Question

The price of a stock, which pays no dividends, is $30 and the strike price of a one year European call option on the stock is $25. The risk-free rate is 4% (continuously compounded). Which of the following is a lower bound for the option such that there are arbitrage opportunities if the price is below the lower bound and no arbitrage opportunities if it is above the lower bound?

A. $5.00
B. $5.98
C. $4.98
D. $3.98
E. $5.34

Answer 1

B. $5.98

Step-by-step explanation:

Calculation to determine the lower bound for the option

Using this formula

Lower Bound =Stock Price -Strike Price*e^(-rt)

Where,

Time years =1

Stock Price =$30

Strike Price =$25

Let Plug in the formula

Lower Bound=$30-$25*e^(-4%*1)

Lower Bound =5.98

Therefore the lower bound for the option is 5.98