Options onStock Indices and CurrenciesChapter

15

The cash marketStock indexes are not traded

per se. Several mutual funds trade portfolio

that are the index portfolio, or a portfolio that

closely mimic the index.The market values of

all stock indexes are calculated virtually

continuously.

STOCK INDEXES (INDICES) A STOCK INDEX IS A

SINGLE NUMBER BASED ON INFORMATION ASSOCIATED

WITH A SET OF STOCK PRICES AND QUANTITIES. A

STOCK INDEX IS SOME KIND OF AN AVERAGE OF THE

PRICES AND THE QUANTITIES OF THE STOCKS THAT ARE

INCLUDED IN A GIVE PORTFOLIO. THE MOST USED

INDEXES ARE A SIMPLE PRICE AVERAGE AND A

VALUE WEIGHTED AVERAGE.

STOCK INDEXES - THE CASH MARKET AVERAGE PRICE

INDEXES DJIA, MMI N The number of stocks

in the portfolio. Pi The i-th stock market

price D Divisor Initially D N and the

index is set at some level. To ensure continuity,

the divisor is adjusted over time.

EXAMPLES OF INDEX ADJUSMENTS STOCK SPLITS 2 for

1. 1. 2. 1. (30 40 50 60 20) /5

40 I 40 and D 5. 2. (30 20 50

60 20)/D 40 The new divisor is D

4.5

CHANGE OF STOCKS IN THE INDEX 1. 2. 1. (32

18 55 56 19)/4.5 40 I 40 and

D 4.5. 2. (32 118 55 56 19)/D 40

The new divisor is D 7.00

STOCK 4 DISTRIBUTED 66 2/3 STOCK DIVIDEND

(22 103 44 58 25)/7.00 36 D 7.00.

Next, (22 103 44 34.8 25)/D 36 The

new divisor is D 6.355. STOCK 2 SPLIT 3 for

1. (31 111 54 35 23)/6.355 39.9685

(31 37 54 35 23)/D 39.9685 The new

Divisor is D 4.5035.

- ADDITIONAL STOCKS
- 1.
- 2.
- (30 39 55 33 21)/4.5035 39.5248
- 2. (30 39 55 33 21 35)/D 39.5248
- D 5.389

VALUE WEIGHTED INDEXES S P500, NIKKEI 225,

VALUE LINE B SOME BASIS TIME

PERIOD INITIALLY t B THUS, THE INITIAL INDEX

VALUE IS SOME ARBITRARILY CHOSEN VALUE M.

Examples The SP500 index base period was

1941-1943 and its initial value was set at M

10. The NYSE index base period was Dec. 31, 1965

and its initial value was set at M 50.

The rate of return on the index The HPRR on a

value weighted index in any period t, is the

weighted average of the individual stock returns

the weights are the dollar value of the stock as

a proportion of the entire portfolio value.

stock Pti Nti Vti wti Pt1i Rti

Federal Mogul 18 9,000 162,000 .0397 19.8 .1000

Martin Arietta 73 8,000 584,000 .1432 75 .0274

IBM 50 4,000 200,000 .0491 48 -.0400

US West 45 5,000 225,000 .0552 49 .0889

BauschLomb 55 15,000 825,000 .2024 52 -.0545

First Union 50 10,000 500,000 .1227 57 .1400

Walt Disney 40 12,000 480,000 .1178 46 .1500

Delta Airlines 55 20,000 1,100,000 .2699 59 .0727

Total 4,076,000 1.000

Rp (.0397)(.1) (.1432(.0274) (.0491)(-.04)

(.0552)(.0889) (.2024)(-.0545)

(.1227)(.14) (.1178)(.15) (.2699)(.0727)

0.0543 or 5.43

Of course, the HPRR on the portfolio may be

calculated directly. With the end-of-period

prices Pt1i we calculate the end-of-period

portfolio value 4,297,200. Thus, the portfolios

HPRR is 4,297,200 4,076,000/4,076,000

.0543 Or 5.43.

THE RATE OF RETURN ON THE INDEX

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THE BETA OF A PORTFOLIO Definitions

THE BETA OF A PORTFOLIO THEOREM A PORTFOLIOS

BETA IS THE WEIGHTED AVERAGE OF THE BETAS OF THE

STOCKS THAT COMPRISE THE PORTFOLIO. THE WEIGHTS

ARE THE DOLLAR VALUE WEIGHTS OF THE STOCKS IN THE

PORTFOLIO. Proof Assume that the index is a well

diversified portfolio, I.e., the index

represents the market portfolio. Let P denote

any portfolio, i denote the individual stock i

1, 2, ,N in the portfolio and I denote the

index.

By definition

STOCK PORTFOLIO BETA

STOCK NAME PRICE SHARES

VALUE WEIGHT BETA

?P .044(1.00) .152(.8) .046(.5) .061(.7)

.147(1.1) .178(1.1) .144(1.4) .227(1.2)

1.06

A STOCK PORTFOLIO BETA STOCK NAME PRICE

SHARES VALUE WEIGHT

BETA

?P .122(.95) .187(1.1) .203(.85)

.048(1.15) .059(1.15) .076(1.0) .263(.85)

.042(.75) .95

Sources of calculated Betas and calculation

inputs Example ß(GE) 6/20/00 Source ß(GE)

Index Data Horizon Value Line Investment

Survey 1.25 NYSECI Weekly

Price 5 yrs (Monthly) Bloomberg

1.21 SP500I Weekly Price

2 yrs (Weekly) Bridge Information Systems

1.13 SP500I Daily Price 2

yrs (daily) Nasdaq Stock Exchange

1.14 Media General Fin. Svcs. (MGFS)

SP500I Monthly P ice 3 (5) yrs

Quicken.Excite.com 1.23 MSN

Money Central

1.20 DailyStock.com

1.21 Standard Poors Compustat Svcs

SP500I Monthly Price 5 yrs

(Monthly) SP Personal Wealth

1.2287 SP Company Report)

1.23 Charles Schwab Equity Report Card 1.20 SP

Stock Report

1.23 AArgus Company Report 1.12

SP500I Daily Price 5 yrs

(Daily) Market Guide

SP500I

Monthly Price 5 yrs (Monthly) YYahoo!Finance

1.23 Motley Fool

1.23

STOCK INDEX OPTIONS 1. One contract

(I)(m) (WSJ) 2. ACCOUNTS ARE SETTLED BY CASH

EXAMPLE Options on a stock index MoneyGone, a

financial institution, offers its clients the

following deal Invest A 1,000,000 for 6

months. In 6 months you receive a guaranteed

return The Greater of 0, or 50 of the return

on the SP500I during these 6 months. For

comparison purposes The annual risk-free rate is

8. The SP500I dividend payout ratio is q 3

and its annual VOL s 25.

MoneyGone offer Deposit A now. Receive

AMax0, .5RI in 6 months. Denote the date in

six month T. Rewrite MoneyGone offer at T

The expression

is equivalent to the at-expiration cash flow of

an at-the money European call option on the

index, if you notice that K I0. Calculate this

options value based on S0 K I0 T t .5

r .08 q .03 and s .25. Using

DerivaGem c .08137. Thus, MoneyGones promise

is equivalent

to giving the client NOW, at time 0, a value

of (.5)(.08137)(A) .040685A. Therefore, the

investors initial deposit is only 95.9315 of

A. Investing .959315A and receiving A in six

months, yields a guaranteed return of 8.3

- STOCK INDEX OPTIONS FOR
- PORTFOLIO INSURANCE
- Problems
- How many puts to buy?
- Which exercise price will guarantee a desired

level of protection? - The answers are not easy because the
- index underlying the puts is not the
- portfolio to be protected.

The protective put with a single stock

STRATEGY ICF AT EXPIRATION AT EXPIRATION

STRATEGY ICF ST lt K ST K

Hold the stock Buy put -St -p ST K - ST ST 0

TOTAL -St p K ST

The protective put consists of holding the

portfolio and purchasing n puts on an index.

Current t 0 Expiration T 1.

STRATEGY ICF (t 0) AT EXPIRATION (T 1) AT EXPIRATION (T 1)

STRATEGY ICF (t 0) I1 lt K I1 K

Hold the portfolio Buy n puts -V0 -nP(m) V1 n(K- I1)(m) V1 0

TOTAL -V0 nP(m) V1n(m)(K- I1) V1

WE USE THE CAPITAL ASSET PRICING MODEL. For

any security i, the expected excess return on

the security and the expected excess return on

the market portfolio are linearly related by

their beta

THE INDEX TO BE USED IN THE STRATEGY, IS TAKEN

TO BE A PROXY FOR THE MARKET PORTFOLIO, M.

FIRST, REWRITE THE ABOVE EQUATION FOR THE INDEX I

AND ANY PORTFOLIO P

Second, as an approximation, rewrite the CAPM

result, with actual returns

In a more refined way, using V and I for the

portfolio and index market values, respectively

NEXT, use the ratio Dp/V0 as the portfolios

annual dividend payout ratio qP and DI/I0 the

index annual dividend payout ratio, qI.

The ratio V1/ V0 indicates the portfolio required

protection ratio.

For example

The manager wants V1, to be down to no more than

90 of the initial portfolio market value, V0

V1 (.9)V0. We denote this desired level of

hedging by (V1/ V0). This is a decision

variable.

1. The number of puts is

2. The exercise price, K, is determined by

substituting I1 K and the required level, (V1/

V0) into the equation

and solving for K

EXAMPLE A portfolio manager expects the market

to fall by 25 in the next six months. The

current portfolio value is 25M. The manager

decides on a 90 hedge by purchasing 6-month puts

on the SP500 index. The portfolios beta with

the SP500 index is 2.4. The SP500 index stands

at a level of 1,250 points and its dollar

multiplier is 100. The annual risk-free rate is

10, while the portfolio and the index annual

dividend payout ratios are 5 and 6,

respectively. The data are summarized below

Solution Purchase

The exercise price of the puts is

Solution Purchase n 480 six-months puts with

exercise price K 1,210.

We rewrite the Profit/Loss table for the

protective put strategy

STRATEGY INITIAL CASH FLOW AT EXPIRATION AT EXPIRATION

STRATEGY INITIAL CASH FLOW I1 lt K I1 K

Hold the portfolio Buy n puts -V0 -n P(m) V1 n(K - I1)(m) V1 0

TOTAL -V0 - nP(m) V1n(m)(K - I1) V1

We are now ready to calculate the floor level of

the portfolio V1n(m)(K- I1)

We are now ready to calculate the floor level of

the portfolio Min portfolio value V1n(m)(K-

I1) This is the lowest level that the portfolio

value can attain. If the index falls below the

exercise price and the portfolio value declines

too, the protective puts will be exercised and

the money gained may be invested in the portfolio

and bring it to the value of V1n(m)K- n(m)I1

Substitute for n

To substitute for V1 we solve the equation

3. Substitution V1 into the equation for the Min

portfolio value

The desired level of protection is made at time

0. This determines the exercise price and

management can also calculate the minimum

portfolio value.

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Example (p326) protection for 3 months

Solution Purchase

The exercise price of the puts is

Solution Purchase n 10 three -months puts with

exercise price K 960.

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CONCLUSION Holding the portfolio and purchasing

10, 3-months protective puts on the SP500 index,

with the exercise price K 960, guarantees that

the portfolio value, currently 500,000 will not

fall below 450,000 in three months.

- A SPECIAL CASE In the case that
- ß 1
- qP qI,
- the portfolio is statistically similar to the
- index. In this case

Assume that in the above example ßp 1 and qP

qI, then

Example (p326-27) ßp 1 and qP qI, then

A Zero cost Collar

STRATEGY ICF AT EXPIRATION AT EXPIRATION

STRATEGY ICF I1 lt KP KP lt I1 lt KC I1 KC

portfolio Buy n puts Sell n calls -V0 -nP(m) nC(m) V1 V1 n(KP-I1)(m) 0 0 0 V1 0 n(I1-KC)(m)

TOTAL -V0 V1 V1 n(m)(KP - I1) V1 n(m)(I1-KC)

A zero cost Collar If the Collar is to be zero

cost that the cost of the puts is equal to the

revenue from the calls, given that n(p)

n(c). Using the same relationship between the

portfolio value and the index value, i.e., the

CAPM the solution for the P/L profile of the

Collar is given by

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FOREIGN CURRENCY (FORX) OPTIONS(p.321) FORX

options are traded all over the world. The main

exchange in the U.S. is the Philadelphia exchange

(PHLX). First we describe several

characteristics of the spot market for FORX.

FOREIGN CURRENCY THE SPOT MARKET EXCHANGE

RATES The value of one currency in one unit of

another currency is the EXCHANGE RATE between the

two currencies. There are two quote formats 1.

S(USD/FC) The number of USD in one unit of the

foreign currency. 2. S(FC/USD) The number of

the foreign currency in one USD. www.x-rates.com

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CURRENCY CROSS RATES Let FC1, FC2 AND FC3 denote

3 different currencies. Then, in the absence of

arbitrage, the following relationship must hold

for their spot exchange rate

CURRENCY CROSS RATES OCT. 13, 04

USD GBP CAD EUR AUD

USD 1 1.7972 0.798212 1.2393 0.731502

GBP 0.556421 1 0.444141 0.689572 0.407023

CAD 1.25279 2.25153 1 1.55259 0.916425

EUR 0.806907 1.45017 .644082 1 0.590254

AUD 1.36705 2.45686 1.09119 1.69418 1

CURRENCY CROSS RATES EXAMPLE FC1 USD FC2

MXP FC3 GBP. USD MXP GBP USA 1.0000 0.09

97 1.6603 MEXICO 10.0301 1.000 16.653 UK 0.602

3 0.06005 1.000

CURRENCY CROSS RATES EXAMPLE

AN EXAMPLE OF CROSS SPOT RATES ARBITRAGE COUNTRY

USD GBP CHF SWITZERLAND 1.7920 2.8200 1.0000

U.K 0.6394 1.0000 0.3546 U.S.A

1.0000 1.5640 0.5580

THE CASH ARBITRAGE ACTIVITIES USD1,000,000 U

SD1,006,134.26 0.6394 0.5580 GBP639,400

CHF1,803,108 2.8200

Forward rates, An example GBP

18.5.99 SPOT USD1.6850/GBP 30 days

forward USD1.7245/GBP 60 days forward USD1.7455/

GBP 90 days forward USD1.7978/GBP 180 days

forward USD1.8455/GBP The existence of forward

exchange rates implies that there is a demand and

supply for the GBP for future dates.

THE INTEREST RATES PARITY Wherever financial

flows are unrestricted, the exchange rates, the

forward rates and the interest rates in any two

countries must maintain a NO- ARBITRAGE

relationship Interest Rates Parity.

NO ARBITRAGE CASH-AND-CARRY TIME CASH FUTURE

S t (1) BORROW DC. rDOM (4) SHORT FOREIGN

CURRENCY (2) BUY FOREIGN CURRENCY

FORWARD Ft,T(DC/FC) DC/S(DC/FC)

DCS(FC/DC) AMOUNT (3) INVEST IN BONDS

DENOMINATED IN THE FOREIGN CURRENCY

rFOR T (3) REDEEM THE BONDS EARN (4) DELIVER

THE CURRENCY TO CLOSE THE SHORT

POSITION (1) PAY BACK THE LOAN RECEIVE IN

THE ABSENCE OF ARBITRAGE

NO ARBITRAGE REVERSE CASH AND -

CARRY TIME CASH FUTURES t (1) BORROW FC .

rFOR (4) LONG FOREIGN CURRENCY (2) BUY

DOLLARS FORWARD Ft,T(DC/FC) FCS(DC/FC)

AMOUNT IN DOLLARS (3) INVEST IN T-BILLS

FOR RDOM T REDEEM THE T-BILLS EARN

TAKE DELIVERY TO CLOSE THE LONG

POSITION PAY BACK THE LOAN RECEIVE IN THE

ABSENCE OF ARBITRAGE

FROM THE CASH-AND-CARRY STRATEGY

FROM THE REVERSE CASH-AND-CARRY STRATEGY

THE ONLY WAY THE TWO INEQUALITIES HOLD

SIMULTANEOUSLY IS BY BEING AN EQUALITY

ON MAY 25 AN ARBITRAGER OBSERVES THE FOLLOWING

MARKET PRICES S(USD/GBP) 1.5640 ltgt S(GBP/USD)

.6393 F(USD/GBP) 1.5328 ltgt F(GBP/USD)

.6524 rUS 7.85 rGB 12 The market

forward rate 1.5328 is overvalued relative to the

theoretical, no arbitrage forward rate

1.5273. CASH AND CARRY

CASH AND CARRY TIME CASH FUTURES MAY 25

(1) BORROW USD100M AT 7. 85 SHORT DEC 20

FOR 209 DAYS GBP68,477,215 FORWARD.

F USD1.5328/GBP (2) BUY GBP63,930,000

(3) INVEST THE GBP63,930,000 IN

BRITISH BONDS DEC 20 RECEIVE GBP68,477,215

DELIVER GBP68,477,215 FOR

USD104,961,875.2 REPAY YOUR LOAN PROFIT

USD104,961,875.2 - USD104,597,484.3

USD364,390.90

Example 2 THE INTEREST RATES PARITY In the

real markets, buyers pay the ask price while

sellers receive the bid price. Moreover,

borrowers pay the ask interest rate while lenders

only receive the bid interest rate. Therefore,

in the real markets, it is possible for the

forward exchange rate to fluctuate within a band

of rates without presenting arbitrage

opportunities.Only when the market forward

exchange rate diverges from this band of rates

arbitrage exists.

Foreign Exchange Quotes for USD/GBP on Aug 16,

2001

Bid Ask

Spot 1.4452 1.4456

1-month forward 1.4435 1.4440

3-month forward 1.4402 1.4407

6-month forward 1.4353 1.4359

12-month forward 1.4262 1.4268

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Example 2 THE INTEREST RATES PARITY We now

show that in the real markets it is possible for

the forward exchange rate to fluctuate within a

band of rates without presenting arbitrage

opportunities.Only when the market forward

exchange rate diverges from this band of rates

arbitrage exists. Given are Bid and Ask domestic

and foreign spot rates forward rates and

interest rates.

NO ARBITRAGE CASH - AND - CARRY TIME CASH FU

TURES t (1) BORROW DC. rD,ASK (4) SHORT

FOREIGN CURRENCY FORWARD (2) BUY FOREIGN

CURRENCY DC/SASK(DC/FC) FBID

(DC/FC) (3) INVEST IN BONDS

DENOMINATED IN THE FOREIGN CURRENCY

rF,BID T REDEEM THE BONDS DELIVER THE CURRENCY

TO CLOSE THE SHORT POSITION EARN PAY

BACK THE LOAN RECEIVE IN THE ABSENCE OF

ARBITRAGE

NO ARBITRAGE REVERSE CASH - AND -

CARRY TIME CASH FUTURES t (1) BORROW FC .

rF,ASK (4) LONG FOREIGN

CURRENCY FORWARD FOR FASK(DC/FC)

(2) EXCHANGE FOR FCSBID

(DC/FC) (3) INVEST IN T-BILLS FOR

rD,BID T REDEEM THE T-BILLS EARN

TAKE DELIVERY TO CLOSE THE LONG

POSITION RECEIVE in foreign

currency, the amount PAY BACK THE LOAN IN

THE ABSENCE OF ARBITRAGE

From Cash and Carry

From reverse cash and Carry

(3) And FASK(DC/FC) gt FBID(DC/FC)

Notice that RHS(1) gt RHS(2)

Define RHS(1) ? BU RHS(2) ? BL

F(/D)

FASK(DC/FC) gt FBID(DC/FC).

FASK

BU BL

BU

BL

FBID

Arbitrage exists only if both ask and bid futures

prices are above BU, or both are below BL.

A numerical example Given the following

exchange rates Spot Forward Interest

rates S(USD/NZ) F(USD/NZ) r(NZ)

r(US) ASK 0.4438 0.4480 6.000

10.8125 BID 0.4428 0.4450 5.875

10.6875 Clearly, F(ask) gt F(bid). (USD0.4480NZ

gt USD0.4450/NZ) We will now check whether or

not there exists an opportunity for arbitrage

profits. This will require comparing these

forward exchange rates to BU and BL

Inequality (1)

0.4450 lt (0.4438)e(0.108125 0.05875)/12

0.4456 BU

Inequality (2)

0.4480 gt (0.4428)e(0.106875 0.06000)/12

0.4445 BL

- No arbitrage.
- Lets see the graph

F

FASK 0.4480

0.4456

BU BL

Clearly FASK(/FC) gt FBID(/FC).

FBID 0.4450

0.4445

An example of arbitrage FASK 0.4480 FBID

0.4465

- Currency options Units
- USD/AUD 50,000AUD
- USD/GBP 31,250GBP
- USD/CAD 50,000CAD
- USD/EUR 62,500EUR
- USD/JPY 6,250,000JPY
- USD/CHF 62,500CHF
- Exercise Style American- or European
- options available for physically settled
- contracts Long-term options are
- European-style only.

- Expiration/Last Trading Day The PHLX offers a

variety of expirations in its physically settled

currency options contracts, including Mid-month,

Month-end and Long-term expirations. Expiration,

which is also the last day of trading, occurs on

both a quarterly and consecutive monthly cycle.

That is, currency options are available for

trading with fixed quarterly months of March,

June, September and December and two additional

near-term months. For example, after December

expiration, trading is available in options which

expire in January, February, March, June,

September, and December. Month-end option

expirations are available in the three nearest

months.

Standardized Options

With the Canadian dollar spot price currently at

a level of USD.6556/CAD, strike prices would be

listed in half-cent intervals ranging from 60 to

70. i.e., 60, 60.5, 61, , 69, 69.5, 70. If the

Canadian dollar spot rate should move to say

USD.7060/CAD, additional strikes would be listed.

E.G, 70, 70.5, 71, , 75.

- Exercise PricesExercise prices are expressed in

terms of U.S. cents per unit of foreign currency.

Thus, a call option on EUR with an exercise price

of 120 would give the option buyer the right to

buy Euros at 120 cents per EUR.

- It is important that available exercise prices

relate closely to prevailing currency values.

Therefore, exercise prices are set at certain

intervals surrounding the current spot or market

price for a particular currency. When significant

price changes take place, additional options with

new exercise prices are listed and commence

trading. - Strike price intervals vary for the different

expiration time frames. They are narrower for the

near-term and wider for the long-term options.

- Premium Quotation premiums for dollar-based

options are quoted in U.S. cents per unit of the

underlying currency with the exception of

Japanese yen which are quoted in hundredths of a

cent. - Example
- A premium of 1.00 for a given EUR option is one

cent (USD.01) per EUR. - Since each option is for 62,500 EURs, the total

option premium would be - 62,500EURUSD.01/EUR USD625.

- FX Options As InsuranceOptions on spot

represent insurance bought or written on the spot

rate. - An individual with foreign currency to sell can

use put options on spot to establish a floor

price on the domestic currency value of the

foreign currency. - For example, a put on EUR with an exercise price

of USD1.180/EUR ensures that, if the value of the

EUR falls below USD1.180/EUR, the EUR can be sold

for USD1.180/EUR.

If the put option costs USD.03/EUR, the floor

price can be roughly approximated

as USD1.180/EUR - USD.O3/EUR

USD1.15/EUR. That is, if the PUT is

used, the put holder will be able to sell the EUR

for the USD1.180/EUR strike price, but in the

meantime, have paid a premium of USD.03/EUR.

Deducting the cost of the premium leaves

USD1.15/EUR as the floor price established by the

purchase of the put. This calculation ignores

fees and interest rate adjustments.

- Similarly, an individual who must buy foreign

currency at some point in the future can use

CALLS on spot to establish a ceiling price on the

domestic currency amount that will have to be

paid to purchase the foreign exchange.

- For example, a call on EUR with an exercise price

of USD1.23/EUR will ensure that, in the event

that the value of the EURO rises above

USD1.23/EUR, the call will be exercised and the

EUR bought for USD1.23/EUR. - If the call costs USD.02/EUR, this ceiling price

can be approximated - USD1.23/EUR USD.02/EUR USD1.25/EUR
- or the strike price plus the premium.

- Several real world considerations
- The calculations so far are only approximate for

essentially two reasons. - First, the exercise price and the premium of the

option on spot cannot be added directly without

an interest rate adjustment. The premium will be

paid now, up front, but the exercise price (if

the option is eventually exercised) will be paid

later. The time difference involved in the two

payment amounts implies that one of the two

should be adjusted by an interest rate factor.

- Second, there may be brokerage or other expenses

associated with the purchase of an option, and

there may be an additional fee if the option is

exercised. The following two examples illustrate

the insurance feature of FX options on spot and

show how to calculate floor and ceiling values

when some additional transactions costs are

included.

- Example 1 An American importer will have a net

cash out flow of GBP250,000 in payment for goods

bought in Great Britain. The payment date is not

known with certainty, but should occur in late

November. On September 16 the importer locks in a

ceiling purchase for pounds by buying 8 PHLX

calls GBP250,000/GBP31,250 8 on the pound, K

USD1.90/GBP and a December expiration. - The call premium on September 16 is USD.0220/GBP.

- With a brokerage commission of USD4/call, the

total cost of the eight calls is - 8(GBP3l,250)(USD.0220/GBP) 8(USD4)
- USD5,532.

- Measured from today's viewpoint, the importer has

essentially assured that the purchased exchange

rate will not be greater than - USD5,532/GBP250,000 USD1.90/GBP
- USD.02213/GBP USD1.90/GBP
- USD1.92213/GBP.
- Notice here that the add factor USD.02213/GBP

is larger than the call premium of USD.0220/GBP

by USD.00013/GBP, which represents the dollar

brokerage cost per pound. - The number USD1.92213/GBP is the importer's

ceiling price. The importer is assured he will

not pay more than this, but he could pay less.

- Case A. The spot rate on the November payment

date is USD1.86/GBP. The importer would not

exercise the call but would buy pounds spot at

the rate of USD1.86/GBP. The importer then sell

the eight calls for whatever market value they

had remaining. Assuming, a brokerage fee of USD4

per contract for the sale, the options would be

sold as long as their remaining market value was

greater than USD4 per option. The total cost

will have turned out to be - USD1.96/GBPUSD.02213/GBP
- - (sale value of options- USD32)/GBP250,000.

- If the resale value is not greater than USD32,

then the total cost per pound is - USD1.86 USD.02213 USD1.88213.
- The USD.02213 that was the original cost of the

premium and brokerage fee turned out in this case

to be an unnecessary expense.

- Now, to be strictly correct, a further adjustment

to the calculation should be made. Namely, the

USD1.86 and USD.02213 represent cash flows at two

different times. Thus, if R is the amount of

interest paid per dollar over the September 16 to

November time period, the proper calculation is

the cost per pound - USD1.86USD.02213(lR)
- - (sale value of options-USD32)/250,000.

- Case B. The spot rate on the November payment

date is USD1.95/GBP. The importer can either

exercise the calls or sell them for their market

value. Assume the importer sells them at a

current market value of USD.055 and pays USD32

total in brokerage commissions on the sale of

eight option contracts. The importer then buys

the pounds in the spot market for USD1.95/GBP.

The total cost is, before adding the premium and

commission costs paid in September - (USD1.95/GBP)(GBP250,000)
- (USD.055/GBP))( GBP250,000) 8(USD4)
- USD473,718.
- This amount implies an exchange rate of
- USD473,718/GBP250,000 USD1.89487/GBP.

- Adding in the premium and commission costs paid

back in September, the exchange rate is - USD1.89487/GBP USD.02213(l R)/GBP.
- If the importer chooses instead to exercise the

call, the calculations will be similar except

that the brokerage fee will be replaced by an

exercise fee. - This concludes Example 1.

- Example 2 A Japanese company must exchange

USD50M into JPY and wishes to lock in a minimum

yen value. The USD50M, is to be sold between

July1 and December 31. Since the company will

sell USD and receive JPY, the company will buy a

put option on USD, with an exercise price stated

in terms of JPY. - The company buys an American put on USD50M with a

strike price of JPY130/USD from a financial

institution. The premium is JPY4/USD. Clearly,

this is an OTC transaction.

- The put was purchased directly from the bank

thus, there is no resale value to the put. Assume

there are no additional fees. Then, the Japanese

firm has established a floor value for its USD,

approximately at - JPY130/USD - JPY4/USD JPY126/USD.
- Again, we can consider two scenarios, one in

which the yen falls in value to JPY145/USD and

the other in which the yen rises in value to

JPY115/USD.

- Case A. The yen falls to JPY145/USD. In this

case the company will not exercise the option to

sell dollars for yen at JPY13O/USD, since the

company can do better than this in the exchange

market. The company will have obtained a net

value of - JPY145/USD - JPY4/USD JPY141/USD.
- In total
- JPY141/USDUSD50M JPY7.050B

- Case B. The JPY rises to JPY115/USD. The company

will exercise the put and sell each U.S. dollar

for JPY130/USD. The company will obtain, net, - JPY130/USD - JPY4/USD JPY126/USD.
- In total
- JPY126/USDUSD50M JPY6.3B
- This is JPY11 better than would have been

available in the FX market and reflects a case

where the insurance paid off. This concludes

Example 2.

- Writing Foreign Currency Options
- General considerations. The writer of a foreign

currency option on spot or futures is in a

different position from the buyer of these

options. The buyer pays the premium up front and

then can choose to exercise the option or not.

The buyer is not a source of credit risk once the

premium has been paid. The writer is a source of

credit risk, however, because the writer has

promised either to sell or to buy foreign

currency if the buyer exercises his option. The

writer could default on the promise to sell

foreign currency if the writer did not have

sufficient foreign currency available, or could

default on the promise to buy foreign currency if

the writer did not have sufficient domestic

currency available.

- If the option is written by a bank, this risk of

default may be small. But if the option is

written by a company, the bank may require the

company to post margin or other security as a

hedge against default risk. For exchange-traded

options, as noted previously, the relevant

clearinghouse guarantees fulfillment of both

sides of the option contract. The clearinghouse

covers its own risk, however, by requiring- the

writer of an option to post margin. At the PHLX,

for example, the Options Clearing Corporation

will allow a writer to meet margin requirements

by having the actual foreign currency or U.S.

dollars on deposit, by obtaining an irrevocable

letter of credit from a suitable bank, or by

posting cash margin.

- If cash margin is posted, the required deposit is

the current market value of the option plus 4

percent of the value of the underlying foreign

currency. This requirement is reduced by any

amount the option is out of the money, to a

minimum requirement of the premium plus .75

percent of the value of the underlying foreign

currency. These percentages can be changed by the

exchanges based on currency volatility. Thus, as

the market value of the option changes, the

margin requirement will change. So an option

writer faces daily cash flows associated with

changing margin requirements.

- Other exchanges have similar requirements for

option writers. The CME allows margins to be

calculated on a net basis for accounts holding

both CME FX futures options and IMM FX futures.

That is, the amount of margin is based on one's

total futures and futures options portfolio. The

risk of an option writer at the CME is the risk

of being exercised and consequently the risk of

acquiring a short position (for call writers) or

a long position (for put writers) in IMM futures.

Hence the amount of margin the writer is

required to post is related to the amount of

margin required on an IMM FX futures contract.

The exact calculation of margins at the CME

relies on the concept of an option delta.

- From the point of view of a company or

individual, writing options is a form of

risk-exposure management of importance equal to

that of buying options. It may make perfectly

good sense for a company to sell foreign currency

insurance in the form of writing FX calls or

puts. The choice of strike price on a written

option reflects a straightforward trade-off. FX

call options with a lower strike price will be

more valuable than those with a higher strike

price. Hence the premiums the option writer will

receive are correspondingly larger. However, the

probability that the written calls will be

exercised by the buyer is also higher for calls

with a lower strike price than for those with a

higher strike. Hence the larger premiums

received reflect greater risk taking on the part

of the insurance seller, ie., the option writer.

- Writing Foreign Currency Options
- a detailed example.
- The following example illustrates the risk/return

trade-off for the case of an oil company with an

exchange rate risk, that chooses to become an

option writer.

- Example 3 Iris Oil Inc., a Houston-based energy

company, has a large foreign currency exposure in

the form of a CAD cash flow from its Canadian

operations. The exchange rate risk to Iris is

that the CAD may depreciate against the USD. In

this case, Iris CAD revenues, transferred to its

USD account will diminish and its total USD

revenues will fall. Iris chooses to reduce its

long position in CAD by writing CAD calls with a

USD strike price.

- By writing the options, Iris receives an

immediate USD cash flow representing the

premiums. This cash flow will increase Iris'

total USD return in the event the CAD depreciates

against the USD or, remains unchanged against the

USD, or appreciates only slightly against the

USD. - Clearly, the calls might expire worthless or they

might be exercised. In either case, however, Iris

walks away with the full amount of the options

premiums

- If the USD value of the CAD remains unchanged,

the option premium received is simply an

additional profit. - If the value of the CAD falls, the premium

received on the written option will offset part

or all of the opportunity loss on the underlying

CAD position. - If the value of the CAD rises sharply, Iris will

only participate in this increased value up to a

ceiling level, where the ceiling level is a

function of the exercise price of the written

option.

- In sum, the payoff to Iris' strategy will depend

both on exchange rate movements and on the

selection of the strike price of the written

calls. - To illustrate Iris' strategy, consider an

anticipated cash flow of CAD300M over the next

180 days. - With hedge ratio of 11, Iris sells

CAD300,000,000/CAD50,000 - 6,000 PHLX calls.
- every CAD option is for CAD50,000.

- Assume Iris writes 6,000 PHLX calls with a

6-month expiration the current spot rate is S

USD.75/CAD and the 6-month forward rate is - F USD.7447/CAD.
- For the current level of spot rate, logical

strike price choices for the calls might be K

USD.74, or USD.75, or USD.76 per CAD, of course. - For the illustration, assume that Iris

brokerage fee is USD4 per written call and let

the hypothetical market values of the options be

as follows

c(K USD.74/CAD) USD.01379 c(K USD.75/CAD)

USD.00650 c(K USD.76/CAD) USD.00313.

K Value One call n Value Total Premium Total Fees USD4/call

.74 USD689.5 6,000 USD4,137,000 USD24,000

.75 USD325.0 6,000 USD1,950,000 USD24,000

.76 USD156.5 6,000 USD939,000 USD24,000

- We now introduce an additional cost that is

associated with the exercise fee, which exists in

the real markets. - If the calls are exercised, an additional OCC fee

of USD35/call is assumed. - In our example then, an exercise of the calls

requires a total OCC fee of - USD35(6,000) USD210,000
- for the 6,000 written calls.

- In six months Iris will receive a cash flow of

CAD300M. At that time, the total value of the

long CAD position of Iris, plus the short calls

position will depend on the strike price chosen. - Let
- S the spot exchange rate at expiration.
- The next three tables show the possible values

for Iris

If K USD.74/CAD

Strategy Initial Cash Flow Cash flow at Expiration Cash flow at Expiration

Strategy Initial Cash Flow Slt USD.74/CAD SgtUSD.74/CAD

Write 6,000, .74 calls USD4,113,000 0 -(S-.74)CAD300M -USD210,000

CAD (S)CAD300M (S)CAD300M

Total P/L USD4,113,000 (S)CAD300M (S)CAD300M USD4.113,000 USD221,780,000 USD225,903,000

If K USD.75/CAD

Strategy Initial Cash Flow Cash flow at Expiration Cash flow at Expiration

Strategy Initial Cash Flow Slt USD.75/CAD SgtUSD.75/CAD

Write 6,000, .75 calls USD1,926,000 0 -(S-.75)CAD300M -USD210,000

CAD (S)CAD300M (S)CAD300M

Total P/L USD1,926,000 (S)CAD300M (S)CAD300M USD1.926,000 USD224,700,000 USD226,716,000

If K USD.76/CAD

Strategy Initial Cash Flow Cash flow at Expiration Cash flow at Expiration

Strategy Initial Cash Flow Slt USD.76/CAD SgtUSD.76/CAD

Write 6,000, .76 calls USD915,000 0 -(S-.76)CAD300M -USD210,000

CAD (S)CAD300M (S)CAD300M

Total P/L USD915,000 (S)CAD300M (S)CAD300M USD915,000 USD227,790,000 USD228,705,000

A consolidation of the three profit profile

tables

SPOT RATE USD/CAD STRIKE PRICE STRIKE PRICE STRIKE PRICE

SPOT RATE USD/CAD USD.74/CAD USD.75/CAD USD.76/CAD

Slt.74 S(CAD300M) USD4,113,000 S(CAD300M) USD1,926,000 S(CAD300M) USD915,000

.74ltSlt.75 USD225,903,000 S(CAD300M) USD1,926,000 S(CAD300M) USD915,000

.75ltSlt.76 USD225,903,000 USD226,716,000 S(CAD300M) USD915,000

.76ltS USD225,903,000 USD226,716,000 USD228,705,000

As illustrated by the consolidated table and the

three separate profit profile tables, the lower

the strike price chosen, the better the

protection against a depreciating CAD. On the

other hand, a lower strike price limits the

corresponding profitability of the strategy if

the CAD happens to appreciate against the USD in

six months. The optimal decision of which

strategy to take is a function of the spot

exchange rate at expiration.

- One possible comparison of the three
- results is to evaluate the options strategy
- vis-à-vis the immediate forward exchange.
- Recall that when Iris enters the options
- strategy the forward exchange rate is
- F USD.7447/CAD.
- Thus, Iris may exchange the CAD300M
- Forward for USD223,410,000 a future
- break-even Spot rate can be calculated for
- Every corresponding exercise price chosen

- F .7447. Iris may exchange today, CAD300M

forward for - CAD300,000,000(USD.7447/CAD)
- USD223,410,000.
- IF K .74,
- S(CAD300M) 4,113,000 USD223,410,000
- ? SBE USD.7310/CAD.
- IF K .75,
- S(CAD300M) 1,926,000 USD223,410,000
- ? SBE USD.7383/CAD.
- IF K .76,
- S(CAD300M) 915,000 USD223,410,000
- ? SBE USD.7416/CAD.

- CONCLUSION
- Writing the calls will protect Iris flow
- in USD better than purchasing the CAD
- forward if the spot rate in six months
- will be above the corresponding
- break- even exchange rates.

- A second possible analysis of the optimal

decision depends on all possible values of the

spot exchange rate, given our assumptions. Recall

that the assumptions are - Iris maintains an open long position of CAD300M

un hedged. Alternatively, Iris writes 6,000 PHLX

calls with 180-day expiration period. Possible

strike prices are USD.76/CAD, USD.75/CAD,

USD.74/CAD. Current spot and forward exchange

rates are USD.75/CAD and USD.7447/CAD,

respectively.

- The terminal spot rate is the market exchange

rate when the calls expire. It is assumed that

Iris pays a brokerage-fee of USD4 per option

contract and an additional fee of USD35 per

option to the Options Clearing Corporation if the

options are exercised.

- Optimal decision as a function of the unknown

terminal spot rate - Terminal Spot rate Optimal Decision
- S gt.76235 Hold long currency only
- .75267 lt Slt .76235 Write options with K

.76 - .74477 lt Slt .75267 Write options with K

.75 - S lt .74477 Write options with K .74

- Final comments on Example 3.
- In the example, the OCC charges a USD35 per

exercised call. Thus, it might be cheaper for

Iris to buy back the calls and pay the brokerage

fee of USD4 per call in the event the options

were in danger of being exercised. In addition,

it is assumed that Iris will have the CAD300M on

hand if the options are exercised. This would

not be the case if actual Canadian dollar

revenues were less than anticipated.

- In that event, the options would need to
- be repurchased prior to expiration.
- Each of the three choices of strike price
- will have a different payoff, depending on
- the movement in the exchange rate. But
- Iris' expectation regarding the exchange
- rate is not the only relevant criterion for
- choosing a risk-management strategy.
- The possible variation in the underlying
- position should also be considered.

- Here are the maximal and minimal
- payoffs for each of the call-writing
- choices, compared to the un hedged
- position and a forward market hedge

- Strategy Max Value Min Value
- Unhedged
- Long
- Position Unlimited Zero.
- Short
- Forward USD223,410,000 USD223,410,000
- .76 call USD228,705,000 Unhedged min

USD915,000. - .75 call USD226,716,000 Unhedged min

USD1,926,000. - .74 call USD225,903,000 Unhedged min
- USD4,113,000.

Futures options A FORWARD IS A CONTRACT IN

WHICH ONE PARTY COMMITS TO BUY AND THE OTHER

PARTY COMMITS TO SELL A PRESPECIFIED AMOUNT OF AN

AGREED UPON COMMODITY FOR A PREDETERMINED PRICE

ON A SPECIFIC DATE IN THE FUTURE.

- BUY means OPEN A LONG POSITION
- SELL means OPEN A SHORT POSITION

Delivery and payment

Buy or sell a forward

t

T

Time

EXAMPLE GBP 18.5.99 SPOT

USD1,6850/GBP 30 days forward USD1,7245/GBP

60 days forward USD1,7455/GBP 90 days

forward USD1,7978/GBP 180 days

forward USD1,8455/GBP The existence of forward

exchange rates implies that there is a demand and

supply for the GBP for future dates.

Profit from aLong Forward Position

F

Profit from a Short Forward Position

F

Futures Contracts

- Agreement to buy or sell an asset for a certain

price at a certain time - Similar to forward contract
- Whereas a forward contract is traded OTC, futures

contracts are traded on organized exchanges

A FUTURES Is a STANDARDIZED FORWARD traded

on an organized exchange. STANDARDIZATION THE

COMMODITY, TYPE AND QUALITY, THE QUANTITY ,

PRICE QUOTES, DELIVERY DATES and

PROCEDURES, MARGIN ACCOUNTS, The MARKING TO

MARKET process.

- NYMEX. Light, Sweet Crude Oil
- Trading Unit
- Futures 1,000 U.S. barrels (42,000 gallons).
- Options One NYMEX Division light, sweet crude

oil futures contract. - Price Quotation
- Futures and Options Dollars and cents per

barrel. - Trading Hours
- Futures and Options Open outcry trading is

conducted from 1000 A.M. until 230 P.M. - After hours futures trading is conducted via the

NYMEX ACCESS - internet-based trading platform beginning at 315

P.M. on Mondays through Thursdays and concluding

at 930 A.M. the following day. On Sundays, the

session begins at 700 P.M. All times are New

York time. Trading Months - Futures 30 consecutive months plus long-dated

futures initially listed 36, 48, 60, 72, and 84

months prior to delivery. - Additionally, trading can be executed at an

average differential to the previous day's

settlement prices for periods of two to 30

consecutive months in a single transaction. These

calendar strips are executed during open outcry

trading hours. - Options 12 consecutive months, plus three

long-dated options at 18, 24, and 36 months out

on a June/December cycle.

- Minimum Price Fluctuation
- Futures and Options 0.01 (1) per barrel

(10.00 per contract). Maximum Daily Price

Fluctuation - Futures Initial limits of 3.00 per barrel are

in place in all but the first two months and rise

to 6.00 per barrel if the previous day's

settlement price in any back month is at the

3.00 limit. In the event of a 7.50 per barrel

move in either of the first two contract months,

limits on all months become 7.50 per barrel from

the limit in place in the direction of the move

following a one-hour trading halt. - Options No price limits.
- Last Trading Day
- Futures Trading terminates at the close of

business on the third business day prior to the

25th calendar day of the month preceding the

delivery month. If the 25th calendar day of the

month is a non-business day, trading shall cease

on the third business day prior to the last

business day preceding the 25th calendar day. - Options Trading ends three business days before

the underlying futures contract.

- Exercise of Options
- By a clearing member to the Exchange

clearinghouse not later than 530 P.M., or 45

minutes after the underlying futures settlement

price is posted, whichever is later, on any day

up to and including the option's expiration. - Options Strike Prices
- Twenty strike prices in increments of 0.50 (50)

per barrel above and below the at-the-money

strike price, and the next ten strike prices in

increments of 2.50 above the highest and below

the lowest existing strike prices for a total of

at least 61 strike prices. The at-the-money

strike price is nearest to the previous day's

close of the underlying futures contract. Strike

price boundaries are adjusted according to

the futures price movements. - Delivery
- F.O.B. seller's facility, Cushing, Oklahoma, at

any pipeline or storage facility with pipeline

access to TEPPCO, Cushing storage, or Equilon

Pipeline Co., by in-tank transfer, in-line

transfer, book-out, or inter-facility transfer

(pumpover).

- Delivery Period
- All deliveries are rateable over the course of

the month and must be initiated on or after the

first calendar day and completed by the last

calendar day of the delivery month. - Alternate Delivery Procedure (ADP)
- An alternate delivery procedure is available to

buyers and sellers who have been matched by the

Exchange subsequent to the termination of trading

in the spot month contract. If buyer and seller

agree to consummate delivery under terms

different from those prescribed in the contract

specifications, they may proceed on that basis

after submitting a notice of

their intention to the Exchange. - Exchange of Futures for, or in Connection with,

Physicals (EFP) - The commercial buyer or seller may exchange a

futures position for a physical position of equal

quantity by submitting a notice to the exchange.

EFPs may be used to either initiate or liquidate

a futures position.

- Deliverable Grades
- Specific domestic crudes with 0.42 sulfur by

weight or less, not less than 37 API gravity nor

more than 42 API gravity. The following domestic

crude streams are deliverable West Texas

Intermediate, Low Sweet Mix, New Mexican Sweet,

North Texas Sweet, Oklahoma Sweet, South Texas

Sweet. - Specific foreign crudes of not less than 34 API

nor more than 42 API. The following foreign

streams are deliverable U.K. Brent and Forties,

and Norwegian Oseberg Blend, for which the seller

shall receive a 30-per-barrel discount below the

final settlement price Nigerian Bonny Light and

Colombian Cusiana are delivered at 15 premiums

and Nigerian Qua Iboe is delivered at a 5

premium. - Inspection
- Inspection shall be conducted in accordance with

pipeline practices. A buyer or seller may appoint

an inspector to inspect the quality of oil

delivered. However, the buyer or seller who

requests the inspection will bear its costs and

will notify the other party of the transaction

that the - inspection will occur.

- Position Accountability Limits
- Any one month/all months 20,000 net futures, but

not to exceed 1,000 in the last three days of

trading in the spot month. - Margin Requirements
- Margins are required for open futures or short

options positions. The margin requirement for an

options purchaser will never exceed the premium. - Trading Symbols
- Futures CL
- Options LO

- NYMEX Copper Futures
- Trading Unit 25,000 pounds.
- Price Quotation Cents per pound. For example,

75.80 per pound. - Trading Hours Open outcry trading is conducted

from 810 A.M. until 100 P.M. After-hours

futures trading is conducted via the NYMEX

ACCESS - Trading Months Trading is conducted for delivery

during the current calendar month and the next 23

consecutive calendar months. - Minimum Price Price changes are registered in

multiples of five one - Fluctuation hundredths of one cent (0.0005, or

0.05) per pound, equal to 12.50 per contract. A

fluctuation of one cent (0.01 or 1) is equal to

250.00 per contract.

- Maximum Daily Initial price limit, based upon the

preceding day's - Price Fluctuation settlement price is 0.20

(20) per pound. Two minutes after either of

the two most active months trades at the limit,

trading in all months of futures and options

will cease for a 15-minute period. Trading will

also cease if either of the two active months is

bid at the upper limit or offered at the lower

limit for two minutes without trading. Trading

will not cease if the limit is reached during the

final 20 minutes of a day's trading. If the limit

is reached during the final half hour of

trading, trading will resume no later than 10

minutes before the normal closing time. When

trading resumes after a cessation of trading, the

price limits will be expanded by increments of

100. - Last Trading Day Trading terminates at the close

of business on the third to last business day of

the maturing delivery month.

- Delivery Copper may be delivered against the

high- grade copper contract only from a

warehouse in the United States licensed or

designated by the Exchange. Delivery must be

made upon a domestic basis import duties or

import taxes, if any, must be paid by the

seller, and shall be made without any

allowance for freight. - Delivery Period The first delivery day is the

first business day of the delivery month the

last delivery day is the last business day of

the delivery month. - Margin Requirements Margins are required for open

futures and short options positions. The

margin requirement for an options purchaser - will never exceed the premium

paid.

CBOT Corn Futures

MARGIN ACCOUNTS A MARGIN is an amount of money

that must be deposited in a margin account in

order to open any futures position, long or

short. It is a good will deposit. The

clearinghouse maintains a system of margin

requirements from all traders, brokers and

futures commercial merchants.

MARGIN ACCOUNTS. There are two types of

margins The initial margin The amount that

every trader must deposit with the broker upon

opening a futures account short or long. The

initial deposit is the investor EQUITY. This

equity changes on a daily basis because all

profits and losses must be realized by the end of

every trading day.

MARGIN ACCOUNTS. The maintenance (variable)

margin This is a minimum level of the traders

equity in the margin account. If the traders

equity falls below this level, the trader will

receive a margin call requiring the trader to

deposit more funds and bring the account to its

initial level. Otherwise, the account will be

closed.

Most of the time, Initial margins are between 2

to 10 of the position value. Maintenance

(variable) margin is usually around 70 - 80 of

the initial margin. Example a position of 10

CBT treasury bonds futures (100,000 face value

each) at a price of 75,000 each. The initial

margin deposit of 5 of 750,000 is 37,500. If

the variable margin is 75 ?Margin call if the

amount in the margin account falls to 26,250.

Example of a Futures Trade

- On JUN 5 an investor takes a long position in 2

NYMEX DEC gold futures. - contract size is 100 oz.
- futures price is USD590/oz
- margin requirement is 5.
- USD2,950/contract or USD5,900 total.
- Maintenance margin is 75.
- USD2,212.5/contract or USD4,425
- Total.

Daily equity changes in the margin

account MARKING TO MARKET Every day, upon the

market close, all profits and losses for that day

must be realized. I.e., SETTLED. The benchmark

prices for this process are SETTLEMENT PRICES

A SETTLEMENT PRICE IS the average price of

trades during the last several minutes of the

trading day. Every day, when the markets close,

SETTLEMENT PRICES for the futures of all

products and for all months of delivery are set.

They are then compared with the previous day

settlement prices and to the trading prices on

that day and the difference must be settled

overnight

Open a long position in 10 JUNE crude oil futures

for 58.50/bbl. VALUE (10)(1,000)(58.50)

585,000INITIAL MARGIN (.03)(585,000)

17,550 VAR. MARGIN 80

13,350/17,550 .761 lt .8

MARGIN CALL SEND 4,200 TO MARGIN

ACCOUNT TO BRING IT UP TO 17,550 DAY 5

58.27 582,700 1,900 19,450

1M face value of 90-day T-bills. P

1,000,0001 - (1 Q/100)(90/360). Initial

Margin is assumed to be 5 of contract fee.

Delivery

- If a contract is not closed out before
- maturity, it is usually settled by delivering
- The assets underlying the contract. When
- There are alternatives about what is
- delivered, where it is delivered, and when it
- is delivered, the party with the short
- position chooses.
- Few contracts are settled in cash.
- For example, those on stock indices and
- Eurodollars.

- A futures markets statistic
- 97-98 of all the futures for all delivery months

and for all underlying commodities do not get to

delivery!! - This means that
- Only 2-3 do reach delivery.
- Most traders close their positions before they

get to delivery. - Most traders do not open futures positions for

business. - Most futures are traded for Risk Management

reasons,

Mechanics of Call Futures Options

- The underlying asset is
- A FUTURES.
- This means that when you exercise a
- futures option you become committed
- to BUY or SELL the asset underlying the
- futures, depending on whether you
- have a call or a put.

Mechanics of Call Futures Options

- When a call futures option is exercised the

holder acquires - 1. A long position in the futures
- 2. A cash amount equal to the excess of
- the most recent settlement futures price,

F(settle) over K. - The writer obtains short position in the futures

and the cash amount in his/her margin account is

adjusted opposite to 2. above.

The Payoff of a futures call exercise

- If the futures position is closed out on date j,

which is immediately upon the call exercise - Payoff
- F(settle) K Fj,T F(settle)
- Fj,T K,
- where Fj,T is futures price at time the futures

is closed.

Mechanics of Put Futures Option

- When a put futures option is exercised the

holder acquires - 1. A short position in the futures
- 2. A cash amount equal to the excess of
- the put strike price, K, over the most
- recent futures settlement price F(settle).
- The put writer obtains a long futures position

and his/her margin account is adjusted opposite

to 2. above.

The Payoff of a futures put exercise

- Payoff from put exercise
- K F(set