Question

Warnes Motors' stock is trading at $20 a share. Three-month call options with an exercise price of $20 have a price of $1.50. Which of the following will occur if the stock price increases 10% to $22 a share?

a.The price of the call option will increase by $2.
b.The price of the call option will increase by less than $2, but the percentage increase in price will be more than 10%.
c.The price of the call option will increase by less than $2, and the percentage increase in price will be less than 10%.
d.The price of the call option will increase by more than $2.
e.The price of the call option will increase by more than $2, but the percentage increase in price will be less than 10%.

Answer 1

B. The price of the call option will increase by less than $2, but the percentage increase in price will be more than 10%.

Step-by-step explanation:

Given

Trading price = $20

Exercise price of call option = $20

Call option price = $1.50

Price increment = 10% to $22

It's not be noted that the discounted present value of a price of an option is represented by its expected payoff.

An increment of $2 in stock price attracts an increment of more than $2 in the payoff option.

Having highlighted that, it's also to be noted that the increment in expected payoff will be by an amount less than $2 and same with present value because the possibility is less than 1. So, the price of the option will increase by less than $2.

Moving to the percentage increase;

This will be larger than 10%.

This is because when stock price increases by 10%, the value of the option will increase by more than 10%.