I.e., a price change of per ounce. If you don’t meet the ...

2. Futures and Forward Markets 2.1. Institutions

1. (Hull 2.3) Suppose that you enter into a short futures contract to sell July silver for $5.20 per ounce on the New York Commodity Exchange. The size of the contract is 5,000 ounces. The initial margin is $4,000 and the maintenance margin is $3,000. What change in the futures price will lead to a margin call?

5, 000($5.20 ? F ) = 26, 000 ? 5, 000F =

F= =

?$1, 000

?1, 000

27,000 5,000

5.40

i.e., a price change of +$0.20 per ounce.

What happens if you do not meet the margin call? If you don't meet the margin call, your position gets liquidated.

1

2. Futures and Forward Markets 2.1. Institutions

2. (Hull 2.11) An investor enters into two long futures contracts on frozen orange juice. Each contract is for the delivery of 15,000 pounds. The current futures price is 160 cents per pound, the initial margin is $6,000 per contract, and the maintenance margin is $4,500 per contract. What price change would lead to a margin call?

There is a margin call if $1,500 is lost on one contract.

15, 000(F ? $1.60) = 15, 000F ? 24, 000 =

F= =

?$1, 500

?1, 500

22,500 15,000

1.50

This happens if the futures price falls to $1.50 per pound.

Under what circumstances could $2,000 be withdrawn from the margin account?

$2,000 can be withdrawn from the margin account if the value of one contract rises by $1,000.

15, 000(F ? $1.60) = 15, 000F ? 24, 000 =

F= =

$1, 000

1, 000

25,000 15,000

1.6667

This happens if the futures price rises to $1.6667 per pound.

2

2. Futures and Forward Markets 2.1. Institutions

3. (Hull 2.15) At the end of one day a clearinghouse member is long 100 contracts, and the settlement price is $50,000 per contract. The original margin is $2,000 per contract. On the following day the member becomes responsible for clearing an additional 20 long contracts, entered into at a price of $51,000 per contract. The settlement price at the end of this day is $50,200. How much does the member have to add to its margin account with the exchange clearinghouse?

$36,000. From the clearinghouse to the member: 100 old contracts with ($50,200-$50,000) settlement each. From the member to the clearinghouse: 20 new contracts with $2,000 original margin each. From the member to the clearinghouse: 20 new contracts with ($50,200-$51,000) settlement each.

3

2. Futures and Forward Markets 2.1. Institutions

4. (Baby Hull 2.24, Papa Hull 2.26) A company enters into a short futures contract to sell 5,000 bushels of wheat for 250 cents per bushel. The initial margin is $3,000 and the maintenance margin is $2,000. What price change would lead to a margin call?

There is a margin call if $1,000 is lost on the contract.

5, 000(?F + $2.50) = 5, 000F ? 12, 500 = F= =

?$1, 000

1, 000

13,500 5,000

2.70

This will happen if the futures price rises to $2.70 per bushel.

Under what circumstances could $1,500 be withdrawn from the margin account?

5, 000(?F + $2.50) = $1, 500

5, 000F ? 12, 500 = ?1, 500

F= =

11,000 5,000

2.20

$1,500 can be withdrawn if the futures price falls to $2.20 per bushel.

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2. Futures and Forward Markets 2.2. Pricing

1. (Baby Hull 5.9, Papa Hull 3.11) A one-year long forward contract on a nondividend-paying stock is entered into when the stock price is $40 and the risk-free rate of interest is 10 percent per annum with continuous compounding. (a) What are the forward price and the initial value of the contract?

F = SerT

=

40e0.1

12 12

= 44.21

f = (F ? K)e-rT

=

0

(b) Six months later, the price of the stock is $45 and the risk-free interest rate is still 10 percent. What are the forward price and the value of the forward contract?

F = SerT

=

45e0.1

6 12

= 47.31

f=

(F ? K)e-rT

=

(47.31

?

44.21)e-0.1

6 12

=

2.95

5

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