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					    Foreign Currency Options
• A foreign currency option is a contract
  giving the option purchaser (the buyer)
  – the right, but not the obligation,
  – to buy or sell a given amount of foreign
    exchange at a fixed price per unit
  – for a specified time period (until the expiration
    date).
    Foreign Currency Options
• There are two basic types of options:
  – A call option is an option to buy foreign
    currency.
  – A put option is an option to sell foreign
    currency.

• A buyer of an option is termed the holder;
  the seller of an option is referred to as the
  writer or grantor.
    Foreign Currency Options
• There are two basic types of options:
  – A call option is an option to buy foreign
    currency.
  – A put option is an option to sell foreign
    currency.

• A buyer of an option is termed the holder;
  the seller of an option is referred to as the
  writer or grantor.
    Foreign Currency Options
• An American option gives the buyer the
  right to exercise the option at
  any time between the date of writing
  and the expiration or maturity date.
• A European option can be exercised only
  on the expiration date, not before.
Currency Options Markets
 • December 10th, 1982, the Philadelphia
   Stock Exchange introduced currency
   options. Growth has been spectacular.
 • OTC currency options are not usually
   traded and can only be exercised at
   maturity (European). Used to tailor specific
   amounts and expiration dates.
Philadelphia Exchange Options
           Philadelphia Exchange Options

          Spot rate, 88.15 ¢/€
    Size of contract:
         €62,500

        Exercise price            The indicated contract price
          0.90 ¢/€                             is:
                                 €62,500  $0.0125/€ = $781.25


            Maturity month
    One call option gives the holder the right to purchase
  One call option gives$56,250 (= €62,500  $0.90/€)
           €62,500 for the holder         Option price for
 the right to purchase €62,500 for        purchase of €1 at
$56,250. This option costs $781.25.         90¢ is 1.25 ¢
   Reading the WSJ Currency
         Options Table
• The option prices are for the purchase or
  sale of one unit of a foreign currency with
  U.S. dollars. For the Japanese yen, the
  prices are in hundredths of a cent. For
  other currencies, they are in cents.
    – Thus, one call option contract on the Euro
      with exercise price of 90 cents and exercise
      month January would give the holder the
      right to purchase Euro 62,500 for U.S.
      $56,250. The indicated price of the contract
      is 62,500  0.0125 or $781.25.
• The spot exchange rate on the Euro on
  12/15/00 is 88.15 cents per Euro.
                                                                         Value of Call Option versus
                                                                        Forward Position at Expiration
                                               $0.90
Value of Forward/Call Option at Expiration .




                                               $0.75
                                               $0.60
                                                                                        A call option allows you to obtain
                                               $0.45                                    only the “nice part” of the
                                               $0.30                                    forward purchase.
                                               $0.15
                                               $0.00
                                               -$0.15
                                               -$0.30                                                                                        Value of Forward Buy at Expiration
                                               -$0.45                                                                                        Value of Call at Expiration
                                               -$0.60
                                               -$0.75
                                               -$0.90
                                                        $0.00

                                                                $0.10

                                                                        $0.20

                                                                                $0.30

                                                                                         $0.40

                                                                                                 $0.50

                                                                                                         $0.60

                                                                                                                 $0.70

                                                                                                                         $0.80

                                                                                                                                 $0.90

                                                                                                                                         $1.00

                                                                                                                                                 $1.10

                                                                                                                                                         $1.20

                                                                                                                                                                 $1.30

                                                                                                                                                                         $1.40

                                                                                                                                                                                 $1.50

                                                                                                                                                                                         $1.60

                                                                                                                                                                                                 $1.70

                                                                                                                                                                                                         $1.80
                                                                                                                 Spot Rate at Expiration
       Call Option Value at Expiration
• To summarize, a call option allows you to
  obtain only the “nice part” of the forward
  purchase. Rather than paying X for the foreign
  currency (as in a forward purchase), you pay
  no more than X, and possibly less than X.
Option Premiums and Option Writing

• Likewise, a firm that expects to receive
  future Euro might acquire a put option on
  Euro.
   – The right to sell at X ensures that this firm
     gets no less than X for its Euro.

   – Thus, buying a put is like taking out an
     insurance contract against the risk of low
     exchange rates.
Option Premiums and Option Writing

 • Like any insurance contract, the insured
   party will pay an insurance premium to
   the insurer (the writer of the option).
 • The price of an option is often called the
   option premium and acquiring an option
   contract is called buying an option.
 • As with ordinary insurance contracts, the
   option premium is usually paid up-front.
   Using Currency Options to
     Hedge Currency Risk
Suppose you expect to receive 10,000,000
 euros in 6 months. Without hedging, your
 underlying position looks like this
Value of 10 million euros




                            $8,000,000
                                         0.8   0.85      0.9       0.95   1
                                                      Spot Price
 If you also buy a put option with a strike price of .90 for .01,
            your underlying position looks like this.




$10,000,000
 $9,800,000
 $9,600,000
 $9,400,000
 $9,200,000
 $9,000,000
 $8,800,000
              0.8      0.85         0.9        0.95         1
            Pricing Options
• Consider a euro call option that has a
  strike price of .90 and that is selling for
  .04.
• If the spot price is .93, the option must be
  worth at least .03. This is called the
  intrinsic value of the option.
• If the option is selling for more than the
  intrinsic value, the difference (in the
  example, .04-.03=.01) is called the time
  value. We might just as well call it the
                Pricing Options
• Consider a euro call option that has a strike price of .90
  and that is selling for .04.
• If the spot price is .93, the option must be worth at least
  .03. This is called the intrinsic value of the option.
• If the option is selling for more than the intrinsic value,
  the difference (in the example, .04-.03=.01) is called the
  time value. We might just as well call it the hope value,
  since it represents the owners hope that the spot price
  will go up by even more.
  We think about volatility in prices as being a bad thing, and for most
   financial assets this is true. A stock whose price fluctuates wildly is
  less desireable (all other things the same) than a more stable stock.
    But an interesting thing about options is that their value is actually
             enhanced by volatility of the underlying asset value.
• Suppose you owned a euro call option with a strike price of .90.
• Imagine that you thought there was a 50% chance the euro would
    fall to .87 and a 50% chance you thought the euro would increase to
    .93 before expiration of the contract. This means there is a 50%
    chance that you will make .03.
• Imagine now that you changed your mind and decided there was a
    50% chance the euro would fall to .85 and a 50% chance you
    thought the euro would increase to .95 before expiration of the
    contract. You now believe there is a 50% chance you will make .05
    and so you should be willing to pay more for the option.
       Pricing Options: the role of interest rates

• Consider two different investment portfolios
   – Portfolio “A” consists of
   – A bond that will pay X at maturity
   – The bond costs X/(1+rus) where rus is the US interest rate
   – A call option with a strike price of X
   – The option will pay S-X if S>X and 0 if S<X
   – The option costs C
   – Thus
   – If St<X, you get X
   – If St>X, you get St-X+X =St
• Portfolio “B” is made up by
   – Making a loan of S0/(1+rforeign) units of the foreign currency,
     where S0 is the current spot rate and rforeign is the foreign interest
     rate.
   – When the loan matures, you get St units of the domestic
     currency. A bond that will pay X at maturity
    Conclude: Portfolio A is better than Portfolio B (A
    never returns less than X and B returns less than
                        X if St<X)
•    But this implies that B can never sell for more than A
•    That is
•    C+X/(1+rus) > S0/(1+rforeign)
•    or
•    C> S0/(1+rforeign)-X/(1+rus)