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# Options Pricing Model: European options

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Question 4: 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?

Question 5: 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.

Question 6: 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?

Question 13: 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?

Question 15: 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 following questions in excel with explanations please

#### Solution Preview

Question 4
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?

S0= 50
X= 55
r= 4%
T= 6/12 years

Lower bound=
p >= Xe-rT - S0 = 3.91 =55*EXP(-4%*6/12)-50

Question 5
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.