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 $.81 $0 $.72 $.66
Let the probability of price UP be "X" so probability of price down is (1-x)
Spot price :[PU*Pu+PD*Pd] /(1+i)
43 = [(46*X)+ 42(1-X)]/(1+.041)
43 *1.041 = 46X +42 -42X
44.763 = 4X +42
44.763 -42 = 4X
X = 2.763/4
= .69075 or 69.075%
Probability of price UP = 69.075 % so probability of price down = 1-.69075 = 30.925%
After one year :
If price is | payoff | probability | payoff *probability |
42 | not exercised since exercise price is higher than spot price | 30.925% | 0 |
46 | 46-45 =1 | 69.075% | 1*.69075=.69075 |
Total payoff in one year | .69075 |
Value of option today = .69075/(1+.041)= $ .6635 (rounded to .66)
correct option is "E"
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