# Put and Call Options

QUESTION 1

Focus on the June 445 call. Suppose you bought this call at the price indicated.

How high must AAPL's price rise at expiration to break even on this option?

QUESTION 2

Now, look at the June 445 put. Provide a table showing the profit at expiration to a put buyer across a range of stock prices.

QUESTION 3

Assume you own 100 shares of AAPL stock (at $434.94 per share).

Use the July 435 put to develop a protective put strategy.

How will this strategy protect your position in AAPL if the stock price falls to $390?

What if the price rises to $470?

Calculate the net profit generated by the stock and the put at these prices and assuming they occur at the time of the option's expiration.

QUESTION 4

Create a strtegy by buying the July 445 call and the July 435 put.

What's the maximum loss for this position and what range of stock prices will produce it? Where will you break even? Why would an investor establish a position like this?

See attached for table

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#### Solution Summary

Answers 4 questions with graphs on an excel file strategies using put and call options.

Textbook: Essentials of Investments. Chapter 16 (1, 2, 5, 6, 7 & 12). Problems on call and put options.

We showed in the text that the value of a call option increases with the volatility of the stock. Is this also true of put option values? In each of the following questions, you are asked to compare two options with parameters as given. What is the hedge ratio of the put? Verify that the put-call parity relationship is satisfied by your answers. Use the Black-Scholes formula to find the value of a call option on the following stock. All else being equal, is a put option on a high beta stock worth more than one on a low beta stock? The firms have identical firm-specific risk.

1.We showed in the text that the value of a call option increases with the volatility of the stock. Is this also true of put option values? Use the put-call parity relationship as well as a numerical example to prove your answer.

2.In each of the following questions, you are asked to compare two options with parameters as given. The risk-free interest rate for all cases should be assumed to be 6%. Assume the stocks on which these options are written pay no dividends.

I.

Put T X s Price of Option

0.5 50 0.20 10

B 0.5 50 0.25 10

Which put option is written on the stock with the lower price?

(1) A

(2) B

(3) Not enough information

II.

Put T X s Price of Option

A 0.5 50 0.2 10

B 0.5 50 0.2 12

Which put option must be written on the stock with the lower price?

a. A

b.B

c. Not enough information

III.

Call S X s Price of Option

A 50 50 0.20 12

B 55 50 0.20 10

Which call option must have the lower time to expiration?

a. A

b. B

c. Not enough information

IV.

Call T X S Price of Option

A 0.5 50 55 10

B 0.5 50 55 12

Which call option is written on the stock with higher volatility?

a. A

b. B

c. Not enough information

Call T X S Price of Option

A 0.5 50 55 10

B 0.5 55 55 7

Which call option is written on the stock with higher volatility?

a. A

b. B

c.Not enough information

5. We will derive a two-state put option value in this problem. Data: S0 = 100; X = 110; 1 + r = 1.10. The two possibilities for ST are 130 and 80.

1. Show that the range of S is 50 while that of P is 30 across the two states. What is the hedge ratio of the put?

2. Form a portfolio of three shares of stock and five puts. What is the (nonrandom) payoff to this portfolio? What is the present value of the portfolio?

3. Given that the stock currently is selling at 100, show that the value of the put must be 10.91.

6. Calculate the value of a call option on the stock in Problem 5 with an exercise price of 110. Verify that the put-call parity relationship is satisfied by your answers to Problems 5 and 6. (Do not use continuous compounding to calculate the present value of X in this example, because the interest rate is quoted as an effective annual yield.)

7. Use the Black-Scholes formula to find the value of a call option on the following stock:

Time to expiration = 6 months

Standard deviation = 50% per year

Exercise price = $50

Stock price = $50

Interest rate = 10%

12. All else being equal, is a put option on a high beta stock worth more than one on a low beta stock? The firms have identical firm-specific risk.

Please see attached for problem. Thanks.

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