Problem 1: What is the lower bound for the price of a six-month European put option on a stock when the stock price is $50, the strike price is $55, the risk-free rate is 4% and there are no dividends?
Problem 2: The price of a European call option on a non-dividend paying stock with a strike price of $60 is $8. The stock price is $62, the risk-free rate is 4% and the time to maturity is one year. What is the price of a one year European put option with a strike price of $60 on the same stock.
Problem 3: A call and a put on a stock have the same strike price and maturity. At 10:00 am on a certain day, the price of the call is $3.50 and the price of the put is $4. At 10:01 am news reaches the market that has no effect on the stock price but increases its volatility. As a result the call price changes to $4.50. What is expected price of the put at 10:01 am?
Problem 4: Consider a six month put option on a stock with a strike price of $30. The current stock price is $30 and over the next six months it is expected to rise to $34 or fall to $27. The risk-free interest rate is 4%. What is the risk-neutral probability of the stock rising to $34?
Problem 5: Consider a six month put option on a stock with a strike price of $30. The current stock price is $30 and over the next six months it is expected to rise to $34 or fall to $27. The risk-free interest rate is 4%. What is the value of the put?
Complete the given questions in excel with explanations please.