Question

Suppose a student borrows the present value of $110, buys a 6-month Put option on stock Y with an exercise price of $150, and sells a 6-month Put option on Y with an exercise price of $40. Draw a position diagram showing the payoffs when the options expire.

Answer 1

6 month option means the option will be exercisedat the end of 6th month.

Put option means right to sell.

Put option holder will get the right to sell the stock. Put option writer will have the obligation to buy the stock when the put option holder exercises his right to sell.

Payoff is the loss or gain to the option owner.

Loss of option holder is limited to premium. Gain is unlimited.

Loss of option writer is unlimited and gain limited to premium.

Position diagram showing payoff is a table showing the payoff.

We need premium to calculate payoff. As not given in the question, i have assumed premium.

*All figures in $

Payoff of Put option holder (assumed premium as $20)

CMP	EP	Action	IV	P	Pay Off
80	150	Exercise	70	20	50
100	150	Exercise	50	20	30
120	150	Exercise	30	20	10
140	150	Exercise	10	20	-10
150	150	Lapse	0	20	-20
160	150	Lapse	0	20	-20
180	150	Lapse	0	20	-20
200	150	Lapse	0	20	-20

*CMP (Current Market Price), EP (Exercise Price), IV (Intrinsic Value), P (premium)

*Payoff =Intrinsic Value - Premium

Payoff table of Put option writer (assumed premium as $5)

CMP	EP	Action	IV	P	Pay Off
20	40	Exercise	0	5	5
30	40	Exercise	0	5	5
40	40	Lapse	0	5	5
50	40	Lapse	10	5	-10
60	40	Lapse	20	5	-15
70	40	Lapse	30	5	-25

* Payoff = Premium - Intrinsic Value