2. A5 - 2
Chapter Objectives
• To explain how forward contracts
are used for hedging based on anticipated
exchange rate movements; and
• To explain how currency futures contracts
and currency options contracts are used
for hedging or speculation based on
anticipated exchange rate movements.
3. A5 - 3
Forward Market
• The forward market facilitates the trading
of forward contracts on currencies.
• A forward contract is an agreement
between a corporation and a commercial
bank to exchange a specified amount of a
currency at a specified exchange rate
(called the forward rate) on a specified
date in the future.
4. A5 - 4
Forward Market
• When MNCs anticipate future need or
future receipt of a foreign currency, they
can set up forward contracts to lock in the
exchange rate.
• Forward contracts are often valued at $1
million or more, and are not normally used
by consumers or small firms.
5. A5 - 5
• As with the case of spot rates, there is a
bid/ask spread on forward rates.
• Forward rates may also contain a premium
or discount.
¤ If the forward rate exceeds the existing
spot rate, it contains a premium.
¤ If the forward rate is less than the existing
spot rate, it contains a discount.
Forward Market
6. A5 - 6
• annualized forward premium/discount
=
forward rate – spot rate ×
360
spot rate n
where n is the number of days to maturity
• Example: Suppose £ spot rate = $1.681,
90-day £ forward rate = $1.677.
$1.677 – $1.681 x
360 = – 0.95%
$1.681 90
Forward Market
7. A5 - 7
• The forward premium/discount reflects the
difference between the home interest rate
and the foreign interest rate, so as to
prevent arbitrage.
Forward Market
8. A5 - 8
Fixed and Option forward contracts
• Forward contracts can be fixed or option forwards. In a
fixed contract the performance date is pre-fixed whereas
performance can be on any day during the period of the
contract for option forwards.
• In a forward contract in the case of indirect quotations
premium is reduced from the spot price and discounted is
added.
• The principle buy high sell low applies.
• The rate is expressed for a unit of home currency.
• The bank which is quoting rates will take the worst case
scenario while quoting rates.
9. A5 - 9
Fixed and option forward contracts
• A British bank has quoted the following
rates for its customer for Belgian Francs
against GBP.
• Belgian Francs Spot 60.25 – 60.30
• One month 10c – 15c discount.
• Calculate rates for the following.
10. A5 - 10
Fixed and Option forwards - Problem
• Bank sells one month Belgian francs fixed
• Bank sells one month Belgian francs
option
• Bank buys one month Belgian francs fixed
• Bank buys one month Belgian Francs
option
11. A5 - 11
Forward contract - solution
• This is a case of indirect quotation. The
domestic currency is the base currency.
• 1. Spot One GBP = 60.25 – 60.30
• So 60.25 is the selling price.
• Discount is 10 cents
• Add discount = 60.25 +0.10 =60.35
12. A5 - 12
Solution
• Banks sells one month Belgian Francs option
• Selling rate is 60.25 and the currency is at
discount. So bank has the option of quoting
either 60.35 (60.25 +0.10) or 60.25. It will consider
the worst case scenario and quote lowest
possible price i.e. 60.25 since the customer has
the option of delivering during any period from
• Spot to one month.
13. A5 - 13
Pay-offs from forward contracts
• Pay-off from a long position in a forward contract on one
unit of an asset is
• St – K from a long position and K –St from a short position.
• Where K is the delivery price and St is the spot price of the
asset at maturity of the contract.
• Consider a six month forward contract for one million GBP
at a USD –GBP exchange rate of 1.4359 entered into by a
corporation which has to pay GBP One million at the end of
six months.
• What will be the worth of the forward contract if the spot
exchange rate rises to 1.50000 at the end of the six month
period?
14. A5 - 14
Pay off from forward contracts
• The agreed price in USD will be I million
multiplied by 1.4359 = USD 1.4359 million.
• The corporation can get GBP One million
at the rate of 1.4359.
• The spot value will be USD1.5000 million,
• The worth of the forward contract will be
1.5 million minus 1.4359 million = USD
64100.
15. A5 - 15
Solution
• Bank buys one month Belgian Francs
fixed.
• 60.25 – 60.30 Discount 10c and 15 c
• The rate will be 60.30 +0.15 = 60.45
• Bank buys one month option
• 60.30 + 0.15 (Taking the worst case
scenario and applying buy high sell low
principle.) =60.45
16. A5 - 16
• A non-deliverable forward contract (NDF)
is a forward contract whereby there is no
actual exchange of currencies. Instead, a
net payment is made by one party to the
other based on the contracted rate and the
market rate on the day of settlement.
• Although NDFs do not involve actual
delivery, they can effectively hedge
expected foreign currency cash flows.
Forward Market
17. A5 - 17
Forward prices and spot prices
• The forward price is the market price that
would be agreed to today for delivery of
the asset at a specified maturity date.
• The two prices are related but the forward
price will be different from the spot price
and varies with the maturity date.
18. A5 - 18
Forward and Spot prices
• Suppose spot price of gold is $300 per
ounce and the risk free interest rate for
investments lasting one year is 5% per
annum. What is the reasonable value for
one year forward price of gold assuming
no storage costs for gold and gold earns
no income.
19. A5 - 19
Forward prices
• The reasonable value will be $315 at the end of
one year.
• If the forward price is more than $315 , say 340
then a trader can take the following actions.
• A. Borrow $300 at 5% for one year
• B. Buy one ounce of gold.
• C. Enter into a short forward contract to sell the
gold for $340 at the end of one year.
• What will be the strategy of an investor whose
portfolio has gold if the forward price is the same
as spot price?
20. A5 - 20
Forward prices
a. Sell gold for $300 per ounce.
b. Invest the proceeds at 5%
c. Enter into a long forward contract to
repurchase gold in one year for $300 per
ounce.
21. A5 - 21
Futures contracts on currencies
• The underlying asset in such contracts is
a certain number of units of foreign
currency.
• Variables S0 and F0 are defined as current
spot price in dollars for one unit of foreign
currency and futures price in dollars of
one unit of foreign currency. (INR/USD)
• This is not consistent with the way spot
and forward exchange rates are quoted.
22. A5 - 22
Currency futures
• A foreign currency has the property that the
holder of the currency can earn interest at the
prevailing risk free rate in the foreign country.
Fore example, the holder can invest the currency
in a foreign denominated bond.
• We define rf as the value of the foreign risk-free
interest rate when money is invested for time T.
• r is the domestic risk free interest rate.
• Thus F0 = S0e(r-rf)T
• e =2.71828
23. A5 - 23
Currency futures -Illustration
• Suppose two year interest rates in
Australia and the United States are 5% and
7% respectively and the spot exchange
rate between the Australian Dollar (AUD)
and U.S.Dollar (USD) is 0.6200 USD per
AUD.
• Calculate the two year futures price.
24. A5 - 24
Currency Futures - Solution
• Rate of interest in U.S.A. ‘r’ = 7%
• Rate of interest in Australia ‘rf’ = 5%
• Spot exchange rate = 0.6200
• Two year futures rate =
• 0.6200e(0.07 – 0.05)x2
=
• 0.07 -0.05 = 0.02 x 2 = 0.04
• e0.04 = 1.0408 x 0.6200 = 0.64530
25. A5 - 25
Currency Futures - Arbitrage
• Suppose the two year futures rate is less than 0.6453, say 0.6300
• An arbitrager can borrow 1000 AUD at 5% per annum, convert to
620 USD and invest it at 7% p.a.
• Enter into a forward contract to buy Australian Dollars at the
exchange rate of 0.6300.
• Total payment to be made in AUD at the end of two years using
continuous compounding will be
• 0.05 x 2 = 0.1. e0.1(For continuous compounding) = 1.10517
• 1.10517 X1000 = 1105.17
• Total USD = 1105.17 x 0.6300 = 696.26
• USD 620 at the end of two years =
• 0.07 X 2 = 0.14 . e0.14 =1.15027 x 620 = 713.17
• Total risk less profit = 713.17 – 696.26 = USD 16.91
26. A5 - 26
Currency futures arbitrage
• Suppose the two year futures rate is
0.6600 i.e. greater than 0.6453 how will the
arbitrager function to make risk less
profit?
27. A5 - 27
Currency futures – arbitrage -solution
• 1.Borrow 1000 USD at 7% per annum for two
years.
• 2. Convert to AUD at 0.6200 = 1000/0.62 = 1612.90
• 3. Lend AUD at 5% which will fetch 1.10517 *
1612.90 =1782.53 after two years with continuous
compounding.
• 4. Enter into a forward contract to sell AUD
1782.53 at 0.6600 = 1176.47 USD
• 5. The amount needed to pay for the 1000 USD
debt is 1150.27.
• Total risk less profit = USD 26.20
28. A5 - 28
Currency Futures Market
• Currency futures contracts specify a
standard volume of a particular currency to
be exchanged on a specific settlement
date, typically the third Wednesdays in
March, June, September, and December.
• They are used by MNCs to hedge their
currency positions, and by speculators
who hope to capitalize on their
expectations of exchange rate movements.
29. A5 - 29
Currency Futures Market
• The contracts can be traded by firms or
individuals through brokers on the trading
floor of an exchange (e.g. Chicago
Mercantile Exchange), on automated
trading systems (e.g. GLOBEX), or over-
the-counter.
• Participants in the currency futures
market need to establish and maintain a
margin when they take a position.
30. A5 - 30
Forward Markets Futures Markets
Contract size Customized. Standardized.
Delivery date Customized. Standardized.
Participants Banks, brokers, Banks, brokers,
MNCs. Public MNCs. Qualified
speculation not public speculation
encouraged. encouraged.
Security Compensating Small security
deposit bank balances or deposit required.
credit lines needed.
Currency Futures Market
31. A5 - 31
Clearing Handled by Handled by
operation individual banks exchange
& brokers. clearinghouse.
Daily settlements
to market prices.
Marketplace Worldwide Central exchange
telephone floor with global
network. communications.
Currency Futures Market
Forward Markets Futures Markets
32. A5 - 32
Regulation Self-regulating. Commodity
Futures Trading
Commission,
National Futures
Association.
Liquidation Mostly settled by Mostly settled by
actual delivery. offset.
Transaction Bank’s bid/ask Negotiated
Costs spread. brokerage fees.
Currency Futures Market
Forward Markets Futures Markets
33. A5 - 33
• Normally, the price of a currency futures
contract is similar to the forward rate for a
given currency and settlement date, but
differs from the spot rate when the interest
rates on the two currencies differ.
• These relationships are enforced by the
potential arbitrage activities that would
occur otherwise.
Currency Futures Market
34. A5 - 34
• Currency futures contracts have no credit
risk since they are guaranteed by the
exchange clearinghouse.
• To minimize its risk in such a guarantee,
the exchange imposes margin
requirements to cover fluctuations in the
value of the contracts.
Currency Futures Market
35. A5 - 35
• Speculators often sell currency futures
when they expect the underlying currency
to depreciate, and vice versa.
Currency Futures Market
36. A5 - 36
• Currency futures may be purchased by
MNCs to hedge foreign currency payables,
or sold to hedge receivables.
Currency Futures Market
37. A5 - 37
• Holders of futures contracts can close out
their positions by selling similar futures
contracts. Sellers may also close out their
positions by purchasing similar contracts.
Currency Futures Market
38. A5 - 38
• Most currency futures contracts are
closed out before their settlement dates.
• Brokers who fulfill orders to buy or sell
futures contracts earn a transaction or
brokerage fee in the form of the bid/ask
spread.
Currency Futures Market
39. A5 - 39
Currency Options Market
• A currency option is another type of
contract that can be purchased or sold by
speculators and firms.
• The standard options that are traded on an
exchange through brokers are guaranteed,
but require margin maintenance.
• U.S. option exchanges (e.g. Chicago
Board Options Exchange) are regulated by
the Securities and Exchange Commission.
40. A5 - 40
• In addition to the exchanges, there is an
over-the-counter market where
commercial banks and brokerage firms
offer customized currency options.
• There are no credit guarantees for these
OTC options, so some form of collateral
may be required.
• Currency options are classified as either
calls or puts.
Currency Options Market
41. A5 - 41
• A currency call option grants the holder
the right to buy a specific currency at a
specific price (called the exercise or strike
price) within a specific period of time.
• A call option is
¤ in the money if spot rate > strike price,
¤ at the money if spot rate = strike price,
¤ out of the money
if spot rate < strike price.
Currency Call Options
42. A5 - 42
• Option owners can sell or exercise their
options. They can also choose to let their
options expire. At most, they will lose the
premiums they paid for their options.
• Call option premiums will be higher when:
¤ (spot price – strike price) is larger;
¤ the time to expiration date is longer; and
¤ the variability of the currency is greater.
Currency Call Options
43. A5 - 43
• Firms with open positions in foreign
currencies may use currency call options
to cover those positions.
• They may purchase currency call options
¤ to hedge future payables;
¤ to hedge potential expenses when bidding
on projects; and
¤ to hedge potential costs when attempting
to acquire other firms.
Currency Call Options
44. A5 - 44
• Speculators who expect a foreign
currency to appreciate can purchase call
options on that currency.
¤ Profit = selling price – buying (strike) price
– option premium
• They may also sell (write) call options on a
currency that they expect to depreciate.
¤ Profit = option premium – buying price
+ selling (strike) price
Currency Call Options
45. A5 - 45
• The purchaser of a call option will break
even when
selling price = buying (strike) price
+ option premium
• The seller (writer) of a call option will
break even when
buying price = selling (strike) price
+ option premium
Currency Call Options
46. A5 - 46
3. Plain vanilla options
3.1 Definitions & Notations
• A European call on an asset confers the right but
not the obligation to buy this asset at a pre-
agreed price and date.
• A European put on an asset confers the right but
not the obligation to sell this asset at a pre-
agreed price and date.
• An American call on an asset confers the right but
not the obligation to buy this asset at a pre-
agreed price until a certain date.
• An American put on an asset confers the right but
not the obligation to sell this asset at a pre-
agreed price until a certain date.
47. A5 - 47
3.1 Definitions & Notations (2)
• K: exercise price or strike: the price at
which the underlying asset is exchanged;
• T: expiry or maturity: the date when or until
when the underlying is exchanged;
• ct : value at time t of a European and
American call;
• pt : value at time t of a European and
American put.
• As with forward contracts, an option value
is expressed per unit of underlying asset
and from the option buyer’s viewpoint.
48. A5 - 48
3.2 Payoff
• Clearly a rational individual will only
exercise his right to buy or sell the
underlying asset conferred by a call or put
option if it is profitable to do so
¤ For a call option this is the case when ST >
K;
¤ For a put option this is the case when ST <
K.
49. A5 - 49
3.2 Payoff
• Therefore, the respective payoffs of the
European call and put with strike K and
maturity T are given as:
¤ For the call: cT = max(0, ST – K);
¤ For the put: pT = max(0, K – ST).
54. A5 - 54
• A currency put option grants the holder
the right to sell a specific currency at a
specific price (the strike price) within a
specific period of time.
• A put option is
¤ in the money if spot rate < strike price,
¤ at the money if spot rate = strike price,
¤ out of the money
if spot rate > strike price.
Currency Put Options
55. A5 - 55
• Put option premiums will be higher when:
¤ (strike price – spot rate) is larger;
¤ the time to expiration date is longer; and
¤ the variability of the currency is greater.
• Corporations with open foreign currency
positions may use currency put options to
cover their positions.
¤ For example, firms may purchase put
options to hedge future receivables.
Currency Put Options
56. A5 - 56
• Speculators who expect a foreign
currency to depreciate can purchase put
options on that currency.
¤ Profit = selling (strike) price – buying price
– option premium
• They may also sell (write) put options on a
currency that they expect to appreciate.
¤ Profit = option premium + selling price
– buying (strike) price
Currency Put Options
57. A5 - 57
• One possible speculative strategy for
volatile currencies is to purchase both a
put option and a call option at the same
exercise price. This is called a straddle.
• By purchasing both options, the
speculator may gain if the currency moves
substantially in either direction, or if it
moves in one direction followed by the
other.
Currency Put Options
58. A5 - 58
Straddle -Illustration
• A straddle involves buying a call and put
with the same strike price and expiration
date. The strike price is denoted by ‘K’
and if the price is close to the strike price
at expiration, the straddle leads to a loss.
However, if there is a sufficiently large
move in either direction, a significant
profit will result.
59. A5 - 59
Straddle
• A Straddle is appropriate when the
investor is expecting a large move in price
of a currency, currently valued at $0.69 in
the market, will move significantly in the
next six months.
• The investor could create a straddle by
buying both put and call at a strike price of
$0.70 and expiration in three months.
60. A5 - 60
Straddle
• Suppose the call costs $0.040 and put
costs $0.030. If the price stays at $0.69
what will be the cost to the investor?
• If the price moves to 0.70 what will be the
cost?
• If the price moves to 0.55 what will be the
net payoff?
61. A5 - 61
Straddle - Solution
• Upfront investment = 0.040 + 0.030 = 0.070
• Call expires worthless
• Put expires worth 0.70 - 0.69 = 0.010
• Total cost = 0.070 – 0.010 = 0.060
• If the price is $ 0.70 total loss= 0.070
62. A5 - 62
Straddle - Solution
• If the price is $ 0.55 at expiration
• Total up front cost = 0.070
• Call expires worthless
• Put is worth 0.70 – 0.55 = 0.15
• Net payoff = 0.15 – 0.07 = 0.08
64. A5 - 64
Straddle
• A straddle seems to be a natural trading strategy
when a big jump in share price is expected when
there is a takeover bid or when the outcome of a
major lawsuit is expected to be announced soon.
• Options on such stocks will however be more
expensive than usual and for straddle to be an
effective strategy an investor’s belief must be
different from those of other market participants.
65. A5 - 65
Payoff from a straddle
• Price range Call Put Total
• PAYOFF
• St <=K 0 K –St K –St
• St > K St – K 0 St -K
66. A5 - 66
Strangles
• An investor buys a put and a call with the same
expiration date but different strike prices. The
call strike price K2 is greater than the put strike
price K1.
• A strangle is a similar strategy to straddle.
• The investor is betting on large price movement
but does not know the direction. However, the
price has to move farther in a strangle than in a
straddle for the investor to make a profit.
However, the downside risk if the stock price
ends up at a central values is less with a strangle.
67. A5 - 67
Payoff from a strangle
• Range Call Put Total
• PAYOFF
• St <=K1 0 K1 –St K1 –St
• K1 < St <K2 0 0 0
• St >=K2 St –K2 0 St –K2
68. A5 - 68
Strangle - Problem
• Calculate payoff from strangle under the
following conditions
• Call premium 0 .040 Put premium 0.030
• Call strike price 0. 72 Put strike price 0.69.
• What will be the net pay off if
• A) spot price = 0.90
• B) spot price = 0.55
• C) spot price = 0.70
69. A5 - 69
Strangle Illustration
• Strike price for call K2 = 0.72
• Strike price for put K1 = 0.69
• Call premium = 0.040
• Put premium = 0.030
• Calculate the Payoff if St = 0.90
• Payoff from call = St > K2. Difference = 0.90 -0.72
= 0.18
• Put expires worthless
• Upfront payment = 0.040 + 0.030 = 0.070
• Net payoff = 0.180 – 0.070 = 0.11
70. A5 - 70
Strangle - Illustration
• St = 0.55
• Call expires worthless
• Put pay off = k1 –St = 0.69 – 0.55 = 0.14
• Total upfront payment = 0.040 + 0.030 =
0.070
• Net payoff = 0.140 – 0.070 = 0.07
71. A5 - 71
Strangle Illustration
• Spot Price = 0.70
• K2 = 0.72
• Call expires worthless since St < K2
• K1 = 0.69
• Put expires worthless since K1 < St
• Net pay off 0.040 + 0.030 = 0.070 loss
72. A5 - 72
Reading Foreign Exchange quotes
• OPTIONS
• PHILADELPHIA EXCHANGE
• Calls Puts
• Vol Last
• German Mark 58.60
• 62500 German Marks – European Style
• 58 Mar 600 0.26
• 62500 German Marks – Cents per unit
• 58.50 Mar 6038 0.60
• Explain the above quotes.
• What will be the minimum upfront payable ?
73. A5 - 73
Philadelphia Exchange quotes
• A 58 Mar European put option give the buyer the
right to sell the mark at 58 U.S.cents. The price of
the option 0.26 means that for one contract the
option buyer must pay $ 0.26 * 62500 = 162.50.
• The option buyer acquires the right to sell the
62500 marks for 58 U.S. cents each at the expiry
date of the option, which is the Friday before the
third Wednesday of March. The option will not be
exercised if the spot rate is above $ 0.58.
• Rather than exercise, the buyer is likely to accept
the difference between exercise price and the
going spot price from the option WRITER.
74. A5 - 74
Philadelphia Exchange –Call Option
• The 58.5 Mar option is an American Option, because it
does not say ‘European Option’. Therefore, it can be
exercised any day prior to maturity. There are 6038 call
options for the day .
• A call option contract will cost
• 0.60 * 62500 = $375.
• If the mark is above 0.5850 on the spot market , the option
will be exercised on or before expiry date or its value will
be collected from the option writer or another buyer. $375
can be thought of as an insurance premium for which if
unfavourable events do not occur, the insurance simply
expires.
75. A5 - 75
Conditional Currency Options
• A currency option may be structured such
that the premium is conditioned on the
actual currency movement over the period
of concern.
• Suppose a conditional put option on £ has
an exercise price of $1.70, and a trigger of
$1.74. The premium will have to be paid
only if the £’s value exceeds the trigger
value.
76. A5 - 76
Conditional Currency Options
• Similarly, a conditional call option on £
may specify an exercise price of $1.70,
and a trigger of $1.67. The premium will
have to be paid only if the £’s value falls
below the trigger value.
• In both cases, the payment of the premium
is avoided conditionally at the cost of a
higher premium.
77. A5 - 77
European Currency Options
• European-style currency options are
similar to American-style options except
that they can only be exercised on the
expiration date.
• For firms that purchase options to hedge
future cash flows, this loss in terms of
flexibility is probably not an issue. Hence,
if their premiums are lower, European-
style currency options may be preferred.
78. A5 - 78
Efficiency of
Currency Futures and Options
• If foreign exchange markets are efficient,
speculation in the currency futures and
options markets should not consistently
generate abnormally large profits.
• A speculative strategy requires the
speculator to incur risk. On the other
hand, corporations use the futures and
options markets to reduce their exposure
to fluctuating exchange rates.
79. A5 - 79
Currency Options -Illustration
• The major exchange for trading foreign currency
options is the Philadelphia Stock Exchange. It
offers both European and American contracts on
a variety of different currencies.
• The size of one contract depends on the
currency. For example, in the case of the British
pound one contract gives the holder the right to
buy or sell GBP 31250.
• In the case of Japanese Yen it is 6.25 million yen.
80. A5 - 80
Currency Option -Illustration
• A speculator buys a British Pound call
option with a strike price of $1.40 paying a
premium of $0.012 per unit. Each option
contract is for 31250 units.
• Just before the expiration date, the spot
rate is $ 1.41 and the speculator exercises
the call option.
• Calculate the net profit/loss in dollars.
82. A5 - 82
Impact of Currency Derivatives on an MNC’s Value
( ) ( )[ ]
( )∑
∑
+
×
=
n
t
t
m
j
tjtj
k1=
1
,,
1
ERECFE
=Value
E (CFj,t ) = expected cash flows in
currency j to be received by the U.S. parent at the
end of period t
E (ERj,t ) = expected exchange rate at
which currency j can be converted to dollars at
the end of period t
Currency Futures
Currency Options
83. A5 - 83
• Forward Market
¤ How MNCs Use Forward Contracts
¤ Non-Deliverable Forward Contracts
Chapter Review
84. A5 - 84
Chapter Review
• Currency Futures Market
¤ Contract Specifications
¤ Comparison of Currency Futures and
Forward Contracts
¤ Pricing Currency Futures
¤ Credit Risk of Currency Futures Contracts
¤ Speculation with Currency Futures
¤ How Firms Use Currency Futures
¤ Closing Out A Futures Position
¤ Transaction Costs of Currency Futures
86. A5 - 86
Chapter Review
• Currency Put Options
¤ Factors Affecting Currency Put Option
Premiums
¤ Hedging with Currency Put Options
¤ Speculating with Currency Put Options
87. A5 - 87
Chapter Review
• Conditional Currency Options
• European Currency Options
• Efficiency of Currency Futures and
Options
• How the Use of Currency Futures and
Options Affects an MNC’s Value
88. A5 - 88
Pay off formulae
• ST = Spot price X = Strike price
• C = Call premium P = Put premium
• 1.Call option buyer’s Profit
• Profit = -c for ST <= X
• (The call option buyer loses the call
premium amount if the spot price, i.e. the
price at the time of closing out the
contract is less or equal to the Strike
price.)
89. A5 - 89
Call option buyer’s profit
• Profit = ST – X –C
• For ST > X
• If the spot price is greater than the strike
price the call option buyer makes a profit.
The pay-off is the amount by which the
spot price exceeds the strike price, less
the call option premium paid.
90. A5 - 90
Option writer’s profit
• Profit = c for ST <= X
• The option writer profits by the option premium received
when the spot price is less than or equal to strike price.
This is because in this scenario, the option buyer will let
the contract lapse by not taking any action.
• Profit = - (ST – X –C) for ST > X.
• When the spot price is greater than the strike price, the call
option buyer exercises his option and the writer loses to
the extent of difference between Spot price and strike price.
His pay off will be his loss in the difference in prices less
the premium amount already received.
91. A5 - 91
Put Option buyer’s profit
• Profit = -p for ST > = X
• If the Spot price is greater than or equal to the
strike price contrary to the expectations of the
put option buyer, the put option buyer takes no
action and ultimately loses the put option
premium amount paid.
• Profit = (X –ST –p ) for ST < X
• If the spot price is less than the strike price, the
put option buyer makes profit to the extent of the
difference between strike and spot prices, less
the put option premium paid.
92. A5 - 92
Put option writer’s profit
• Profit = p for ST > = X
• Put option writer makes profit if the spot price is more than
the strike price contrary to the bearish sentiments of the
put option buyer who loses the premium.
• Profit = - (X –ST –p) for ST <X
• If the put option buyer’s prediction comes true and the spot
price is less than the strike price, the put option writer
loses to the extent of the ruling difference between the
strike price and the spot price and eventual loss is this
difference less the put option premium already collected.
93. A5 - 93
Close out of forward contracts
• Some times a customer may not require to
take up all the foreign currency he has
bought under a forward contract.
• Suppose a bank contracts to sell the
customer $50000 for delivery over three
months. At the end of three months, the
customer takes up only $40000 and the
bank is required to calculate what must
happen to the remaining $10000.00
94. A5 - 94
Closed out forward contracts
• The customer is deemed to hav taken up the
whole contract but to have sold back to the bank,
at the bank’s spot buying price the unutilised
balance of the forward contract.
• The detailed procedure is as follows.
• Banks sells at the forward price the remaining
balance of 10000 and the customer is debited
with that amount.
• The bank then buys back 10000 at the spot
buying price and the customer is credited with
the proceeds.
95. A5 - 95
Closed out forward contracts
• In actual fact, the bank merely does two
calculations $10000 at the forward selling
price and $10000 bought back at spot
buying price. The GBP difference between
the two is debited or credited to the
customer’s account depending upon
which way the exchange rates have
moved.
96. A5 - 96
Closed out forward contract
-Illustration
• Suppose the remaining amount is $10000 which
has to be adjusted.
• The bank has originally sold $50000 to an
importer under a forward contract over three
months at $2.0020.
• What will be the net credit/debit to the customer
account if the spot rates on the close out day are
• A. 2.0040 -2.0060
• B. 1.9980 -2.0000
97. A5 - 97
Closed out forward contract - Solution
• A.Contract amount $10000 at 2.0020 =
• GBP 4995.00
• Closed out rate = 2.0060 = GBP 4985.04
• Net debit to customer account = GBP 9.96
• B. Closed out rate = 2.0000 = GBP 5000
• Net credit = GBP 5.00
98. A5 - 98
Extension of contract
• It can happen that the customer who is unable to
deliver, requests the bank to continue the
forward deal without interruption.
• The dealer does this by deducting the applicable
premium from or adding the applicable discount
to the closing out (spot price).
• Thus under an extended forward contract to
purchase currency from customer, the bank will
deduct the premium (on the buying side) from the
close out spot price (on the selling side).
99. A5 - 99
Extension solution
• Bank buys 10000 at 2.0020 = 4995
• Bank sells 10000 at 2.0040 = 4990.02
• Credit = 4.98
• Bank buys 4995
• Bank sells at 1.9980 = 5005.01
• Debit 10.01
