Question

1. A put option with an exercise price of $17 that expires in 4 months is currently worth (costs) $3. The stock price is currently $19 and the risk free rate of return is 0.09.

a) What is a call option with the same exercise price and expiry worth?

b) Draw the profit diagram (at expiry) for the put option from part a.

Answer 1

a)

This can be solved using call put parity. It states following
C+ PV(X) = P+S
C= Price of call option
PV(X) = Present value of strike price
P= Price of Put option
S=Stock Price
thus
C+ [17/(1+0.09)^4/12] = 3+19
C + 16.51861 = 22
C = 5.48$

b)

Table showing payoff

Price as on expiry	Profit on put option with strike price @ 17	Premium paid	Net profit
10	7	-3	4
11	6	-3	3
12	5	-3	2
13	4	-3	1
14	3	-3	0
15	2	-3	-1
16	1	-3	-2
17	0	-3	-3
18	0	-3	-3
19	0	-3	-3
20	0	-3	-3
21	0	-3	-3
22	0	-3	-3
23	0	-3	-3
24	0	-3	-3
25	0	-3	-3

Profit diagram