$8.)$ Consider a call option on an asset with an exercise price of $$100,$ a put option on the same asset

with an exercise price of $$100,$ and a forward contract on the asset with an exercise price of

$$100,$ all expiring at the same time. Assume that at the expiration, the price of the asset is each

of the following two values. Explain what happens from the perspective of the long position for

each derivative.

A$.$ $$105$

B$.$ $$95$

$9.)$ Suppose a European put price exceeds the value predicted by put$-$call parity. How could an

investor profit? Demonstrate your strategy is correct by constructing a payoff table$\mathrm{.}4$

$10.)$ Assume the current market price of a stock is $$820.$ A two$-$month European call option with an

exercise price of $$860$ is currently priced at $$15.$ What is the intrinsic value of this option. What

is the time value of this option.

$11.)$ Consider a stock trading at $$400$ that can go up or down by $20$ percent per period. The risk$-$free

rate is $8\%.$ Using the one period binomial model:

a$.$ Determine the two possible stock prices for the next period.

b$.$ Determine the intrinsic value at expiration of a European call with an exercise price of $$420\mathrm{.}5$

c$.$ Find the value of the option today.

d$.$ Compute the hedge ratio and construct the hedge portfolio. Show that the return on the hedge

portfolio is the risk$-$free rate regardless of the outcome assuming the call sells for the value you

obtained in part c$\mathrm{.}6$

$12.)$ Consider a two$-$period, two$-$state world. Let the current stock price be $45$ and the risk$-$free rate

be $5$ percent. Each period the stock can go up by $10$ percent or down by $10$ percent. A call

option expiring at the end of the second period has an exercise price of $40.$

a$.$ Find the stock price sequence.

b$.$ Determine the possible prices of the call at expiration.

c$.$ Find the possible prices of the call at the end of the first period.

d$.$ What is the current price of the call?$7$

e$.$ What is the initial hedge ratio?

f$.$ What are the two possible hedge ratios at the end of the first period?

g$.$ Construct an example showing that the hedge works. Make sure the example illustrates how

the hedge portfolio earns the risk$-$free rate over both periods$\mathrm{.}8$

h$.$ What would the investor do if the call were overpriced? If it were underpriced?