Futures and Options Market

Currency futures• Currency futures are a standardized form of forward type of financial

instrument. Currency futures are very similar to commodity futures.• Currency futures are usually traded in a formal market place, like the

International Monetary Market (IMM) of the Chicago Mercantile Exchange or the London International Financial Futures Exchange (LIFFE).

• The contracts are only for a limited number of dates (four dates, the 3rd Wednesday of March, June, September and December) and for fixed amounts. E.g.:

• Contract Face Amount£ 62,500DM 125,000Can$ 100,000

• INR 50,00,000

• Futures Forward• Daily cash flow Single CF at maturity• Futures are traded only in standardized amts; Fwds any• Futures have fixed maturity (only 4) dates; Fwds don't • Futures are traded in central mkts; Fwds in OTC markets • Futures have daily price limits; Fwds do not

• The major difference is that while a fwd contract requires cash flows only on the maturity date, future contracts (may) require daily cash flows to maintain your margin at the required level.

Margin and maintenance level

• When one opens a futures contract, one is required pay a fee to the broker and to post a margin. The margin is posted to ensure that deals are honored.

• When the equity position falls, then this margin must be supplemented by additional cash to bring it up to the maintenance level.

• Suppose the margin on a futures contract on the £ is $3000 and the maintenance level is $2500.

• Then as long as the decline in the futures position is less than $500 you need not take any action, but once the futures position declines by more than $500 you need to post additional margin equal to the full decline in value in the futures position.

Hedging with futures

• Suppose you have exported goods to the UK and expect to receive £ in the future. Thus, you want to sell the £ in future.

• You are expecting the future £ price to decline, so you would like to hedge this position.

• To hedge this, you wish to take short position in the futures that when your original position loses money, the position in the futures should gain money. Exporter sells the fc in future,

And takes short position in futures market

Example on hedging with futures and cost of borrowing • On March 31, a Canadian firm borrows DM 2 m for 3 months

at 6% p.a. compounded annually in Germany. Since the firm needs the money in Canada, it hedges against exchange risk.

• On March 31, the spot rate $ .50/DM, the 90-day forward rate is $ .51/DM and the DM June futures is $ .51.

• At the end of June, the spot rate is $ .48. Assume the firm hedges only the principal and not the interest payments.

• (a) What is the effective cost of borrowing (in percent p. a.) if the firm hedges in the forward market?(b) What is the effective cost of borrowing (in percent p. a.) if the firm hedges in the futures market? Assume that the margin is $3000 per contract (remember, each contract is for DM 125,000), that the firm liquidates the futures contracts at a price of $ .48 at the end of June, and that the firm borrows $ at 14% in order to pay for the margins.

• To calculate the effective rate of interest we need to find out how much we are receiving today, and how much we are paying at the end of 3 months; and we need to look at these amounts in Can$ terms.

• The amount that is received today is DM 2m ($0.50/DM) = $1m

Unhedged position

• First, let us calculate the interest on this loan:• DM interest on the loan is DM 2m [(1.06)1/4 -1]

= DM 0.029348m• Since we do not hedge this, the $ value of this

(at St+1) is • = DM 0.029348 ($ 0.48/DM) = $0.014087m

2 m DM loan taken

$0.50/DM

1 m $ loan taken

Interest @ 6% pa=1.06^1/4 – 1 = 0.14674

Loan to be repaid=2.029348 m

$0.48/DM

0.97408 m $

Forward hedge calculation

• (1) Buy DM 2m fwd, @ $0.51/DM to hedge the principal payment = - $1.02m

• (2) Add the interest payment amount = - $0.014087m

• (3) Total amount to be paid back is (1) +(2) = - $1.034087m

• Thus, the effective rate of interest is = 1.0340874 - 1 = 0.14347 pa

2 m DM loan taken

$0.50/DM

1 m $ loan taken

Interest @ 6% pa=1.06^1/4 – 1 = 0.14674

Loan to be repaid=2.029348 m

$0.48/DM

0.97408 m $

$0.51/DM

Sign a long forward to buy 2m DM You need $1.02 to buy 2m DM @ 0.51

You need $0.014087 to buy 0.029348 m DM @ 0.48Total $1.034087 neededEquivalent to 14.34% pa in $ terms

$0.48/DM

Hedging with futures• (1) The interest payment amount = - $0.014087m• (2) Add the interest payment on the margins = - $3000 (16) (1.141/4

- 1) = - $0.001598m• (3) Change in value of underlying position = - DM2m ($/DM 0.48 -

0.50) = + $0.04m• (4) Change in value of futures position = + DM2m ($/DM 0.48 -

0.51) = - $0.06m• (5) Total amount to be paid back is (1) +(2) + (3) +(4) - $1m = -

$1.035587• Thus, the effective rate of interest is = 1.0355874 - 1 = 0.1505% pa• Thus it was cheaper to hedge with forwards, ex post.

No. of contracts=2 m/125000=16

$0.51/DM

Sign a long futures to buy 2m DM

You sell the futures contract @0.48With a loss of $0.03/DM. Total loss= $0.06 m

$0.48/DM

$0.50/DM

You want to buy 2DM in Spot market

$0.48/DM

Gain of $0.02/DM. Total gain = $0.04 m

Total position = 0.04-0.06 = loss of $0.02m

2 m DM loan taken

$0.50/DM

Interest @ 6% pa=1.06^1/4 – 1 = 0.14674

Loan to be repaid=2.029348 m

$0.48/DM

Margin amount borrowed= 3000*16=$48,000

Interest on margin amount to be paid = $48,000 [(1.14^1/4) -1]=$0.001598 m

It is given in the problem that only principal $1 m will be hedged. i.e. Interest of DM 0.029348 or equivalent of $ 0.014087 m will not be hedged.

Total amount to be paid =$1.035587 which is equivalent to 15.05%

CURRENCY OPTIONS

Call option

• A call option is a right to buy the underlying security (in our case the fx) for a fixed price (strike or exercise price) on or before a certain date (maturity date).

• The normal logic will work if the price of the option is quoted as HC/FC. Otherwise, either convert the price, or think of the call on the HC as put on the FC, and vice-versa.

• European option: can be exercised only at maturityAmerican option: can be exercised at any time

Example• Suppose that you went shopping during a X'mas sale for a Sony

camcorder, selling for $700 - a must have item in today’s yuppie world and the store had run out of this item. Then the store might issue you with a rain-check which would permit you to get back to the store within a month and buy the camcorder for $700. Suppose the day you went back to the store camcorders were selling for $680 then would you use your rain-check? No the rain-check would be worthless and you would just throw it away.

• Going back to call options, suppose you have an option on the £, with a strike price of $1.75, and a life of 3 months. This means that during the next 3 months you may buy a £ by paying $1.75, and if the £ is selling for less than that then your option is worthless. Thus,

• c = max {S - K, 0 }

Payoff diagram

X + C0T

X

Long call

Expiration date price of the underlying security

Contract payoff

0

C0T

- C0T

Out the money In the money

Put Option

• The story with put options is the similar. Put options give you the right to sell the underlying security for a fixed price (strike price) on or before a certain date (the expiration date).

Example

• Suppose you buy a new BMW for $30,000 and you have it insured for $25,000.

• This means that in the event of an accident you have the right to sell the car to the insurance company for a price of $25,000. However, if the damage done to the car is slight and the car is worth $28,000 after the accident then you would obviously not exercise the option to sell your car.

Fx example

• Going back to options on fx, suppose you have a put option on the DM with a strike price of $2.00, and a life of 3 months.

• This means that during the next 3 months you have the right to sell your DM for $2. You will obviously do this only if the DM price in the market is less than $2. Otherwise, it would be to your advantage to throw away the put option and sell the £ in the open market. Thus,

• p = max { K - S, 0 )

Payoff diagram

X + C0T

X Expiration date price of the underlying security

Long put

Contract payoff

0

C0T

- C0T

in the money out the money

Using options to set a ceiling on a fx payment

• Suppose a Canadian firm has to pay £5 m sometime during the next 3 months. On the £, the call option premium is $0.0220/£, for options with K = $1.50/£

• Q1. What option should the importer buy? Q2. What is the cost incurred today?

Solution

• 1. Since the importer is has to make a £ payment, that is £ will be bought in future. To hedge this, the importer buys a call options

• 2. £ 5 m * 0.0220 = $0.11 m

• Q3. What is the ceiling that the importer has set on the price of the £? Q4. What is the actual amount that the importer will pay if the spot rate at the end of 3 months is $1.46/£? Q5. What is the actual amount that the importer will pay if the spot rate at the end of 3 months is $1.55/£?

Solution

• 3. The max that he will have to pay for each £ is $.022/£ + $1.50/£ = $1.552/£

• 4. Since ST < K, the options are worthless and the importer can do better by buying at the market rate of $1.46/£. Thus, his total cost, ignoring time value of the payments, is $1.46 +$.022 = $1..482/£

• 5. Now, ST > K and therefore it is worth exercising the options. The importer will pay his ceiling price, $1.522/£.

Using put options to set a floor on a fx receivable

• Suppose a Japanese company, Matsushita, has to sell Can$ 50 m sometime during the next 6 months, and would like to lock in a minimum ¥ value for this. The price of a put option with a strike price of K = ¥ 230/$ is ¥ 4/$

• Q1. What option should the importer buy? Q2. What is the cost incurred today?

• 1. Since Matsushita wishes to sell $, it should buy a put option on the $. This is, of course, the same as wanting to buy ¥, and therefore, an call option on the ¥.

• 2. $ 50 m . ¥ 4 /$= ¥ 200

• Q3. What is the floor that the Matsushita has set on the price of the £?Q4. What is the actual amount that they receive if the spot rate at the end of 3 months is ¥ 245/$?Q5. What is the actual amount that they receive if the spot rate at the end of 3 months is ¥ 215/$?

• 3. The min that they will have to receive for each $ is = K - premium= ¥ 230 - ¥4 = ¥ 226/$

• 4. Since ST >K, the options are worthless and Matsushita can do better by selling at the market rate of ¥ 245/$, rather than the exercise price of ¥ 230/$. Thus, their total receipts will be= ¥ 245/$ - ¥ 4/$ = ¥ 241/$

• 5. Now, ST < K and therefore it is worth exercising the options. Matsushita will receive their floor price, ¥ 230 - ¥4 = ¥ 226/$

Writing options to hedge against fx risk.

• Texaco, USA has a large fx exposure in the form of a Can$ cash inflow from its Canadian operations. The risk to Texaco is that the Can$ may depreciate, thereby decreasing the US$ value of Texaco's Can$.

• Texaco can reduce its long position in the Can$ by writing options on the Can$. This strategy is called "fully covered call writing.“

• The advantage of this strategy is that when Texaco writes options it receives a positive cash flow today (from the premium on the options). If the value of the Can$ falls (S($/c$) decreases) then this positive cash flow helps offset the loss from depreciation. The price of this strategy is that if the Can$ appreciates, then the option buyer reaps the gains from this - rather than Texaco.

• As a financial officer, your job would be to pick the best strike price. There is the following trade-off between the risk and return:As you increase K, the premium decreases, so your revenue falls, but the chance of the options being exercised against you decreases.As you decrease K, ...