Options on Stock Indices, Currencies, and Futures Chapter 13

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Options onStock Indices, Currencies, and
FuturesChapter 13
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STOCK INDEX OPTIONS ONE CONTRACT VALUE
(INDEX VALUE)(MULTIPLIER) One contract
(I)(m) ACCOUNTS ARE SETTLED BY CASH
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• STOCK INDEX OPTIONS FOR
• PORTFOLIO INSURANCE
• Problems
• How many puts to buy?
• Which exercise price will guarantee the desired
  level of protection?
• The answers are not easy because the
• index underlying the puts is not the
• portfolio to be protected.

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The protective put with a single stock
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The protective put consists of holding the
portfolio and purchasing n puts.
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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
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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
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Second, rewrite the CAPM result, with actual
returns
In a more refined way, using V and I for the
portfolio and index market values, respectively
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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.
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For example
The manager wants V1, to be down to no more than
90 of the initial portfolio market value, V0
V1 V0(.9). We denote this desired level by
(V1/ V0). This is the decision variable.
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1. The number of puts is
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2. The exercise price, K, is determined by
substituting I1 K and the required level, (V1/
V0) into the equation
and solving for K
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We rewrite the Profit/Loss table for the
protective put strategy
We are now ready to calculate the floor level of
the portfolio V1n(m)(K- I1)
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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
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Substitute for n
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To substitute for V1 we solve the equation
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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 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 is summarized below
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Solution Purchase
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The exercise price of the puts is
Solution Purchase n 480 six-months puts with
exercise price K 1,210.
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CONCLUSION Holding the portfolio and purchasing
480, 6-months protective puts on the SP500
index, with the exercise price K 1210,
guarantees that the portfolio value, currently
25M, will not fall below 22,505,000 in six
months.
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Example (page 274) protection for 3 months
Solution Purchase
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The exercise price of the puts is
Solution Purchase n 10 six-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.
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• A SPECIAL CASE In the case that
• ß 1 and 2. qP qI, the portfolio is
• statistically similar to the index.
• In this case

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Assume that in the above example, ßp 1 and qP
qI, then
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Example (page 273) ßp 1 and qP qI, then
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FOREIGN CURRENCY FUTURES Standardized Options
Currencies Traded The PHLX lists six
dollar-based standardized currency option
contracts, which settle in the actual physical
currency. These are the most heavily traded
currencies in the global inter bank
market. Contract Size The amounts of currency
controlled by the various currency options
contracts are geared to the needs of the widest
possible range of participants.
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• Currency options Units
• USD/AUD 50,000AUD
• USD/GBP 31,250GBP
• USD/CD 50,000CD
• 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.

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• 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.

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Standardized Options
With the Canadian dollar spot price currently at
a level of USD.6556/CD, 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/CD, 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 82 would give the option buyer the right to
  buy Euros at 82 cents per EUR.

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• 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.

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• 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
• 62,500DMUSD.01/EUR USD625.

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Customized Currency Options

• Currencies Traded
• Customized currency options can be traded on any
  combination of the currencies currently available
  for trading. Currently, AUD must be denominated
  in U.S. dollars. AUD premiums must be denominated
  in USD.

In the case of an option on the USD in CD, the
underlying currency is U.S. dollars. The strike
prices and premiums are quoted in Canadian
dollars. E.G, a call option on the USD with a
strike price of 1.542 gives the buyer the right
to purchase 50,000 USD at CD1.542/USD.
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• Underlying CurrencyThe underlying currency is
  that currency which is purchased (in the case of
  a call) or sold (in the case of a put) upon
  exercise of the contract.
• Base CurrencyThe base currency is that currency
  in which terms the underlying is being quoted,
  i.e. strike price.
• Expiration/Last Trading DayExpirations can be
  established for any business day up to two years
  from the trade date. Customized option contracts
  expire at 1015 a.m., Eastern Time on the
  expiration day in contrast with standardized
  options which expire at 1159 p.m., Eastern Time
  on the expiration day.

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• In addition, the exercise and assignment process
  for customized options is more akin to the OTC
  market in terms of expiration timeframe. Unlike
  the process utilized for standardized options,
  exercise notices must be received by 1000 a.m.,
  Eastern Time and the writer is then notified of
  the number of contracts assigned. If necessary,
  contact the PHLX for more details.
• The contract size for customized currency options
  is

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Underlying currency Contract size Australian
dollar 50,000AUD British Pound 31,250GBP Canadi
an dollar 50,000CD Euro 62,500EUR Japanese
Yen 6,250,000JPY Mexican
Peso 250,000MXP Spanish Peseta
5,000,000ESP Swiss Frank 62,500CHF USD 50,0
00USD.
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• Exercise PricesExercise or strike prices may be
  expressed in any increment out to four
  characters. For example, a USD/GBP option could
  have an exercise price of 1.543.
• Exercise-style European-style only.
• Minimum Transaction SizeSince customized
  currency options were designed for the
  institutional market, there is a minimum opening
  transaction size which equals or exceeds 50
  contracts.

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A call option on the EUR quoted in American terms
would have a strike price expressed in USD. For
example, USD.8484 per EUR. A similar option
expressed in European terms would be a put option
on USD with a strike price expressed in EUR. For
example, 1.1787 EUR per USD.
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• Contract TermsAn option may be expressed in
  either American terms or European terms (inverse
  terms). For example, an option in American terms
  would have exercise prices quoted in terms of
  U.S. dollar per unit of foreign currency. An
  option in European or inverse terms would have
  exercise prices quoted in terms of units of
  foreign currency per U.S. dollar.

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• Trading ProcessTrading is conducted in an open
  outcry auction market, just as in standardized
  option contracts. When initial interest in a
  customized option series is expressed, a floor
  member must first present a Request For Quote
  (RFQ) to an Exchange staff member for
  dissemination. Subsequently, responsive quotes
  are generated by competing market makers and
  floor brokers representing off floor interest.

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• PremiumsPremiums may be expressed either in
  terms of the base currency per unit of the
  underlying currency or in percent of the
  underlying currency (based on contract size). For
  example, the premium for an option on the USD/EUR
  (USD being the base currency and EURO being the
  underlying currency) could be expressed in U.S.
  cents per EUR or as a percentage of 62,500 EUROS.

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• Price and Quote DisseminationRequest For Quotes
  (RFQs), responsive quotes and trades will be
  disseminated to the Option Price Reporting
  Authority (OPRA) for availability to quote
  vendors

The premium for an option on the EUR with a
strike price in USD (EUR is the underlying
currency and the USD is the base currency) quoted
in cents per EUR(premium of 2.50) would be
calculated as follows the aggregate premium for
each contract USD1562.50(USD.025 x 62,500EUR
per contract ).Similarly, if this option were
quoted in percentage of underlying and the
premium was 2.5, the premium amount for each
contract 1562.5 EUR (.025 x 62,500 EUR per
contract).
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• Position LimitsPosition limits are the maximum
  number of contracts in an underlying currency
  which can be controlled by a single entity or
  individual. Currently, position limits are set at
  200,000 contracts on each side of the market
  (long calls and short puts or short calls and
  long puts) for each currency except the Mexican
  peso, and the Spanish peseta which are 100,000
  contracts. For purposes of computing position
  limits, all options involving the U.S. dollar
  against another currency will be aggregated with
  each other for each currency (i.e., USD/EUR and
  EUR/USD on the same side of the market will be
  aggregated - USD/EUR long calls and short puts
  with EUR/USD short calls and long puts).

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• FX Options As InsuranceOptions on spot
  represent insurance bought or written on the spot
  rate. (options on futures represent insurance
  bought or written on the futures price.) 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 option on EUR with
  an exercise price of USD.80/EUR ensures that, if
  the value of the EUR falls below USD.80/EUR, the
  EUR can be sold for USD.80/EUR.

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If the put option costs USD.01/EUR, the floor
price can be roughly approximated as USD.80/EUR
- USD.O1/EUR USD.79/EUR. That is, if the
option is used, the put holder will be able to
sell the EUR for the USD.80/EUR strike price, but
in the meantime, have paid a premium of
USD.01/EUR. Deducting the cost of the premium
leaves USD.79/EUR as the floor price established
by the purchase of the put. This calculation
ignores fees and interest rate adjustments.
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• Similarly, an individual who has to buy foreign
  currency at some point in the future can use call
  options on spot to establish a ceiling price on
  the domestic currency amount that will have to be
  paid to purchase the foreign exchange.

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• For example, a call option on EUR with an
  exercise price of USD.80/EUR will ensure that, in
  the event the value of the EURO rises above
  USD.80/EUR, the EUR can be bought for USD.80/EUR
  anyway. If the call option costs USD.02/EUR,
  this ceiling price can be approximated
• USD.80/EUR USD.02/EUR USD.82/EUR
• or the strike price plus the premium.

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• To summarize these two important points involving
  FX puts and calls 
• 1- Foreign currency put options on spot can be
  used as insurance to establish a floor price on
  the domestic currency value of foreign exchange.
  This floor price is approximately 
• Floor price exercise price of put
• - put premium 
• 2- Foreign currency call options on spot can be
  used as insurance to establish a ceiling price on
  the domestic currency cost of foreign exchange.
  This ceiling price is approximately  
• Ceiling price exercise price of call
• call premium.

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• These calculations 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.

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• Example 1 A U.S. importer will have a net cash
  out flow of 250,000 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 250,000/31,250 8 on the pound, a
  strike price K USD1.50/GBP and a December
  expiration. The option premium on September 16 is
  USD.0220/GBP. With a brokerage commission of
  4/option, the total cost of the eight contracts
  is
• 8(3l,250)(.0220/) 8(4) 5,532.

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• Measured from today's viewpoint, the importer has
  essentially assured that the purchase price for
  pounds will not be greater than 
• 5,532/250,000 1.50/ .02213/ 1.50/
  USD1.52213/GBP. 
• Notice here that the add factor USD.02213/GBP
  is larger than the option premium of USD.0220/GBP
  by USD.00013/GBP, which represents the dollar
  brokerage cost per pound. The number
  USD1.52213/GBP is the importer's ceiling price.
  The importer is assured he will not pay more than
  this, but he could pay less. The price the
  importer will actually pay will depend on the
  spot price on the November payment date. To
  illustrate this, we can consider two scenarios
  for the spot rate.

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• Case A. The spot rate on the November payment
  date is USD1.46/GBP. The importer would not
  exercise the call but would buy pounds spot at
  the rate of USD1.46/GBP. The importer then sell
  the eight calls for whatever market value they
  had remaining. Assuming, a brokerage fee of 4
  per contract for the sale, the options would be
  sold as long as their remaining market value was
  greater than 4 per option. The total cost will
  have turned out to be
• USD1.46/GBPUSD.02213/GBP
• - (sale value of options- 32)/250,000.

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• If the resale value is not greater than 32, then
  the total cost per pound is 1.46 .02213
  1.48213.
• The USD.02213/GBP 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 1.46 and .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
• 1.46.02213(lR)
• - (sale value of options-32)/250,000.

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• Case B. The spot rate on the November payment
  date is USD1.55/GBP. The importer can either
  exercise his options or sell them for their
  market value. Assume the importer sells them at
  a current market value of .055 and pays 32
  total in brokerage commissions on the sale of
  eight option contracts. The importer then buys
  the pounds in the spot market for USD1.55/GBP.
  The total cost is, before adding the premium and
  commission costs paid in September
• (USD1.55/GBP)(250,000)
• (USD.055/GBP))( 250,000) 8(4)
• 373,782.
• This amount is
• 373,782/250,000 USD1.49513/GBP.
•  

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• Adding in the premium and commission costs paid
  back in September, the total cost is
• USD1.49513/GBP USD.02213(l R)/GBP
•  
• If the importer chooses instead to exercise the
  option, the calculations will be similar except
  that the brokerage fee will be replaced by an
  exercise fee.
• This concludes Example 1.

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• Example 2  A Japanese company wants to lock in a
  minimum yen value of USD50M, this amount to be
  sold between July1 and December 31. Since the
  company wishes to sell USD and receive JPY, the
  company will buy a put option on USD, with an
  exercise price stated in terms of JPY.
• Suppose the company buys from its bank an
  American put on USD50M with a strike price of
  JPY130/USD.

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• This call is purchased directly from the bank
  thus, there is no resale value to the option. The
  company pays a premium of JPY4/USD. In this
  case, assume there are no additional fees. Then,
  the Japanese company 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.

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• 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.

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• 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.
• 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.

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• 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.

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• 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.

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• 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.

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• 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.

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• 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.

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• Writing Foreign Currency Options
• an example.
• The following example will illustrate
• the risk/return trade-off for the case of an oil
  company with an exchange rate risk, that chooses
  to become an option writer.

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• Example 3 Iris Oil Inc., a Houston-based energy
  company, has a large foreign currency exposure in
  the form of a CD cash flow from its Canadian
  operations. The exchange rate risk to Iris is
  that the CD may depreciate against the USD. In
  this case, Iris CD revenues, transferred to its
  USD account will diminish and its total USD
  revenues will fall. Iris chooses to reduce its
  long position in CD by writing CD calls with a
  USD strike price. The strategy chosen is one of
  hedge ratio 11.

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• By writing options, Iris will receive an
  immediate USD cash flow representing the
  premiums. This cash flow will increase Iris'
  total USD return in the event the CD depreciates
  against the USD or, remains unchanged against the
  USD, or appreciates only slightly against the
  USD.
• Clearly, the options might expire worthless or
  they might be exercised. In either case, however,
  Iris walks away with the full amount of the
  options premium

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• If the USD value of the CD remains unchanged, the
  option premium received is simply additional
  profit.
• If the value of the CD falls, the premium
  received on the written option will offset part
  or all of the opportunity loss on the underlying
  CD position.
• If the value of the CD 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 option
  written.

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• In short, the payoff to Iris' strategy will
  depend both on exchange rate movements and on the
  selection of the strike price of the written
  options.
• To illustrate Iris' strategy, consider an
  anticipated cash flow of CD300M over the next 180
  days. With hedge ratio of 11, Iris sells
  CD300,000,000/CD50,000 6,000 PHLX calls.

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• Assume Iris writes 6,000 PHLX calls with a
  6-month expiration the current spot rate is S
  USD.75/CD and the 6-month forward rate is
• F USD.7447/CD.
• For the current level of spot rate, logical
  strike price choices for the calls might be X
  USD.74, or USD.75, or USD.76.
• For the illustration, assume that Iris
  brokerage fee is USD4 per written call and let
  the hypothetical market values of the options be
  those listed in the following

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c(K USD.74/CD) USD.01379 c(K SUD.75/CD)
USD.00650 c(K USD.76/CD) USD.00313.
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• The payoff to the total position depends on the
  choice of exercise price, K, and the spot
  exchange rate, S(USD/CD), at the calls
  expiration. We now introduce an additional cost,
  that is associated with the exercise fee, which
  exists in the real markets. If the options are
  exercised, an additional Options Clearing
  Corporation fee of USD35 per option 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. The
  total value of the long CD position of Iris, plus
  short option position will be

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Actually, the above table consolidates three
profit profile tables, each corresponding to one
of the three strike prices under
consideration. The three tables are as follows
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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 CD. On the
other hand, a lower strike price limits the
corresponding profitability of the strategy if
the CD 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 is to evaluate the options strategy
vis-à-vis the immediate forward exchange.
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• Recall that when Iris enters the
• options strategy the forward
• exchange rate is
• F USD.7447/CD.
• Thus, a future break-even spot
• rate can be calculated for every
• corresponding exercise price
• chosen

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• F .7447. Iris may exchange today, CD300M
  forward for
• CD300,000,000(USD.7447/CD)
• USD223,410,000.
• IF K .74,
• S(CD300M) 4,113,000 USD223,410,000
• ? SBE USD.7310/CD.
• IF K .75,
• S(CD300M) 1,926,000 USD223,410,000
• ? SBE USD.7383/CD.
• IF K .76,
• S(CD300M) 915,000 USD223,410,000
• ? SBE USD.7416/CD.

84

• CONCLUSION
• Writing the calls will protect Iris flow
• in USD six months from now better
• than an immediate forward exchange,
• for all spot rates (in six months) that
• are above the corresponding break-
• even exchange rates.

85

• 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 either maintains an open long position of
  CD300M un hedged. Alternatively, Iris writes
  6,000 PHLX calls with 180-day expiration period.
  Possible strike prices are USD.76/CD, USD.75/CD,
  USD.74/CD. Current spot and forward exchange
  rates are USD.75/CD and USD.7447/CD, respectively.

86

• The terminal spot rate is the market exchange
  rate when the calls expire. It is assumed 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.

87

• Optimal Decision Under Iris' Strategy as a
  Function Of The (Unknown) Terminal Spot Rate
• Terminal Spot rate Optimal Decision
• S .76235 Hold long currency only
• .75267 .76
• .74477 .75
• S

88

• Final comments on Example 3.
• Because of the large OCC fee of USD35 per
  exercised call assumed in the example, it might
  be less expensive for Iris to buy back the calls
  and pay the brokerage fee of USD4 per call in the
  event the options were in dancer of being
  exercised. In addition, it is assumed that Iris
  will have the CD300M 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.

89

• 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.

90

• 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

91

• Strategy Max Value Min Value
• Unhedged
• Long
• Position None. Zero.
• Sell
• forward USD223,410,000 USD223,410,000
• .76 call USD228,705,000 Unhedged minimum
  USD915,000.
• .75 call USD226,716,000 Unhedged minimum
  USD1,926,000.
• .74 call USD225,903,000 Unhedged minimum
  USD4,113,000.

92
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 over
  the strike price

93
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 strike price over the most recent
  settlement futures price

94
The Payoffs

• If the futures position is closed out
  immediately
• Payoff from call F0 K
• Payoff from put K F0
• where F0 is futures price at time of exercise

95
Put-Call Parity for Futures Options (Equation
13.13, page 284)

• Consider the following two portfolios
• 1. European call plus Ke-rT of cash
• 2. European put plus long futures plus cash
  equal to F0e-rT
• They must be worth the same at time T so that
• cKe-rTpF0 e-rT

96
Valuing European Futures Options

• We can use the formula for an option on a stock
  paying a dividend yield
• Set S0 current futures price (F0)
• Set q domestic risk-free rate (r )
• Setting q r ensures that the expected growth
  of F in a risk-neutral world is zero

97
Blacks Formula (Equations 13.17 and 13.18,
page 287)

• The formulas for European options on futures are
  known as Blacks formulas