Question

Suppose you are given the following prices: Current stock price is $41. Call(X=40)=$4.5, Call(X=45)=$3, Put(X=$45)=$3, Put(X=$40)=$2, 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?

Answer 1

Since the options are american type they can be exercised any time before expiration.

Call profit = max[S ?X,0]?future value of premium

Where S=curent stock price

X= Strike price

Future price of premium for $4.5= $4.5(1+risk free rate)

= $4.5(1.05)= 4.73

Future price of premium for $3= $3(1.05)= $3.15

Future price of premium for $2= $2(1.05)= $2.1

1) Call profit = max[$41 ?$40,0]? $4.73

= $1- $4.73= -$3.73 (Hence it is a loss)

2) Call profit = max[$41 ?$45,0]? $3.15

= $0- $3.15= -$3.15 ( Hence it is a loss)

Put profit = max[X ?S,0]?future value of premium

Where S=curent stock price

X= Strike price

3) Put profit = max[$45 ?$41,0]? $3.15

= $4- $3,15 = $ 0.85 ( Hence it is a profit)

4) Put profit = max[$40 ?$41,0]? $2.1

= $0- $2.1= -$2.1 ( Hence it is a loss)

Therefore there is an profit of $0.85 in Put option when the strike price is $45, and all the other three scenarios leads to a loss.