# Options Pricing Model: European options

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

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#### Solution Preview

Please see attached file

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?

Answer: $3.91

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.

Answer: $3.65

We will use put-call parity condition ...

#### Solution Summary

Calculates the price of options, lower bound for the value of options, risk neutral probability etc.