Show me step by step how to do these problems? Also, please give solutions with a 3-4 decimal place. Explaination would be appreciated.
1. A put option on a stock with a current price of $39 has an exercise price of $41. The price of the corresponding call option is $3.15. According to put-call parity, if the effective annual risk-free rate of interest is 6% and there are three months until expiration, what should be the value of the put?
Value of the put:
2. A call option on Jupiter Motors stock with an exercise price of $65 and one-year expiration is selling at $7. A put option on Jupiter stock with an exercise price of $65 and one-year expiration is selling at $6.5. If the risk-free rate is 9% and Jupiter pays no dividends, what should the stock price be?
Stock price $
3. You are considering purchasing a put option on a stock with a current price of $44. The exercise price is $47, and the price of the corresponding call option is $3.55. According to the put-call parity theorem, if the risk-free rate of interest is 5% and there are 90 days until expiration, the value of the put should be ____________.
A. $3.55
B. $5.99
C. $6.11
D. $7.58