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• no physical delivery. in the case of a forward/future. this is notional amount multiplied by the difference between the market price of the underlying asset at maturity and the forward&amp;#x2019;s delivery price.\nin the case of an option, it is the intrinsic value of the option. \n
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• n(d)&lt;- standard norml CDF, use tabels, scientifi calculator or excel to find it\nalso N(-d)=1-N(d)\n
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• ### Lecture 07 student

1. 1. International Finance IBS 621 Lecture 6Page
2. 2. World Financial Markets and Institutions • International Banking and Money Market • International Bond Market • International Equity Markets • Futures and Options on Foreign Exchange • Currency and Interest Rate Swaps • International Portfolio Investment Page
3. 3. Futures Contracts• A futures contract specifies that a certain currency will be exchanged for another at a specified time in the future at prices specified today.• A futures contract is different from a forward contract: – Futures are standardized contracts trading on organized exchanges with daily resettlement through a clearinghouse.• Standardizing Features: easier to find a counterparty compared to forwards – contract Size – delivery Month: reduced counterparty (credit) risk compared to forwards – Daily resettlement: among other things, it allows you to close your position and get out of the contract on any day. it is called “to offset the position” if you are 1 contract long and want to get out, take 1 short position in the same contract on the same exchange and your done.• margin requirements (initial, maintenance margins) – initial margin – maintaince margin- in your account in order to be active Page
4. 4. Currency Futures Markets• The Chicago Mercantile Exchange (CME) is by far the largest.• Others include: – The Philadelphia Board of Trade (PBOT) – The MidAmerica Commodities Exchange – The Tokyo Financial Exchange – The London International Financial Futures Exchange (LIFFE) – expiry cycle: march, june, september, december. deliver date 3rd wednesday of delivery month. last trading day is the second business day preceding the delivery day – cme hours 7:20 am to 2:00 pm cst Page
5. 5. After Hours Trading• extended -hours trading on CME GLOBEX runs from 2:30 p.m. to 4:00 p.m dinner break and then back at it from 6:00 p.m. to 6:00 a.m. CST.• Singapore Exchange (SGX) offers contracts.• There are other markets, but none are close to CME and SGX trading volume.• Page
6. 6. Daily Resettlement: An Example • Suppose you want to speculate on a rise in the \$/¥ exchange rate (specifically you think that the dollar will appreciate).Currently \$1-Y140. The 3-month forward price is \$1-Y150. Page
7. 7. Daily Resettlement• Currently \$1 = ¥140 and it appears that the dollar is strengthening.• If you enter into a 3-month futures contract to sell ¥ at the rate of \$1 = ¥150 you will make money if the yen depreciates. The contract size is ¥12,500,000• You do not have to have ¥ now, either way you have committed yourself to sell ¥12,500,000 and receive in exchange ¥12,500,000 * 1/150 [\$/ ¥] = \$ 83,333.33• Your initial margin is 4% of the contract value:• initial margin- to initiate deal, maintenance is roughly 75% of the initial, lets say 3% here. if your margin account is bellow maintenance, ass \$ up to the initial margin, otherwise your position will be liquidated. Page
8. 8. Daily Resettlement• If tomorrow, the futures rate closes at \$1 = ¥149, then your position’s value drops. Here’s why.• Your original agreement was to sell ¥12,500,000 and receive \$83,333.33• But now ¥12,500,000 is worth: ¥12,500,000 * 1/149 [\$/ ¥] = \$ \$83,892.62,• If you sell ¥ under the new terms, you receive \$559.28 more compared your current contract.• That is, you have lost \$ \$559.28 overnight• The \$559.28 comes out of your \$3,333.33 margin account, leaving \$2,774.05• maintainance margin is 0.03*¥12,500,00*1/149[\$/¥]=\$2516.78• no need to add money now to your margin account. note that the initial margin requirement is now 0.04*¥12,500,000*1/149[\$/¥]=\$3355.70 Page
9. 9. Reading a Futures QuotePage
10. 10. Reading a Futures Quote Daily Change Highest and lowest prices over the Closing price lifetime of the Lowest price that day contract. Highest price that day Opening priceExpiry month Number of open contracts Page
11. 11. Currency Futures Trading: Example • \$CAN futures contract expiring on June 14 trades on CME at US \$0.7761 on January 9. On the last trading day of the contract in June the spot rate is US\$0.7570. The contract size is CAN\$100,000. 1. What is the profit/loss for a trader who took a long position in the contract on January 9? 2. What is the profit/loss for a trader who took a short position in the contract on January 9? 3. 1. long position. the futures contract locked at US\$0.7761 while in June it is possible to buy \$CAN at US\$0.07570. the trade overpaid for \$CAN- 4. -> loss. how much? US\$ (0.07570-0.7761)*100=-1,910 5. as F-> S with T->0 the \$1,910 would be the total \$ subtracted from the traders margin account during the daily resettlements. 6. effective cost of the CAN\$100,00 is \$75,700+\$1910=\$77,610 Page
12. 12. Currency Futures Trading: Example short position. the trader can sell at US\$.07761 while in june it is only possible to sell \$CAN at US \$0.7570. the trader gets more \$CN at US\$0.7570. the trader gets more \$CAN -> profit. how much? ->US\$ (0.7761-0.7570)*100,000= 1,910 as F-> S with T->0 the \$1910 would be the total \$ added to the traders margin account during the daily resettlement. effective revenue from the short position is CAN\$100,000 is \$75,700+1,910= \$77,610 **it is possible to buy at \$0.7570 and immediately deliver at \$0.7761 **point #1. futures is a zero sum game, your gain is your counterpaty’s loss, and vice cersa. however, if you want to hedgeFX risk, you can lock in a fixed rate Page
13. 13. Eurodollar Interest Rate Futures• Widely used futures contract for hedging short-term U.S. dollar interest rate risk.• The underlying asset is a \$1,000,000 90-day Eurodollar deposit—the contract is cash settled.• Traded on the CME and the Singapore International Monetary Exchange.• Eurodollar futures prices are stated as an index number of three-month LIBOR calculated as F = 100 – LIBOR. – For example, if the closing price for is 98.23, the implied yield is 5.77 percent = 100-98.23• Hedging/speculation just like with forwards, except standardized amounts and daily resettlement• ***no physical delivery. in the case of a forward/future. this is notional amount multiplied by the difference between the market price of the underlying asset at maturity and the forward’s delivery price.in the case of an option, it is the intrinsic value of the option. Page
14. 14. Example • The size of a yen futures contract at CME is 12.5 million yen. The initial margin is \$2,025 per contract and the maintenance margin is \$1,500. You decide to buy ten contracts with maturity on June 17, at the current futures price of \$0.01056. Today is April 1 and the spot rate is \$0.01041. Indicate cash flows on your position if the following prices are subsequently observed. April 1 April 2 April 3 April 4 June 16 June 17 Spot, \$/Y 0.01041 0.01039 0.01000 0.01150 0.01150 0.01100Futures, \$/Y 0.01056 0.01054 0.01013 0.01160 0.01151 0.01100 • Page
15. 15. Example solved April 1 April 2 April 3 April 4 June 16 June 17 Spot, \$/Y 0.01041 0.01039 0.01000 0.01150 0.01150 0.01100 Futures, \$/Y 0.01056 0.01054 0.01013 0.01160 0.01151 0.01100 Gain/Loss -2500 -51250 -184750 -11250 -63750Margin before CF 17750 -33500 2040000 9000 -43500CF from investor 20250 0 0.010395 -184750 11250 43500 Margin after CF 20250 17750 20250 20250 20250 0 Text Page
16. 16. Example• It is 1 April now and current 3-month LIBOR is 6.25%. Eurodollar futures contracts are traded on CME with size of \$1 million at 93.280 with June delivery. The initial margin is \$540 and the maintenance margin is \$400. You are a corporate treasurer and you know your company will have to pay \$10 million in cash for goods that will be delivered on June 17. You will sell the goods for profit, but you will not receive payment until September 17. Thus, you know you will have to borrow \$10 million for 3 months in June.1. What is the forward rate implicit in the Eurodollar futures price?2. How to lock in 3-month borrowing rate for June 17 using Eurodollar futures?3. On June 17, the Eurodollar futures is quoted at 91%, and the current Eurodollar rate is 9%. You close your position at that time. What are your cash flows? Page
17. 17. Example solved you inte wh bor exp Page
18. 18. Example solved1. Implicit rate = 100-93.280 = 6.72% Note that forward rate 6.72% > spot 6.25%, term structure upward sloping you inte wh bor exp Page
19. 19. Example solved1. Implicit rate = 100-93.280 = 6.72% Note that forward rate 6.72% > spot 6.25%, term structure upward sloping you2. You will have to borrow \$10 million for 3 months as you know. Borrow = inte sell deposite instruments. Borrow in the future and lock in the % rate = wh sell forward. You sell 10 Eurodollar contracts. bor exp Page
20. 20. Example solved1. Implicit rate = 100-93.280 = 6.72% Note that forward rate 6.72% > spot 6.25%, term structure upward sloping you2. You will have to borrow \$10 million for 3 months as you know. Borrow = inte sell deposite instruments. Borrow in the future and lock in the % rate = wh sell forward. You sell 10 Eurodollar contracts. bor exp3. Interest rates 6.25% to 9% Page
21. 21. Example solved1. Implicit rate = 100-93.280 = 6.72% Note that forward rate 6.72% > spot 6.25%, term structure upward sloping you2. You will have to borrow \$10 million for 3 months as you know. Borrow = inte sell deposite instruments. Borrow in the future and lock in the % rate = wh sell forward. You sell 10 Eurodollar contracts. bor exp3. Interest rates 6.25% to 9% But your profit from the short position in the futures contracts is 10*1,000,000*(0.9328-0.9100)/4-\$57,000. Page
22. 22. Example solved1. Implicit rate = 100-93.280 = 6.72% Note that forward rate 6.72% > spot 6.25%, term structure upward sloping you2. You will have to borrow \$10 million for 3 months as you know. Borrow = inte sell deposite instruments. Borrow in the future and lock in the % rate = wh sell forward. You sell 10 Eurodollar contracts. bor exp3. Interest rates 6.25% to 9% But your profit from the short position in the futures contracts is 10*1,000,000*(0.9328-0.9100)/4-\$57,000. Your borrowing cost is 10,000,000*0.9/4=\$225,000 Page
23. 23. Example solved1. Implicit rate = 100-93.280 = 6.72% Note that forward rate 6.72% > spot 6.25%, term structure upward sloping you2. You will have to borrow \$10 million for 3 months as you know. Borrow = inte sell deposite instruments. Borrow in the future and lock in the % rate = wh sell forward. You sell 10 Eurodollar contracts. bor exp3. Interest rates 6.25% to 9% But your profit from the short position in the futures contracts is 10*1,000,000*(0.9328-0.9100)/4-\$57,000. Your borrowing cost is 10,000,000*0.9/4=\$225,000 Your total borrowing CF = \$225,000-\$57,000 = \$168,000. For 3 months borrowing you pay \$168,000/ 10,000,000 = 1.68% Convert this into per annum: 1.68% *4= 6.72% Page
24. 24. Options Contracts• An option gives the holder right, but not the obligation, to buy or sell a given quantity of an asset in the future, at prices agreed upon today.• Call vs. Put options. Call/Put options gives the holder the right, to buy/sell a given quantity of some asset at some time in the future, at prices agreed upon today.• European vs. American options. – European options can only be exercised on the expiration date. American options can be exercised at any time up to and including the expiration date. – Since this option to exercise early generally has value, American options are usually worth more than European options, other things equal. – Page
25. 25. Options Contracts• In-the-money options – Profitable to exercise today• At the money options – Profit = 0 if exercise today• Out of the money options – loss if exercise under the option’s terms• Intrinsic Value – In the money: The difference between the exercise price of the option and the spot price of the underlying asset. – Out of the money: zero Page
26. 26. Currency Options Markets• Currency – 20-hour trading day. – OTC is much bigger than exchange volume. – Trading is in six major currencies against the U.S. dollar. – View standard specifications from PHLX• Options on currency futures – Options on a currency futures contract. Exercise of a currency futures option results in a long futures position for the ________ of a call or the __________of a put. – Exercise of a currency futures option results in a short futures position for the __________ of a call or the __________ of a put. Page
27. 27. Basic Relationships at Expiry• At expiry, an American call option is worth the same as a European option with the same characteristics.• If the call is in-the-money, it is worth Sr-E• If the call is out-of-the-money, it is worthless. • CaT = CeT = Max[ST - E, 0] Page
28. 28. Basic Relationships at Expiry• At expiry, an American call option is worth the same as a European option with the same characteristics.• If the call is in-the-money, it is worth Sr-E• If the call is out-of-the-money, it is worthless. • CaT = CeT = Max[ST - E, 0]• At expiry, an American put option is worth the same as a European option with the same characteristics.• If the put is in-the-money, it is worth E-Sr• If the put is out-of-the-money, it is worthless. • PaT = PeT = Max[E - ST, 0] Page
29. 29. Basic Option Profit ProfilesCall. Long position (buy). If the call is in-the-money, it is worth ST – E. If thecall is out-of-the-money, it is worthless and the buyer of the call loses hisentire investment of c0.Call. Short position (sell). If the call is in-the-money, the writer loses ST – E. Ifthe call is out-of-the-money, the writer keeps the option premium.Put. Long position (buy). If the put is in-the-money, it is worth E –ST. If the put isout-of-the-money, it is worthless and the buyer of the put loses his entireinvestment of p0.Put. Short position (sell). If the put is in-the-money, it is worth E –ST. If the put isout-of-the-money, it is worthless and the seller of the put keeps the optionpremium of p0. Page
30. 30. American Option Pricing• With an American option, you can do everything that you can do with a European option—this option to exercise early has value. • CaT > CeT = Max[ST - E, 0] • PaT > PeT = Max[E - ST, 0] • Page
31. 31. Market Value, Time Value andIntrinsic Value for an American CallThe black line showsthe payoff at maturity(not profit) of a calloption.Note that even an out-of-the-money optionhas value—time value. Page
32. 32. Example• Calculate the payoff at expiration for a call option on the euro in which the underlying is \$0.90 at expiration, the option is on EUR 62,500, and the exercise price is1. \$0.752. \$0.953. E=\$0.75. C=max(.90-.75,0)*62500=\$9,3754. E=\$.95. C=max (0.90-.95,0)*62500=0 Page
33. 33. Example• Calculate the payoff at expiration for a put option on the euro in which the underlying is \$0.90 at expiration, the option is on EUR 62,500, and the exercise price is1. \$0.752. \$0.953. E=\$0.75. P=max(.75-.90,0)*62,500=\$ 04. E=\$0.95. P=max(.95-.90,0)*62,500= \$3,125 Page
34. 34. Example this is futures rate no spot rate• Calculate the payoff at expiration for a call option on a currency futures contract in which the underlying is at \$1.13676 at expiration, the futures contract is for CAN\$1,000,000 and the exercise price is:1. \$1.130002. \$1.140003. E=1.1304. C=max(1.13676-1.30,0)*1,000,000=6,7605. E= \$1.140006. C= max(1.13676-1.40,0)*1,000,000=0 Page
35. 35. Example• Calculate the payoff at expiration for a put option on a currency futures contract in which the underlying is at \$1.13676 at expiration, the futures contract is for CAN\$1,000,000 and the exercise price is:1. \$1.130002. \$1.140003. E= \$1.130004. P=max(1.130-1.13676 ,0)*1,000,000= \$05. E=\$1.1406. P=max(1.140-1.13676 ,0)*1,000,000=\$3,240 Page
36. 36. Pricing currency options• Bounds on option prices are imposed by arbitrage conditions (ignore in this course)• Exact pricing formulas (theoretical) – Lattice models, for example binomial model (ignore for now) – Pricing based on continuous time modeling and stochastic calculus (mathematics used in modeling heat transfers, flight dynamics, and semiconductors). No derivations here. More precise than binomial. • Idea: model evolution of the underlying asset’s price in continuous time (i.e. not week-by-week) and calculate expected value of the option payoff. Page
37. 37. Currency Option Pricing r = the interest rate (foreign or domestic), T – time to expiration, years S – current exchange rate, E – exercise exchange rate, DC/FC Page
38. 38. Example• Consider a 4-month European call option on GBP in the US. The current exchange rate is \$1.6000, the exercise price is \$1.6000, the riskless rate in the US is 8% and in the UK is 11%. The volatility is 20%. What is the call price? Page
39. 39. Example• Consider a 2-month European put option on GBP in the US. The current exchange rate is \$1.5800, the exercise price is \$1.6000, the riskless rate in the US is 8% and in the UK is 11%. The volatility is 15%. What is the put price? Page
40. 40. Put-call parity for currency options put +underlying asset= call +pv of exercise price -put and call have the same strike price and maturity Page
41. 41. Option Value Determinants Call Put1. Exchange rate + -2. Exercise price - +3. Interest rate at home + -4. Interest rate in other country - +5. Variability in exchange rate + +6. Expiration date + + The value of a call option C0 must fall within max (S0 – E, 0) < C0 < S0.The precise position will depend on the above factors. Page
42. 42. Empirical Tests• The European option pricing model works fairly well in pricing American currency options.• It works best for out-of the money and at the money options.• When options are in-the-money, the European option pricing model tends to underprice American options. Page
43. 43. World Financial Markets and Institutions • International Banking and Money Market • International Bond Market • International Equity Markets • Futures and Options on Foreign Exchange • Currency and Interest Rate Swaps • International Portfolio Investment Page
44. 44. Types of Swaps• In a swap, two counterparties agree to a contractual arrangement wherein they agree to exchange cash flows at periodic intervals.• There are two types of interest rate swaps: – Single currency interest rate swap • “Plain vanilla” fixed-for-floating swaps are often just called intrest rate swaps – Cross-Currency interest rate swap • This is often called a currency swap; fixed for fixed rate debt service in two (or more) currencies. Page
45. 45. Swap Market• In 2001 the notional principal of: Interest rate swaps was \$58,897,000,000. Currency swaps was \$3,942,000,000• The most popular currencies are: – US\$, JPY, Euro, SFr, GBP• A swap bank is a generic term to describe a financial institution that facilitates swaps between counterparties. It can serve as either a broker or a dealer. – A broker matches counterparties but does not assume any of the risks of the swap. – A dealer stands ready to accept either side of a currency swap, and then later lay off their risk, or match it with a counterparty. Page
46. 46. Size of the Swap MarketPage
47. 47. Example of an Interest Rate Swap • Consider this example of a “plain vanilla” interest rate swap. • Bank A is a AAA-rated international bank located in the u.k. and wishes to raise \$10,000,000 to finance floating-rate Eurodollar loans. – Bank A is considering issuing 5-year fixed-rate Eurodollar bonds at 10 percent. – It would make more sense to for the bank to issue floating-rate notes at LIBOR to finance floating-rate Eurodollar loans. Page
48. 48. Example of an Interest Rate Swap• Firm B is a BBB-rated u.s company. It needs \$10,000,000 to finance an investment with a five-year economic life. – Firm B is considering issuing 5-year fixed-rate Eurodollar bonds at 11.75 percent. – Alternatively, firm B can raise the money by issuing 5-year floating- rate notes at LIBOR + ½ percent. – Firm B would prefer to borrow at a fixed rate. Page
49. 49. Example of an Interest Rate Swap• The borrowing opportunities of the two firms area: Page
50. 50. Example of an Interest Rate Swap 1/2% of \$10,000,000=50,0 00. thats quite a cost saving per Swap year for 5 yrs Bank 10 3/8% libor -1/8%Bank 10 3/8-10-(libor- 1/8) A Libor- 1.2% which is 1/2% better than they can borrow 10% floating without a swap Page
51. 51. Example of an Interest Rate Swap 1/2% of \$10,000,000=50,0 The swap bank makes 00. thats quite a cost saving per Swap this offer to Bank A: You year for 5 yrs pay libor -1/8% per year Bank on \$10 million for 5 years 10 3/8% and we will pay you 10 3.8% on \$10 million for 5 libor -1/8% yearsBank 10 3/8-10-(libor- 1/8) A Libor- 1.2% which is 1/2% better than they can borrow 10% floating without a swap Page
52. 52. Example of an Interest Rate Swap1/2% of\$10,000,000=50,000. thats quite acost saving per Swapyear for 5 yrs Bank 10 3/8% LIBOR – 1/8%Bank 10 3/8-10-(libor- 1/8) A Libor- 1.2% which is 1/2% better than they can borrow floating without a swap 10% Page
53. 53. Example of an Interest Rate Swap1/2% of\$10,000,000=50,000. thats quite acost saving per Swapyear for 5 yrs Bank 10 3/8% LIBOR – 1/8%Bank 10 3/8-10-(libor- 1/8) A Libor- 1.2% which is 1/2% better than they can borrow floating without a swap 10% Page
54. 54. Example of an Interest Rate Swap Swap Bank 10 ½% LIBOR – ¼% Page
55. 55. Example of an Interest Rate Swap The swap bank makes this offer to company B: Swap You pay us 10 1/2% per year on \$10 million for 5 Bank years and we will pay you 10 ½% libor 1/4% per year on \$10 million for 5 years. LIBOR – ¼% Company B Page
56. 56. Example of an Interest Rate Swap Swap 1/2% of 10,000,000= Bank 50,000 thats quite a 10 ½% cost saving per year LIBOR – ¼% for 5 years they can borrow externally at Libor +1/2% and have a net borrowing position of Company 10 1/2 +(libor+1/2)=(libor-1/2)=11.25% which is 1/2% better then they can borrow floatinf=g B Page
57. 57. Example of an Interest Rate SwapHere’s what’s in it for B: Swap 1/2% of 10,000,000= Bank 50,000 thats quite a 10 ½% cost saving per year LIBOR – ¼% for 5 years they can borrow externally at Libor +1/2% and have a net borrowing position of Company 10 1/2 +(libor+1/2)=(libor-1/2)=11.25% which is 1/2% better then they can borrow floatinf=g B Page
58. 58. Example of an Interest Rate SwapHere’s what’s in it for B: Swap 1/2% of 10,000,000= Bank 50,000 thats quite a 10 ½% cost saving per year LIBOR – ¼% for 5 years they can borrow externally at Libor +1/2% and have a net borrowing position of Company LIBOR+ ½% 10 1/2 +(libor+1/2)=(libor-1/2)=11.25% which is 1/2% better then they can borrow floatinf=g B Page
59. 59. Example of an Interest Rate Swap 1/4% of 10M Swap Bank 10 3/8% 10 ½% LIBOR – 1/8% LIBOR – ¼% Bank Company A B Page
60. 60. Example of an Interest Rate Swap 1/4% of 10M Swap Bank 10 3/8% 10 ½% LIBOR – 1/8% LIBOR – ¼% Bank Company LIBOR – 1/8 – [LIBOR – ¼ ]= 1/8 A 10 ½ - 10 3/8 = 1/8 B ¼ Page
61. 61. The Quality Spread Differential• The Quality Spread Differential represents the potential gains from the swap that can be shared between the counterparties and the swap bank. – QSD = Fixed Differential – Floating Differential = – answer in notebook• There is no reason to presume that the gains will be shared equally.• In the above example, company B is less credit-worthy than bank A, so they probably would have gotten less of the QSD, in order to compensate the swap bank for the default risk. Page
62. 62. Example• Determine the upcoming payment in a plain vanilla interest rate swap in which the notional principal is 70 million Euro. The end user makes semi-annual fixed 7% payments, and the dealer makes semi-annual floating payments at Euribor, which was 6.25% on the last settlement period. The floating payments are made on the basis of 180 days in the settlement period and 360 days in a year. The fixed payments are made on the basis 180 days in the settlement period and 365 days in a year. Payments are netted, determine which party pays and what amount.• fx payment= 70,000,000*0.07*(180/365)=2,416,483 Euro• floating payment= 70,000,000*0.0625*(180/360)= 2,187,500 Euro• fixed payment is greather, the swap end user will pay the dealer 2,416, 438-2,187,500= 228,928 Euro Page
63. 63. Example• A US company enters into an interest rate swap with a dealer. In this swap, the notional principal is \$50 million and the company will pay a floating rate of LIBOR and receive a fixed rate of 5.75%. Interest is paid semiannually and the current LIBOR is 5.15%. The floating rate are made on the basis of 180/360 and the fixed rate payments are made on the basis of 180/365. Calculate the first payment and indicate which party pays.• fx payments= 50,000,000*0.0575*(180/365)= 1,417,808• floating payment= 50,000,000*0.0515*(180/360)= 1,287,500• fx payment s greater the dealer will pay to the us company \$1,417,808-1,287500=\$130,308 Page
64. 64. Interest rate swap valuation• You can represent a swap as a bond portfolio or a series of FRAs. We use bond portfolio representation.• From the point of view of floating-rate payer, this is a long position in the fixed rate bond and short position in the floating rate bond. – Vswap=Bffixed-Bfloating• From the point of view of fixed-rate payer, this is a long position in the floating rate bond and short position in the fixed rate bond. – Vswap=Bflaoting-Bfixed• Immediately after the interest payment, the floating rate bond is worth exactly the notional amount Page
65. 65. Example• Consider a financial institution that pays LIBOR – 0.25% and receives 10.50% p.a. (annual compounding) from a swap end user on a notional principal of \$10 million. The swap has remaining life of 4 years. The fixed rates have fallen from 10.5% to 9% and the swap end user wants to get out of the deal. How much should the financial institution charge for the right to cancel the agreement?• the swap bank pays floating and receives fixed rate, therfore the value of the wao for the institution Vswap=Bffixed-Bfloating• Bfloating= 10,000,000 right after the coupon payment• Bfixed= [N=4 omt=1,050,000; i/y=0; fv=10000000= 10, 485, 957.98 – Vswap=Bffixed-Bfloating= 10485,957.98-10000000=485957.98 – the bank will be willing to cancel the deal for a fee of 485957.98 Page
66. 66. Currency Swaps• Currency swaps evolved from parallel and back-to-back loans – a way to hedge long-term exchange exposure• The two counterpart firms lend directly to each other Page
67. 67. An Example of a Currency Swap• Suppose a Us wants to finance a £10,000,000 expansion of a British plant.• They could borrow dollars in the US where they are well known and exchange for dollars for pounds. – This will give them exchange rate risk: financing a sterling project with dollars.• They could borrow pounds in the international bond market, but pay a premium since they are not as well known abroad. Page
68. 68. An Example of a Currency Swap• If they can find a britsh MNC with a mirror-image financing need they may both benefit from a swap.• If the spot exchange rate is S0(\$/£) = \$1.60/£, the U.S. firm needs to find a British firm wanting to finance dollar borrowing in the amount of \$16,000,000 Page
69. 69. Comparative Advantage as theBasis for Swaps• Firm A has a comparitive advantage in borrowing in dollars.• Firm B has a comparative advantage in borrowing in pounds.• If they borrow according to their comparative advantage and then swap, there will be gains for both parties. – Caution: credit risk Page
70. 70. Swap Market Quotations• Swap banks will tailor the terms of interest rate and currency swaps to customers’ needs• They also make a market in “plain vanilla” swaps and provide quotes for these. Since the swap banks are dealers for these swaps, there is a bid-ask spread. Page
71. 71. Variations of Basic Currency and Interest Rate Swaps • Currency Swaps – fixed for fixed – fixed for floating – floating for floating • Interest Rate Swaps – zero for floating – floating for floating Page
72. 72. Risks of Interest Rate and Currency Swaps• Interest Rate Risk – Interest rates might move against the swap bank after it has only gotten half of a swap on the books, or if it has an unhedged position.• Basis Risk – If the floating rates of the two counterparties are not pegged to the same index (i.e. LIBOR)• Exchange rate RiskPage
73. 73. Risks of Interest Rate and Currency Swaps• Credit Risk – This is the major risk faced by a swap dealer—the risk that a counter party will defult on its end of the swap.• Mismatch Risk – It’s hard to find a counterparty that wants to borrow the right amount of money for the right amount of time.• Sovereign Risk – The risk that a country will impose exchange rate restrictions that will interfere with performance on the swap. Page
74. 74. Swap Market Efficiency• Swaps offer market completeness and that has accounted for their existence and growth.• Swaps assist in tailoring financing to the type desired by a particular borrower. – Since not all types of debt instruments are available to all types of borrowers, both counterparties can benefit (as well as the swap dealer) through financing that is more suitable for their asset maturity structures. Page
75. 75. Example• A US company can issue a US\$-denominated bond but needs to borrow in GBP. Consider a currency swap in which the US company pays a fixed rate in the foreign currency, GBP, and the counterparty pays a fixed rate in US \$. The notional principals are \$50 million and GBP 30 million, and the fixed rates are 5.6% in US\$ and 6.25% in GBP. Both sets of payments are made on the basis of 30 days per month, 365 days per year, and the payments are made semi-annually.• What are the following cash flows: (i) initial, (ii) semi-annual, (iii) final• (i)US company pays 50M, uk company pays GBP 30M• (ii) us company pays GBP 30m*0.0625*(180/365)= gbp 924,658• uk company pays 50m*o.056*(180/360)=1,380,822• us company pays GBP 30 m, uk company pays 50 m Page
76. 76. Valuation of currency swaps• Currency swaps can be represented as bond portfolios or a series of forwards. We use bond representation.• From the point of view of foreign currency payer (domestic currency receiver), this is a long position in the domestic bond and short position in the foreign bond. – ________________________________________________• From the point of view of domestic currency payer (foreign currency receiver), this is a long position in the foreign bond and short position in the domestic bond. – ________________________________________________ Page
77. 77. Example• In Japan term structure of interest rates is flat at 4% and in the US it is 9%. A financial institution has entered into a currency swap in which it receives 5% p.a. in JPY and pays 8% p.a. in USD once a year. The principals are \$10 million and JPY 1,200 million. The swap will last for another 3 years, and the current JPY/USD exchange rate is JPY 110. What is the value of this swap for the financial institution? Page
78. 78. Swaptions• An option to enter into swap• Types: – Payer swaption • Gives the right to enter into a swap as a _________ rate payer and __________ rate receiver • Equivalent to ___________ option – Receiver swaption • Gives the right to enter into a swap as a __________ rate payer and ___________ rate receiver • Equivalent to ___________ option Page