Question

Aphorisms Inc. has an expected cash inflow of €1 million on an accounts receivable balance due in six months. The owner, Laozi, wants to hedge this exposure with an option contract at a strike price of KCNY/EUR = 8.00 CNY/EUR and with a due date in 6 months. At this strike price, call option and put option prices are, respectively, CallCNY/EUR = 1.00 CNY/EUR and PutCNY/EUR = 2.00 CNY/EUR. Graph the following positions (a–c) on the figure below.

a. The exposure of Laozi’s underlying position

b. The payoff of Laozi’s option contract at expiration including the option premium

c. The payoff of Laozi’s combined position including the option premium

Answer 1

Aphorisms Inc. has an expected cash inflow of €1 million on an accounts receivable balance due in six months. The owner, Laozi, wants to hedge this exposure with an option contract at a strike price of KCNY/EUR = 8.00 CNY/EUR and with a due date in 6 months.

Laozi would like to sell the €1 million at a pre determined exchange rate. Hence, he should enter into put option contract.

Exposure in Euro, E = 1,000,000

Strike Price = K = 8.00 CNY/EUR

Put otpipon premium, P = 2.00 CNY/EUR.

Let S be the exchange rate on the date of maturity ie. 6 months down the line.

Hence,

Part (a)

The exposure of Laozi’s underlying position = S x E = S x 1,000,000 = 1,000,000S

Part (b)

The payoff of Laozi’s option contract at expiration including the option premium = {max (K - S, 0) - P} x E = {max (8 - S) - 2} x 1,000,000

Part (c)

The payoff of Laozi’s combined position including the option premium = 1,000,000S + {max (8 - S) - 2} x 1,000,000

Hence, the table of payoff:

S	Part (a)	Part (b)	Part (c )
0	-	6,000,000	6,000,000
1	1,000,000	5,000,000	6,000,000
2	2,000,000	4,000,000	6,000,000
3	3,000,000	3,000,000	6,000,000
4	4,000,000	2,000,000	6,000,000
5	5,000,000	1,000,000	6,000,000
6	6,000,000	-	6,000,000
7	7,000,000	-1,000,000	6,000,000
8	8,000,000	-2,000,000	6,000,000
9	9,000,000	-2,000,000	7,000,000
10	10,000,000	-2,000,000	8,000,000
11	11,000,000	-2,000,000	9,000,000
12	12,000,000	-2,000,000	10,000,000
13	13,000,000	-2,000,000	11,000,000
14	14,000,000	-2,000,000	12,000,000
15	15,000,000	-2,000,000	13,000,000
16	16,000,000	-2,000,000	14,000,000
17	17,000,000	-2,000,000	15,000,000
18	18,000,000	-2,000,000	16,000,000
19	19,000,000	-2,000,000	17,000,000
20	20,000,000	-2,000,000	18,000,000

The graph for each of them is shown below: