# 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.

1) Conduct research on two different models used to price call options.

1) Conduct research on two different models used to price call options. Detail each model in a Word document and focus on comparing and contrasting the models.

2) Consider a two-period, two-state world. Let the current stock price be $60 and the risk-free rate be 10%. In each period, the stock price can either go up by 15% or down by 20%. A call option expiring at the end of the second period has an exercise price of $50.

Find the stock price sequence.

Determine the possible prices of the call at expiration.

Find the possible prices of the call at the end of the first period.

What is the current price of the call?

What is the initial hedge ratio?