Strike $
Interest rate
Time to X (% of yr)
Call Option Price =
Put Option Price =
Solution
A call option on Jupiter Motors stock with an exercise price of $75
and one-year expiration is selling at $3. A put option on Jupiter stock
with an exercise price of $75 and one-year expiration is selling at
$2.50. If the risk-free rate is 8% and Jupiter pays no dividends, what
should the stock price be?
X
So
Su
Sd
r
Solution
a. XPu Pd Hedge ratio
0.00 0.00 0.00 #DIV/0!
We will derive a two-state put option value in this problem. Data: S = 100; X
= 110; 1 + r = 1.10. The two possibilities for S(t) are 130 and 80.
a. 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?
b. 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?
X
So
Su
Sd
r
Solution
XCu Cd Hedge ratio
0.00 0.00 0.00 #DIV/0!
You are attempting to value a call option with an exercise price of $100 and
one year to expiration. The underlying stock pays no dividends, its current
price is $100, and you believe it has a 50% chance of increasing to $120 and a
50% chance of decreasing to $80. The risk-free rate of interest is 10%.
Calculate the call option’s value using the two-state stock price model.
X
So
% change
Su
Sd
r
Solution
a. XPu Pd Hedge ratio
0.00 0.00 0.00 #DIV/0!
You would like to be holding a protective put position on the stock of XYZ Co.
to lock in a guaranteed minimum value of $100 at year-end. XYZ currently sells
for $100. Over the next year, the stock price will either increase by 10% or
decrease by 10%. The T-bill rate is 5%. Unfortunately, no put options are traded
on XYZ Co.
a. Suppose the desired put option were traded. How much would it cost to
purchase?
b. What would have been the cost of the protective put portfolio?
c. What portfolio position in stock and T-bills will ensure you a payoff equal to
the payoff that would be provided by a protective put with X = $100? Show that
the payoff to this portfolio and the cost of establishing the portfolio matches
that of the desired protective put.