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Aphorisms Inc. has an expected cash inflow of €1 million on an accounts receivable balance due...

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

Solutions

Expert Solution

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:

jeff jeffy answered 2 years ago
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