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# Currency derivatives

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### Currency derivatives

1. 1. Currency Derivatives
2. 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. A5 - 2
3. 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. A5 - 3
4. 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. A5 - 4
5. 5. Forward Market• 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. A5 - 5
6. 6. Forward Market• 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 A5 - 6
7. 7. Forward Market• The forward premium/discount reflects the difference between the home interest rate and the foreign interest rate, so as to prevent arbitrage. A5 - 7
8. 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. A5 - 8
9. 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. A5 - 9
10. 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 A5 - 10
11. 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 A5 - 11
12. 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. A5 - 12
13. 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? A5 - 13
14. 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. A5 - 14
15. 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 A5 - 15
16. 16. Forward Market• 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. A5 - 16
17. 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. A5 - 17
18. 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. A5 - 18
19. 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? A5 - 19
20. 20. Forward pricesa. 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. A5 - 20
21. 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. A5 - 21
22. 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 A5 - 22
23. 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. A5 - 23
24. 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 A5 - 24
25. 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 A5 - 25
26. 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? A5 - 26
27. 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 A5 - 27
28. 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. A5 - 28
29. 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. A5 - 29
30. 30. Currency Futures Market A5 - 30
31. 31. Currency Futures Market Forward Markets Futures MarketsClearing 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. A5 - 31
32. 32. Currency Futures Market Forward Markets Futures MarketsRegulation 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. A5 - 32
33. 33. Currency Futures Market• 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. A5 - 33
34. 34. Currency Futures Market• 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. A5 - 34
35. 35. Currency Futures Market• Speculators often sell currency futures when they expect the underlying currency to depreciate, and vice versa. A5 - 35
36. 36. Currency Futures Market• Currency futures may be purchased by MNCs to hedge foreign currency payables, or sold to hedge receivables. A5 - 36
37. 37. Currency Futures Market• 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. A5 - 37
38. 38. Currency Futures Market• 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. A5 - 38
39. 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. A5 - 39
40. 40. Currency Options Market• 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. A5 - 40
41. 41. Currency Call Options• 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. A5 - 41
42. 42. Currency Call Options• 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. A5 - 42
43. 43. Currency Call Options• 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. A5 - 43
44. 44. Currency Call Options• 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 A5 - 44
45. 45. Currency Call Options• 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 A5 - 45
46. 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. A5 - 46
47. 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. A5 - 47
48. 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 >¤ For a put option this is the case when ST < A5 - 48
49. 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). A5 - 49
50. 50. Figure p.52: Call Payoff cT max(ST – K, 0) ST K A5 - 50
51. 51. Figure p.52: Put PayoffpT max(K – ST, 0) ST K A5 - 51
52. 52. FIGURE 22-1 Profit from call. A5 - 52
53. 53. FIGURE 22-2 Profit from put. A5 - 53
54. 54. Currency Put Options• 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. A5 - 54
55. 55. Currency Put Options• 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. A5 - 55
56. 56. Currency Put Options• 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 A5 - 56
57. 57. Currency Put Options• 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. A5 - 57
58. 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. A5 - 58
59. 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. A5 - 59
60. 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? A5 - 60
61. 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 A5 - 61
62. 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 A5 - 62
63. 63. FIGURE 22-3 Profit from straddle. A5 - 63
64. 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. A5 - 64
65. 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 A5 - 65
66. 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. A5 - 66
67. 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 A5 - 67
68. 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 A5 - 68
69. 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 A5 - 69
70. 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 A5 - 70
71. 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 A5 - 71
72. 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 ? A5 - 72
73. 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. A5 - 73
74. 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. A5 - 74
75. 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. A5 - 75
76. 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. A5 - 76
77. 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. A5 - 77
78. 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. A5 - 78
79. 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. A5 - 79
80. 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. A5 - 80
81. 81. Currency options - Solution• Purchase price of contract in dollars• 31250 * 1.40 = 43750• Call option premium paid• 31250 * 0.012 = 375• Selling price• 31250 * 1.41 = 44062.50• Loss = USD 62.50 A5 - 81
82. 82. Impact of Currency Derivatives on an MNC’s Value Currency Futures Currency Options m  n ∑ [ E ( CFj , t ) × E (ER j , t ) ]   j =1  Value = ∑   t =1  (1 + k ) t      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 A5 - 82
83. 83. Chapter Review• Forward Market ¤ How MNCs Use Forward Contracts ¤ Non-Deliverable Forward Contracts A5 - 83
84. 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 A5 - 84
85. 85. Chapter Review• Currency Options Market• Currency Call Options ¤ Factors Affecting Currency Call Option Premiums ¤ How Firms Use Currency Call Options ¤ Speculating with Currency Call Options A5 - 85
86. 86. Chapter Review• Currency Put Options ¤ Factors Affecting Currency Put Option Premiums ¤ Hedging with Currency Put Options ¤ Speculating with Currency Put Options A5 - 86
87. 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 A5 - 87
88. 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.) A5 - 88
89. 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. A5 - 89
90. 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. A5 - 90
91. 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. A5 - 91
92. 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. A5 - 92
93. 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 A5 - 93
94. 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. A5 - 94
95. 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. A5 - 95
96. 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 A5 - 96
97. 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 A5 - 97
98. 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). A5 - 98
99. 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 A5 - 99