Question

1. a) A call option with a strike price of $68 on a stock selling at $82 costs $15.3. What are the call option’s intrinsic and time values?

2. b) A put option on a stock with a current price of $37 has an exercise price of $39. The price of the corresponding call option is $2.85. According to put-call parity, if the effective annual risk-free rate of interest is 4% and there are three months until expiration, what should be the price of the put?

3. c) A call option on Jupiter Motors stock with an exercise price of $75 and one-year expiration is selling at $6. A put option on Jupiter stock with an exercise price of $75 and one-year expiration is selling at $4.0. If the risk-free rate is 10% and Jupiter pays no dividends, what should the stock price be? show all steps and formula plz

Answer 1

a) A call option with a strike price of $68 on a stock selling at $82 costs $15.3. What are the call option’s intrinsic and time values?

Call value = 15.3 = Intrinsic value + time value

Intrinsic value = S - K = 82 - 68 = $ 14

Time value = Call value - intrinsic value = 15.3 - 14 = $ 1.30

b) A put option on a stock with a current price of $37 has an exercise price of $39. The price of the corresponding call option is $2.85. According to put-call parity, if the effective annual risk-free rate of interest is 4% and there are three months until expiration, what should be the price of the put?

C – P = S – K / ( 1 + r)^T.

Hence,  P = C - S + K / ( 1 + r)^T = 2.85 - 37 + 39 / (1 + 4%)^3/12 = $ 4.47

c) A call option on Jupiter Motors stock with an exercise price of $75 and one-year expiration is selling at $6. A put option on Jupiter stock with an exercise price of $75 and one-year expiration is selling at $4.0. If the risk-free rate is 10% and Jupiter pays no dividends, what should the stock price be? show all steps and formula plz

C – P = S – K / ( 1 + r)^T.

Hence, S = C - P + K / ( 1 + r)^T = 6 - 4 + 75 / (1 + 10%)¹ = $ 70.18