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 $3a.[2] What is the name of this option strategy?b.[3] Why would you use such a strategy?c.[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)d.[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

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

The name of this option strategy is bull call spread.

The investor is bullish on the stock and thinks it may go above $25. So, he buys the call option with strike price of $25. But, he also thinks that the stock may not go above $30. So, he sells the call option with a higher strike price of $30. Selling 30 strike call option reduces the cost of the long call option.

Long Call Profit = max(St - X1, 0) - Premium paid

Long Call Profit = max(St - 25, 0) - 5

Short Call Profit = -max(St - X2, 0) + Premium received

Short Call Profit = -max(St - 30, 0) + 2

Strategy Profit = Long Call Profit + Short Call Profit

Strategy Profit = max(St - 25, 0) - 5 - max(St - 30, 0) + 2

Screenshot with formulas

This strategy is better if the stock price expires does not go above $30

This strategy is worst if the stock price goes above $30 than buying the underlying asset because we would not benefit from the strategy if the stock price goes above $30.