There exist call and put options on one share of Options'R'Real Inc. $($ORR$).$ Each option is

EUROPEAN, expires exactly one year from today, has an exercise price of $$45$ per share, and

has a premium of $$3$ per share. The current share price of ORR is $$45,$ and ORR never pays

dividends. Assume that taxes and transaction costs, including short selling costs, are zero.

a$)$ You buy one share of ORR, buy one European put option on ORR, and write one European

call option on ORR. Using the data above calculate your cash flow on expiration day. How

does your cash flow on expiration day depend on the stock price on expiration day?

EXPLAIN.

$(2$ points$)$

b$)$ Suppose that the riskless interest rate over the period until expiration is zero. Are the options

priced correctly?

$(2$ points$)$

c$)$ Suppose that the riskless interest rate over the period until expiration is zero. The put price is

$$3$ per share and the call price is $$4$ per share. Can you buy a synthetic CALL option for less

than $$4?$ If yes, construct the strategy and calculate the price of the synthetic call. How much

money did you save relative to buying the call directly?

$(2$ points$)$

d$)$ Suppose that the riskless interest rate over the period until expiration is zero. The put price is

$$4$ per share and the call price is $$3$ per share. Can you buy a synthetic PUT option for less

than $$4?$ If yes, construct the strategy and calculate the price of the synthetic put. How much

money did you save relative to buying the put directly?

$(2$ points$)$

e$)$ Suppose that the current riskless interest rate from today until the options expiration date

rises to $4\mathrm{.}65\%.$ Both the call and put have premiums of $$3$ per share. Are the options priced

correctly? If not, assume that the call price is $$3$ and calculate the put price. Second, assume

that the put price is $$3$ and calculate the call price. Third, explain how and why the increase

in interest rate had affected the put and call prices.

$(3$ points$)$

f$)$ Suppose that the current riskless interest rate from today until the option's expiration date

remains $4\mathrm{.}65\%.$ However, suppose that the current share price of ORR fell to $$43.$ Are the

options priced correctly? If not, assume that the call price is $$3$ and calculate the put price.

Second, assume that the put price is $$3$ and calculate the call price. Third, explain why the

decline in the share price had affected the put and call prices.

$(3$ points$)$

g$)$ Suppose that the current riskless borrowing and lending interest rate from today until the

option's expiration date remains $4\mathrm{.}65\%,$ and that the current share price of ORR remains $$45.$

But ORR will pay cash dividends. The present value of all the cash dividends paid over the

life of the options is $$2.$ How would your answers to the previous question change?

EXPLAIN.

$(2$ points$)$