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# Call option & Put option values

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8-1
A call option on Bedrock Boulders stock has a market price of \$7. The stock sells for \$30 a share and the option has an exercise price of \$25 a share.
a. What is the exercise value of the call option?
b. What is the premium on the option?

8-3

Assume that you have been given the following information on Purcell Industries.
Current Stock price=\$15 Strike price of option =\$15
Time to maturity of option =6 mos Risk-free rate =6%
Variance of stock return=0.12
d1 = 0.24495 N(d1) =0.59675
d2 = 0.00000 N(d2)= 0.50000
According to the Black-Scholes option pricing model, what is the options' value?

8-4

The current price of a stock is \$33, and the annual risk-free rate is 6%. A call option with an exercise price of \$32 and one-year until expiration has a current value of \$6.56.
What is the value of a put option written on the stock with the same exercise price and expiration date as the call option?

8-6
The current price of a stock is \$20 . In 1 year, the price will be either \$26 or \$16. The annual risk -free rate is 5%. Find the price of a call option on the stock that has a strike price of \$21 and that expires in 1 year. (Hint: Use daily compounding.)

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#### Solution Summary

Assume that you have been given the following information on Purcell Industries.
According to the Black-Scholes option pricing model, what is the options' value?

\$2.19
See Also This Related BrainMass Solution

## 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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