Question

Consider the following option portfolio whose components have the same maturity:

• A long call option with a strike of $25 and a premium of $5

• A short call option with a strike of $30 and a premium of $3

1. [2] What is the name of this option strategy?

2. [3] Why would you use such a strategy?

3. [10] Draw the profit graph of this portfolio at expiration as a function of the spot price of

   the underlying asset (label as much as you can to ensure the diagram is to scale)

4. [5] Considering only the total profit, identify when this strategy does better and when it

   does worse than simply buying the underlying asset

Answer 1

Long call option with strike of $25 (X1) and a premium of $5 (C1)

Short call option with strike of $30 (X2) and a premium of $3 (C2)

The name of this strategy is a bull call spread.

The investor is bullish about the stock, so he buys a call option with strike $25. At the same time the investor thinks that the stock may not go above $30. So, he sells a call option with strike $30.

Profit of a long call option = max(St - X1, 0) - C1 = max(St - 25, 0) - 5

Profit of a short call option = -max(St - X2, 0) + C2 = -max(St - 30, 0) + 3

Profit of bull call spread = Profit of a long call option + Profit of a short call option

Profit of bull call spread = max(St - 25, 0) - 5 + (-max(St - 30, 0) + 3)

The strategy does best when the stock expires at $30 or below $23

The strategy does worst when the stock expires significantly above $30 or when it expires in the range of $23 and $30