Question

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 there are no transaction costs and no taxes.

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? (1 point)

c) Suppose that the current riskless interest rate from today until the options expiration date rises to 4.65%. 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)

d) Suppose that the current riskless borrowing and lending interest rate from today until the option’s expiration date remains 4.65%. 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)

e) Suppose that the current riskless borrowing and lending interest rate from today until the option’s expiration date remains 4.65%, 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.

Answer 1

a) If Stock price at maturity > $45

the call option will be exercised and put option will be worthless,

Sold the option for $45 , Cash flow = $45

If Stock price at maturity < $45

the put option will be exercised and Call option will be worthless,

Sold the option for $45 , Cash flow = $45

So, Cashflow on expiration day is $45 and does not depend on the stock price at expiration. This is because one of the call and put options is exercised and the cashflow is the same.

b) From put call parity

value of put option + stock price today (net of present value of dividends) = value of call option + present value of strike price

Left hand side = $3+$45 = $48

Right hand side = $3+ $45/(1+0) = $48 (as interest rate is 0)

As put call parity holds, the options are correctly priced

c) Now as per Put call parity

Left hand side = $3+$45 = $48

Right hand side = $3+ $45/(1+0.0465) = $46 (as interest rate is 4.65%)

Left hand side is not equal to Right hand side

As put call parity does not hold, the options are not correctly priced

If call option has a value of $3

p = $46- $45 = $1

Put option's value = $1

If put option has a value of $3

c = $48- $43 = $5

Call option's value = $5

Increase in interest rates has affected put option prices in a negative way and call option prices in a positive way as the risk neutral probability of stock going up increases with interest rates.

d) Now, p+S= $3+$43 = $46

c+ K/(1+r) = $3+45/1.0465 = $46

So, as put call parity holds, the options are correctly priced

Decrease in Share price has affected put option prices in a positive way and call option prices in a negative way as the call option prices increase with increase in stock price and put option price decrease with increase in stock price.

e) If present value of dividends paid = $2

p+S - present value of dividends = $3+$45-$2 = $46

c+K/(1+r) = $3 + $45/1.0465 = $46

So, as put call parity holds, the options are correctly priced

Dividends decrease the effective Share price and affects put option prices in a positive way and call option prices in a negative way as the call option prices increase with increase in stock price and put option price decrease with increase in stock price.