_L<K_H$. If $S_T\leq K_L$, both calls have zero payoff. If $K_L<S_T\leq K_H$, only the lower-strike call has a positive payoff, equal to $S_T-K_L$. If $S_T>K_H$, both calls have positive payoffs, and the difference is

$$ (S_T-K_L)-(S_T-K_H)=K_H-K_L. $$

The subtraction cancels the common change in the underlying price once both calls are in the money. This case check justifies the combined max-function formula: the portfolio payoff is the sum of the two leg payoffs at every possible expiration price.

Record the contract details.
Confirm the underlying, expiration date, option type, both strikes, position in each leg, quantities, and contract multiplier.

Calculate each option’s payoff.
For a call, use $\max(S_T-K,0)$; for a put, use $\max(K-S_T,0)$. A long position takes that payoff, and a short position takes its negative.

Add and scale.
Add the signed leg payoffs per unit. Then multiply by the number of spreads and the contract multiplier, if a total dollar payoff is requested.

Worked Payoffs From Call Legs

Worked Example: Long Lower-Strike Call, Short Higher-Strike Call

A hypothetical investor holds one long call with strike $K_L=\$40$ and one short call with strike $K_H=\$47$. Both options are on the same asset and expire on the same date. The contract multiplier is 100 shares, and the position is one spread. Find the payoff when $S_T=\$35$, $\$43$, and $\$52$.

The interest rate is not used because only the expiration payoff is requested; no discounting is performed. No mortality assumption applies. No distribution is assumed for $S_T$; the three prices are specified scenarios. Premiums and transaction costs are excluded.

Method. Calculate the payoff of each call using $\max(S_T-K,0)$, apply a negative sign to the short call, and add. The per-share position payoff is

\max(S_T-40,0)-\max(S_T-47,0).

At $S_T=\$35$, the long call pays $\max(35-40,0)=0$, and the short call has payoff $-\max(35-47,0)=0$. The combined payoff is $0+0=\$0$ per share, or $0\times100=\$0$ for the contract.

At $S_T=\$43$, the long call pays $\max(43-40,0)=\$3$, and the short call has payoff $-\max(43-47,0)=0$. The combined payoff is $\$3+0=\$3$ per share, or $3\times100=\$300$.

At $S_T=\$52$, the long call pays $\max(52-40,0)=\$12$, and the short call has payoff $-\max(52-47,0)=-\$5$. The combined payoff is $\$12-\$5=\$7$ per share, or $7\times100=\$700$.

Check. At $\$52$, both calls are in the money, so their common $S_T$ component cancels: $(52-40)-(52-47)=12-5=7$. This agrees with the leg calculation. The common mistake this method avoids is treating the short call’s payoff as a positive amount instead of a liability.

Worked Payoffs From Put Legs

Worked Example: Long Higher-Strike Put, Short Lower-Strike Put

A hypothetical account holds three spreads. Each spread consists of one long put with strike $K_H=\$65$ and one short put with strike $K_L=\$58$, both on the same asset and with the same expiration. Each option contract has a multiplier of 100. Find the total expiration payoff if $S_T=\$50$, $\$61$, or $\$70$.

The interest rate is not used, and no discounting is performed. No mortality assumption applies. No distribution is assumed; each $S_T$ is a specified scenario. Premiums and transaction costs are excluded.

Method. A long put pays $\max(K-S_T,0)$; a short put has the negative of that payoff. Thus, per share, one spread pays

\max(65-S_T,0)-\max(58-S_T,0).

At $S_T=\$50$, the long put pays $\max(65-50,0)=\$15$. The short put contributes $-\max(58-50,0)=-\$8$. The spread payoff is $15-8=\$7$ per share. Three spreads with a multiplier of 100 cover $3\times100=300$ shares, so the total is $7\times300=\$2{,}100$.

At $S_T=\$61$, the long put pays $\max(65-61,0)=\$4$, while the short put pays $-\max(58-61,0)=0$. The spread payoff is $\$4$ per share, for a total of $4\times300=\$1{,}200$.

At $S_T=\$70$, both puts have zero payoff because both strikes are below the underlying price. The total payoff is $0\times300=\$0$.

Check. At $\$50$, the long put’s $\$15$ payoff exceeds the short put’s $\$8$ liability by $\$7$ per share. A common error is to ignore the short put when it is in the money; its payoff must be subtracted even though the position is short.

Reversing the Position Reverses the Sign

Worked Example: Short Lower-Strike Call, Long Higher-Strike Call

A hypothetical investor holds one short call at $K_L=\$44$ and one long call at $K_H=\$52$. They have the same underlying and expiration. The multiplier is 100 shares, and the investor holds two spreads. Calculate the total payoff at $S_T=\$40$, $\$48$, and $\$60$.

The interest rate is not used, and no discounting is performed. No mortality assumption applies. No probability distribution is assumed; the three expiration prices are given scenarios. Premiums and transaction costs are excluded.

Method. The short lower-strike call contributes $-\max(S_T-44,0)$, and the long higher-strike call contributes $\max(S_T-52,0)$. Per share, one spread pays

-\max(S_T-44,0)+\max(S_T-52,0).

At $S_T=\$40$, the short call contributes $-\max(40-44,0)=0$, and the long call contributes $\max(40-52,0)=0$. The combined payoff is zero.

At $S_T=\$48$, the short call contributes $-\max(48-44,0)=-\$4$, and the long call contributes $\max(48-52,0)=0$. The payoff is $-\$4$ per share. Two spreads with multiplier 100 cover $2\times100=200$ shares, giving $-4\times200=-\$800$.

At $S_T=\$60$, the short call contributes $-\max(60-44,0)=-\$16$, while the long call contributes $\max(60-52,0)=\$8$. The net payoff is $-16+8=-\$8$ per share, or $-8\times200=-\$1{,}600$.

Check. The position described is the reverse of a long lower-strike, short higher-strike call position with the same strikes. Its payoff is therefore the negative of that position’s payoff at every $S_T$. The common mistake avoided here is assigning the long position to the lower strike simply because it is lower.

Payoff Is Not Profit

The formulas above calculate what the option legs pay or require at expiration. They do not include the cash exchanged when the options were purchased or sold. To calculate profit, one would also need the initial premiums and, where relevant, financing or transaction costs. Keeping payoff and profit distinct prevents an answer to an expiration-settlement question from being altered by information that does not belong in the requested calculation.

Before finalizing a vertical-spread calculation, check that the options share an underlying, expiration, and type; that the strikes are different; and that each leg’s position is correctly signed. Then verify the contract multiplier and number of spreads. If the result is requested per share, do not multiply by a contract multiplier. If a total contract payoff is requested, apply the multiplier to the combined per-share payoff.

Key takeaway: Construct the position leg by leg: use the call or put expiration-payoff formula, reverse the sign for a short option, and add. Only then apply quantities and contract multipliers. The resulting amount is expiration payoff, not profit.

Check Your Understanding

For each problem, calculate the stated expiration payoff from the option legs only. Premiums and transaction costs are excluded.

A one-spread position is long a call at $K=\$30$ and short a call at $K=\$36$, with the same underlying and expiration. What is the per-share payoff if $S_T=\$34$? (Answer: $\$4$ per share)
A one-spread position is short a call at $K=\$44$ and long a call at $K=\$50$, with the same underlying and expiration. What is the per-share payoff if $S_T=\$47$? (Answer: $-\$3$ per share)
Two spreads each consist of a long put at $K=\$72$ and a short put at $K=\$64$. Each contract has a multiplier of 100. What is the combined payoff if $S_T=\$60$? (Answer: $\$1{,}600$)
A one-spread position is long a put at $K=\$39$ and short a put at $K=\$45$, with the same underlying and expiration. What is the per-share payoff if $S_T=\$42$? (Answer: $-\$3$ per share)
Four spreads each consist of a long call at $K=\$25$ and a short call at $K=\$31$. Each contract has a multiplier of 50. What is the combined payoff if $S_T=\$28$? (Answer: $\$600$)

What You'll Learn