A one-year call option on a stock with a strike price of $30 costs $3; a one-year put option on the stock with a strike price of $30 costs $4. Suppose that a trader buys two call options and one put option. The breakeven stock price above which the trader makes a profit is: $35 $40 $30 $36
Question
A one-year call option on a stock with a strike price of 3; a one-year put option on the stock with a strike price of 4. Suppose that a trader buys two call options and one put option. The breakeven stock price above which the trader makes a profit is:
$35
$40
$30
$36
Solution
The correct answer is $36.
Here's the reasoning behind this choice:
The trader buys two call options and one put option. The total cost of the options is (2*4 = $10.
For the trader to break even, the total payoff from the options must be equal to the total cost of the options.
The payoff from a call option is max(0, S - K), where S is the stock price and K is the strike price. Since the trader has two call options, the total payoff from the call options is 2 * max(0, S - $30).
The payoff from a put option is max(0, K - S). Since the trader has one put option, the total payoff from the put option is max(0, $30 - S).
Setting the total payoff equal to the total cost gives us:
2 * max(0, S - 30 - S) = $10
Solving this equation for S gives us S = 36.
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