4097-Finance

C1. Value a one-year call option on a stock (Alpha PLC, Ltd.) whose
current price is $35.

In one year the stock will be worth either $42 or $29.75, and the
riskless interest

rate for the next year is (what else?) 10% The option’s exercise price
is $40.

What is the option’s payoff in the stock’s “up” state? Why? What
is the option’s

payoff in the stock’s “down” state? Why? What is the options’
value today?

C2. Value another one-year european call option. This time the stock
(Omega Corp.) is

currently selling for $50 and the interest rate on one-year treasury
bills is 8%.

The stock’s terminal value will be either up 40% from its present
value or down

35%. The option’s strike price is $40.

C3. Now let’s see how the riskless interest rate affects the value of
the call option on

Omega Corp. Re-do problem #C2 with the riskless rate set to 12% instead
of 8%.

What happens to the call option’s value? Why do you think this occurs?

C4. Return again to the case of Alpha PLC, Ltd. in Problem C1. What
happens to the

call option’s value if Alpha’s stock price becomes more variable? In
particular,

value the call option if the terminal stock price could be either $49 or
$26.25.

Why is the option worth more when the Alpha’s stock value is more
variable?

C5. Return one more time to the initial conditions in problem C1. What
is the value of a

call option on Alpha PLC when the option’s strike price is $37.50
(instead of

$40.00)? Explain the change in value.

P1. Value a one-year put option on a stock (Alpha PLC, Ltd.) whose
current price is $35.

In one year the stock will be worth either $42 or $29.75, and the
riskless interest

rate for the next year is (naturally!) 10% The option’s exercise price
is $30.

What will the option pay off in the stock’s “up” state? Why? What
will the option

pay off in the stock’s “down” state? Why? What is the option worth
today?

P2. What is the effect on the option value you computed in P1 if the
riskless rate rises?

Why?

P3. Starting from the conditions in Problem P1, what happens to the
option’s value if

Alpha’s stock could be worth either $25 or $45 on the option’s
maturity date?

Why does the option value rise?

P4. Put options are often compared to insurance. Like insurance, you can
choose to

protect yourself to a greater or lesser extent. With an insurance
policy, you do

this by varying the policy’s deductible. With an option, you vary your
protection

by varying the option’s strike price. Return again to the conditions
in Problem P1.

What is the put option worth today if price changes to $35? What if the
exercise

price is $40?

What do you think these option price movements imply about the cost of
buying

an insurance policy with a higher vs. a lower deductible?