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Title: Options on Stock Indices and Currencies Chapter 15


1
Options onStock Indices and CurrenciesChapter
15
2
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.
3
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.
4
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.
5
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
6
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
7
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.
8
  • 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

9
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.
10
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.
11
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
12
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.
13
THE RATE OF RETURN ON THE INDEX
14
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15
THE BETA OF A PORTFOLIO Definitions
16
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.
17
By definition
18
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
19
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
20
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
21
STOCK INDEX OPTIONS 1. One contract
(I)(m) (WSJ) 2. ACCOUNTS ARE SETTLED BY CASH
22
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.
23
MoneyGone offer Deposit A now. Receive
AMax0, .5RI in 6 months. Denote the date in
six month T. Rewrite MoneyGone offer at T
24
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
25
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
26
  • 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.

27
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
28
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
29
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
30
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
31
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
32
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.
33
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.
34
1. The number of puts is
35
2. The exercise price, K, is determined by
substituting I1 K and the required level, (V1/
V0) into the equation
and solving for K
36
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
37
Solution Purchase
38
The exercise price of the puts is
Solution Purchase n 480 six-months puts with
exercise price K 1,210.
39
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)
40
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
41
Substitute for n
42
To substitute for V1 we solve the equation
43
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.
44
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45
Example (p326) protection for 3 months
Solution Purchase
46
The exercise price of the puts is
Solution Purchase n 10 three -months puts with
exercise price K 960.
47
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48
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.
49
  • A SPECIAL CASE In the case that
  • ß 1
  • qP qI,
  • the portfolio is statistically similar to the
  • index. In this case

50
Assume that in the above example ßp 1 and qP
qI, then
51
Example (p326-27) ßp 1 and qP qI, then
52
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)

53
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
54
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55
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.
56
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
57
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58
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
59
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
60
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
61
CURRENCY CROSS RATES EXAMPLE
62
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
63
THE CASH ARBITRAGE ACTIVITIES USD1,000,000 U
SD1,006,134.26 0.6394 0.5580 GBP639,400
CHF1,803,108 2.8200
64
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.
65
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.
66
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
67
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
68
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
69
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
70
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
71
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.
72
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
73
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74
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.
75
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
76
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
77
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
78
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.
79
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
80
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

81
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
82
  • 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.

83
  • 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.

84
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.

85
  • 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.

86
  • 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.

87
  • 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.

88
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.
89
  • 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.

90
  • 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.

91
  • 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.

92
  • 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.

93
  • 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.

94
  • 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.

95
  • 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.

96
  • 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.

97
  • 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.

98
  • 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. 

99
  • 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.

100
  • 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.

101
  • 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.

102
  • 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

103
  • 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.

104
  • 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.

105
  • 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.

106
  • 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.

107
  • 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.

108
  • 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.

109
  • 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.

110
  • 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.

111
  • 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

112
  1. If the USD value of the CAD remains unchanged,
    the option premium received is simply an
    additional profit.
  2. 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.
  3. 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.

113
  • 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.

114
  • 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

115
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
116
  • 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.

117
  • 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

118
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
119
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
120
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
121
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
122
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.
123
  • 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

124
  • 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.

125
  • 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.

126
  • 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.

127
  • 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.

128
  • 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

129
  • 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.

130
  • 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.

131
  • 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

132
  • 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.

133
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.
134
  • BUY means OPEN A LONG POSITION
  • SELL means OPEN A SHORT POSITION

Delivery and payment
Buy or sell a forward
t
T
Time
135
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.
136
Profit from aLong Forward Position
F
137
Profit from a Short Forward Position
F
138
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

139
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.
140
  • 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.

141
  • 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.

142
  • 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).

143
  • 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.

144
  • 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.

145
  • 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

146
  • 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.

147
  • 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.

148
  • 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.

149
CBOT Corn Futures
150
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.
151
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.
152
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.
153
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.
154
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.

155
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
156
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
157
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
158
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
159
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.
160
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.

161
  • 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,

162
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.

163
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.

164
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.

165
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.

166
The Payoff of a futures put exercise
  • Payoff from put exercise
  • K F(set
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