Question

Explain and show on a diagram the profit at maturity from the following combinations of positions. Please show the profit from each option or stock and the profit from the combined position on ONE graph. You should have one graph each for a, b, and c. Please label carefully all turning points and profit levels. To find the future value, use continuous compounding, where r, risk-free interest is 1% annually and time to maturity is 15 days (Please use 360 days count in a year). All options expire at the same time. You can use ranges of $65, 66, 67, 68, 69...........$82 for DELL stock price at maturity. DELL Stock Price    Strike Expiration . Call Premium . Put premium

71.76 70 Sep 2.25 0.45

71.76 75 Sep 0.10 3.40 71.76 80 Sep 0.05 8.30

a) Buy one 70 Sep call and buy one 80 Sep Put

b) Buy one 70 Sep put, buy one 80 Sep put, and short a round lot (100 shares) of the underlying stock

c) Buy one 75 Sep call and sell one 75 Sep put option.

Answer 1

Calculate the payoffs individually for all the calls and puts given in the question. (assuming 100 shares = 1 lot of options)

Profit/loss of long call at expiry = max(Dell price at expiry - strike price - premium,-premium)

and profit/loss of long put at expiry = max(strike price - dell stock price at maturity - premium, -premium)

profit/loss of shorting dell stock = 71.76 * - dell price at expiry in 15 days

Reverse the sign of Profit/loss while shorting calls and puts.

Calculating payoff for all stock price from 65 - 82 at expiry for A, B, C and A+B+C. Just add payoff of individual calls and puts to get A, B and C respectively.

A = payoff of long 70 call + payoff of long 80 put

B = payoff of long 70 put + payoff of long 80 put + payoff from shorting stock worth 1 lot of option at 71.76. (when you short a stock at 71.76 for 15 days, you need to add interest received from the short sell proceeds as well to the payoff

C = payoff of long 75 call + payoff from short 75 put.

A+B+C = payoff from A + payoff from B + payoff from C

Payoff from A chart :

Payoff from B chart :

Payoff from C chart :

Payoff from A+B+C :

Snapshot of working :

Happy learning!