Question

The price of TSC stock will be either $42 or $46 at the end of the year. Currently, T-bills yield 4.1 percent and TSC sells for $43 a share. What is the per share value of a one-year TSC call option if the exercise price is $45 per share?

Multiple Choice

• $1.03

• $.66

• $.72

• $.81

• $0

Answer 1

Current Price = $ 43. Possible Prices = $ 42 and $ 46

u = [(46 - 43) / 43] +1 = 1.06977 and d = 1-[(42-43)/43] = 0.9767

Risk-Free Rate = T-Bill Rate = Rf = 4.1 %

Therefore, Probability of Up Move in Price = [(1+Rf) - d] / [u - d] = [(1.041) - 0.9767] / [1.06977 - 0.9767] = 0.69088

Exercise Price = $ 45

If Price is $ 42, then Payoff = $ 0 and if Price is $ 46, then Payoff = (46 - 45) = $ 1

Therefore, Call Price = [0.69088 x 1 + (1-0.69088) x 0] / 1.041 = $ 0.66367 ~ $0.66

Hence, the correct option is (b)