Suppose you are given the following prices Current stock pri

Suppose you are given the following prices: Current stock price is $42. Call(X=35)=$4.5, Call(X=40)=$3, T=1 year, risk-free interest rate=5%. All options are American type. Is there a profit opportunity based on these prices? If so, what would you do? If not, why not?

Solution

Current Stock Price = $42

Call premium at Strike = $35 : $4.5

Call premium at Strike = $40 : $3

Now call option is in the money when the market price is greater than the strike price.

So if we see, both the options are already in the money options, and for in the money options, call price should be atleast equals to the difference by which the call is in the money, otherwise there will be arbitrage opportunity will exist.

When X=$35, Difference in the stock price and strike price = 42-35 =$7

So call option price should be atleast $7

Call option price in market = $4.5

So we should buy the call option and should excercise it right away to make instant profit of $2.5 per share. We can exercise it any time since it is American option.

So $2.5 per share can be invested back in the market@ 5%

So after 1 year, we will have profit of $2.625 per share

In 2nd case,

When X=$40, Difference in the stock price and strike price = 42-40 =$2

Call price in the market = $3

So it is correctly priced and we should not buy it because there is no profit opportunity here.