Mini Case: 8 – 8
c. Consider Triple Play’s call option with a $25 strike price. The following table
contains historical values for this option at different stock prices:
Stock Price Call Option Price
$25 $ 3.00
30 7.50
35 12.00
40 16.50
45 21.00
50 25.50
1. Create a table which shows (a) stock price, (b) strike price, (c) exercise value, (d)
option price, and (e) the time value, which is the option’s price less its exercise
value.
Answer: Price Of Strike Exercise Value Market Price Time Value
Stock Price Of Option Of Option (D) – (C) =
(A) (B) (A) – (B) = (C) (D) (E)
$25.00 $25.00 $ 0.00 $ 3.00 $3.00
c. 2. What happens to the option’s time value as the stock price rises? Why?
d. Consider a stock with a current price of P = $27. Suppose that over the next 6
months the stock price will either go up by a factor of 1.41 or down by a factor of
0.71. Consider a call option on the stock with a strike price of $25 which expires
in 6 months. The risk-free rate is 6%.
1. Using the binomial model, what are the ending values of the stock price? What
are the payoffs of the call option?
d. 2. Suppose you write 1 call option and buy Ns shares of stock. How many shares
must you buy to create a portfolio with a riskless payoff (which is called a hedge
portfolio)? What is the payoff of the portfolio?
Answer:
Ns =
Cu – Cd
=
0.69153
P(u – d)
$38.07
$26.33
$13.07
$19.17
$13.26
=
$12.865
1.03045
$5.81
Mini Case: 8 – 11
d. 4. What is a replicating portfolio? What is arbitrage?
e. In 1973, Fischer Black and Myron Scholes developed the Black-Scholes Option
Pricing Model (OPM).
1. What assumptions underlie the OPM?
the option.
e. 2. Write out the three equations that constitute the model.
Answer: The OPM consists of the following three equations:
V = P[N(d1) –
trRF
Xe
[N(d2)].
e. 3. What is the value of the following call option according to the OPM?
Stock Price = $27.00.
Strike Price = $25.00
Time To Expiration = 6 Months = 0.5 years.
Risk-Free Rate = 6.0%.
Stock Return Standard Deviation = 0.49.
Answer: The input variables are:
Mini Case: 8 – 14
f. What impact does each of the following call option parameters have on the value
of a call option?
1. Current Stock Price
2. Strike Price
3. Option’s Term To Maturity
4. Risk-Free Rate
5. Variability Of The Stock Price
Answer: 1. The value of a call option increases (decreases) as the current stock price
increases (decreases).
can climb.
g. What is put-call parity?
Answer: Put-call parity specifies the relationship between puts, calls, and the underlying stock
price that must hold to prevent arbitrage: