If the risk-free interest rate is 8% per year, what must be the price of a 3-month put option on P. U.T. T. stock at an exercise price of $90

(a) The price of a 3-month put option on P.U.T.T. stock at an exercise price of $90 is $5.28.

(b) The stock price will have to move in either direction by $12.24 for you to make a profit on your initial investment when time value of money is NOT taken into consideration. However, Therefore, the stock price will have to move in either direction by $12.52 for you to make a profit on your initial investment when time value of money is taken into consideration.

Explanation:

Note: This question is not complete. The complete question is therefore provided before answering the question as follows:

The explanations to the answers are now given as follows:

a. If the risk-free interest rate is 8% per year, what must be the price of a 3-month put option on P.U.T.T. stock at an exercise price of $90? (The stock pays no dividends.)

This can be computed using put-call parity theorem (PCPT) which is employed when we know the price of either put or call option as well as the current stock price, exercise price, interest rate, and the option period.

PCPT formula is given as follows:

VS + P – C = E / (1 + r)^t ……………………………….. (1)

Where, for this question;

VS = Current price of the stock = $90

P = Price of put option = ?

C = Price of call option = $7

E = Exercise price = $90

r = risk-free interest rate = 8%, or 0.08

t = period of option = 3 months / 12 months = 0.25

Substituting the values into equation (1) and solve P, we have:

$90 + P -  $7 = $90 / (1 + 0.08)^0.25

$83 + P = $90 / 1.08^0.25

$83 + P = $90 / 1.01942654690827

$83 + P = $88.2849286914817

P = $88.2849286914817 - $83

P = $5.28

Therefore, the price of a 3-month put option on P.U.T.T. stock at an exercise price of $90 is $5.28.

b. A straddle would be a simple options strategy to exploit your conviction about the stock price’s future movements. How far would it have to move in either direction for you to make a profit on your initial investment?

To determine this, we have to compute the total cost of the straddle. Since a straddle option refers to the purchase of both a put and a call on the stock, the total cost of the straddle can be calculated as follows:

Total cost of the straddle = Price of the put option + Price of the call option ………….. (2)

Since Price of put option is $5.24 as computed in part a and the price of a call option is $7 as already given in the question, we substitute these into equation (2) and have:

Total cost of the straddle = $5.28 + $7 = $12.28

Therefore, the stock price will have to move in either direction by $12.24 for you to make a profit on your initial investment when time value of money is NOT taken into consideration.

To account for the time value of money, we compute the future value (FV) of the Total cost of the straddle as follows:

FV of the Total cost of the straddle = Total cost of the straddle / (1 + r)^t ………………….. (3)

Where;

Total cost of the straddle = $12.28

r = risk-free interest rate = 8%, or 0.08

t = time of the put option in a year = 3 months / 12 months = 0.25

Substituting the values into equation (3), we have:

PV of the Total cost of the straddle = $12.28 * (1 + 0.08)^0.25

PV of the Total cost of the straddle = $12.28 * 1.08^0.25

PV of the Total cost of the straddle = $12.28 *1.01942654690827

PV of the Total cost of the straddle = $12.52

Therefore, the stock price will have to move in either direction by $12.52 for you to make a profit on your initial investment when time value of money is taken into consideration.

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