Option Strategies and Payoff Combinations › Vertical Spreads

Vertical spreads involve buying and selling options of the same type (both calls or both puts) with the same expiration but different strike prices. The "vertical" terminology comes from how options are traditionally displayed, with strikes listed vertically.

Spreads reduce both the cost and the profit potential compared to single options. They're useful when you have a directional view but want to limit your capital outlay or when you believe the underlying will move to a certain level but not beyond it.

A bull call spread profits from a moderate rise in the underlying price. You construct it by:

1. Buying a call at a lower strike price $K_1$
2. Selling a call at a higher strike price $K_2$ (where $K_2 > K_1$)

Both options have the same expiration. The premium received from selling the higher-strike call partially offsets the cost of buying the lower-strike call, reducing your net investment.

The combined payoff is:

$$\text{Bull\_Call\_Spread} = \max(S_T - K_1, 0) - \max(S_T - K_2, 0) - (C_1 - C_2)$$

where:

• $S_T$: stock price at expiration
• $K_1$: lower strike price (long call)
• $K_2$: higher strike price (short call), where $K_2 > K_1$
• $C_1$: premium paid for the $K_1$ call
• $C_2$: premium received for the $K_2$ call
• $(C_1 - C_2)$: net debit paid to establish the spread
• $\max(S_T - K_1, 0)$: payoff from the long call
• $-\max(S_T - K_2, 0)$: obligation from the short call

The spread works by buying upside exposure at $K_1$ and selling away upside above $K_2$. The short call partially finances the long call, reducing the net cost. When the stock rises above $K_2$, both options are in-the-money and their intrinsic values offset each other, capping the spread's profit at the difference between strikes minus the net cost. This capping mechanism is essential to understand: above $K_2$, every additional dollar the stock rises adds one dollar to your long call's value but also adds one dollar to your short call's obligation, netting to zero additional profit.

Analyzing the payoff structure at different price levels shows three regions with different outcomes.

Below $K_1$ ($S_T \leq K_1$): Both calls are out-of-the-money and expire worthless. The loss is the net debit paid. This represents the worst-case scenario where your bullish view was entirely wrong. The consolation is that your loss is limited to what you paid to enter the position.

Between $K_1$ and $K_2$ ($K_1 < S_T < K_2$): The long call at $K_1$ is in-the-money with value $S_T - K_1$, while the short call at $K_2$ remains worthless. Profit increases linearly. This is the range where your directional bet is paying off. Each dollar increase in the stock price adds a dollar to your profit.

Above $K_2$ ($S_T \geq K_2$): Both calls are in-the-money. The long call gains $(S_T - K_1)$ but the short call loses $(S_T - K_2)$, netting to a constant $(K_2 - K_1)$. You have reached maximum profit. Further stock appreciation doesn't help you because you sold away that upside when you established the short call.

This creates three distinct regions:

$$\text{Profit} = \begin{cases} -(C_1 - C_2) & \text{if } S_T \leq K_1 \\ S_T - K_1 - (C_1 - C_2) & \text{if } K_1 < S_T < K_2 \\ (K_2 - K_1) - (C_1 - C_2) & \text{if } S_T \geq K_2 \end{cases}$$

where:

• $-(C_1 - C_2)$: net debit paid (maximum loss when both calls expire worthless)
• $S_T - K_1 - (C_1 - C_2)$: long call intrinsic value minus net cost (linear profit zone)
• $(K_2 - K_1) - (C_1 - C_2)$: maximum profit when both calls are in-the-money

Each region represents a different outcome. The first region represents complete failure of your bullish thesis. The second region shows partial success where your view was directionally correct. The third region represents full success where the stock moved enough to maximize your profit.

The bull call spread caps maximum profit, sacrificing unlimited upside in exchange for reduced capital outlay. This net cost also represents the maximum loss, creating a defined-risk profile that simplifies position sizing. The breakeven point falls between the two strikes, requiring a moderate move to achieve profitability. This structure trades unlimited profit potential for lower cost and defined risk parameters.

A bear put spread is the bearish counterpart to the bull call spread. You construct it by:

1. Buying a put at a higher strike price $K_2$
2. Selling a put at a lower strike price $K_1$ (where $K_1 < K_2$)

The strategy profits when the underlying price falls moderately. The construction mirrors the bull call spread but uses puts instead of calls and profits from downward price movement rather than upward movement. The put you buy at the higher strike gains value as the stock falls, while the put you sell at the lower strike limits your profit potential but reduces the cost of the position.

Why use spreads instead of single options? The key tradeoff is cost versus profit potential.

Suppose we are bullish and want to buy a call option. A single at-the-money call might cost $8. If we are right and the stock rises $15 above the strike, our profit is $7. If wrong, our loss is $8. With a bull call spread, we might pay $5 net after selling the higher-strike call. If we are right and the stock rises beyond the upper strike, our profit is capped at perhaps $5 (the spread width minus the net cost). But if wrong, our loss is only $5 instead of $8.

The spread has a better risk/reward ratio in the sense that both the maximum loss and maximum gain are reduced, but the breakeven point is also lower.

Spreads are particularly attractive when implied volatility is high, making single options expensive. By selling an option as part of the spread, you partially offset the inflated premium you're paying.