Answer to Question #222670 in Financial Math for Collins

Question

(a) ABC Company Ltd purchased 5000 cocoa futures contract at a price of $150

per contract. As part of the contract, ABC was required to deposit $10 per

contract initially in their account with the maintenance margin set at $5 per

contract. If the price per contract falls to $142 overnight, what action will the

exchange require ABC to undertake?

b) Emmanuella purchased a put option on British pounds for $.06 per unit. The strike price

was $1.85, and the spot rate at the time the pound option was exercised was $1.69.

Assume there are 31,250 units in a British pound option. What was Emmanuella’s net

profit on the option?

c) Caleb sold a put option on Canadian dollars for $.05 per unit. The strike price was $.85,

and the spot rate at the time the option was exercised was $.92. Assume Caleb

immediately sold off the Canadian dollars received when the option was exercised. Also

assume that there are 50,000 units in a Canadian dollar option. What was Caleb’s net

profit on the put option?

Answer 1

a)

For the compensation amount:

$Compensation\space Amount=(Initial\space Margin+Maintenance\space Margin)×Number\space of\space Future \space Contract\\=(\$10+\$5)×5,000\\=\$15×5,000\\=\$75,000$

The company will not exercise the futures contract as the price per contract falls to $142 from $150 which leads to the loss for the company. Thus, the company only has to pay a compensation amount of $75,000.

b)

given,

put = $0.06 per unit

k = $1.85

s= $1.69

units = 31250

$long \space put\space profit= ([max(k−s),0]−put)×units\\=([max(1.85−1.69,0)]−0.06)×31250\\=([max(0.16,0)]−0.06)×31250\\=(0.16−0.06)×31250\\=0.1×31250\\=3125$

answer: $3125

c)

The holder of the call option, whoever Caleb has sold the option to will exercise it if $S-X\geq0$, otherwise he/she will let the option expire.

In this case,

$S-X=\$0.92-\$0.85=\$0.07\ge0$so the holder of the option will exercise it. In that case,the option sellers' Caleb net profit per unit of Canadian dollar is calculated as follows:

Net profit per C$\$=$ selling price of currency-Buying price of currency+premium on the option.

$=0.92-0.85+0.07=0.14$

Since each option contract contains 50000units of Canadian dollars, Net profit per option$=50000 units×0.14 =\$7000$