Why futures and forward prices are equal?

Mid term Derivatives

Open questions

Why futures and forward prices are equal?

When the risk free interest rate is constant and the same for all maturities, the forward price for a contract with a certain delivery date is the same as the future price for a contract with that delivery date.

Why settlements on Repo market have a little credit risk?

Because if the borrower does not honor the agreement, the lending company simply keeps the securities. If the lending company does not keep to its side of the agreement, the original owner of the securities keeps the cash.

Problem 2.11

A trader buys two July futures contracts on orange juice. Each contract is for the delivery of 15000 pounds. The current futures price is 160 cents per pound, the initial margin is $6000 per contract and the maintenance margin is $4500 per contract.

a) what price change would lead to a margin call?

b) under what circumstances could $2000 be withdrawn from the margin account?

Answer:

a) if futures price of frozen orange juice falls to 150 cents per lb:

for margin call reduction required in the margin account = $6000 -$4500=$1500 – per contract, 10 cents per pound.

b) $2000 can be withdrawn if each contract rises by $1000= rise of $1000/1500 per pound = rise of 6,67 cents.

If futures prices of frozen orange juice rises to 166,67 cents per lb.

Problem 2

Suppose that sterling – usd spot and forward exchange are as follows:

Spot 20080

90-day forward 2.0056

190-day forward 2.0018

What opportunities are open to an arbitrageur in the following situations?

a) a 180-day European call option to buy ₤1 for $1.97 costs 2 cents.

b) A 90-day European put option to sell ₤1 for $2.04 costs 2 cents.

Answer:

a) A trader buys 180-day call option and takes a short position in a 180-day forward contract.

If St is the terminal spot price, the profit from the call option is = max (St – 1.97) -0.02

The profit from the short forward contract = 2.0018-St

The profit from the strategy is therefore =max(St-1.97) – 0.02 + 2.0018 –St= max(St-1.97) + 1.9818 – St

This is

1.9818 – St, when St < 1.97

0.0018 when St> 1.97

Hence profit is always positive.

b) The trader buys a 90-day put option and takes a long position in a 90-day forward contract.

The profit from the put option is=max(2.04-St,o) -0.02

The profit from the long forward contract = St-2.0056

The profit from the strategy is therefore= max(2.04 – S,o) -0.02 + S -2.0056= max(2.04 –S,o) -2.0256 +S

This is

S-2.0256 when St<2.04

0.0144 when St> 2.04

The profit is therefore always positive.

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