(c) Ver. 01-12-14 521 CZK
PART 1 Chapter 1 QUESTION 1 : INTEREST RATE CALCULATION What are the flows of payment for a loan of 71.000.000 on 521 days at 5,125 % Consider that this coming year has 366 days We have an annual interest payment QUESTION 2 : DATES VALUES If we are in December 2014 trading value the last day of the month What the maturities of the 1 month to 12 months? How many euro days on each maturity? QUESTION 3 : CHANGES IN INTEREST CALCULATION METHODS With the following information, please complete the table On EUR (MMBasis 360) From To Euro Days Bond Days Euro Rate (%) Bond Rate (%) Euro APR (%) 5/01/2015 27/05/2015 5,625 10/02/2015 11/05/2015 2,5625 27/03/2015 15/05/2015 8,1875 3/08/2015 26/11/2015 13,3125 QUESTION 4 : BROKEN DATE CALC Knowing the rates of the 9 months (275 days) and 12 months (366 days) USD being respectively 2,5625 % and 2,75 %, What is the good level, caeteris paribus, of the 10 months (305 days) and 11 months (336 days) via the linear approach? QUESTION 5 : CASH POSITION The bank QPRFC borrows SEK 71.000.000 at 2,5625 % After borrows again SEK 35.500.000 at 2,75 % And finally the bank lends SEK 26.625.000 at 2,6875 % Describe the position of that Bank in Swedish Krona Chapter 2 QUESTION 1 : US TREASURY BILL PRICE We have a 366 days US TBILL issued at 2,75 % for USD 35.500.000 What is the issuance price? What is the amount of discount? QUESTION 2 : UK TREASURY BILL AMOUNT OF DISCOUNT What is the amount of discount for a 214 days UK T-Bill having a rate of 5,375 % for GBP 170 Million? QUESTION 3 : YIELD / PURE DISCOUNT RATE We have a 183 days US TBILL issued at 4,125 % : what is its yield?
QUESTION 4 : PURE DISCOUNT RATE / YIELD We have a 122 days UK TBILL having a yield of 1,375 % What is its pure discount rate? QUESTION 5 : PURE DISCOUNT RATE / YIELD A bank purchases a US TBILL 244 days at 5,1 % for USD 250.000.000,00 The bank sells this TBILL after 61 days at 5,14 % What is the yield achieved during the holding period? QUESTION 6 : CD SECONDARY MARKET VALUE A bank resells a EUR CD at 4,92 % (EUR 350.000.000,00) value the 03/02/15 The CD was initially a 6 month CD issued value the 03/12/14 at 4,88 % What is the secondary market value of this CD? What is the yield achieved during the holding period? QUESTION 7 : CD YIELD ACHIEVED A bank buys a 183 days CD for SGD 500.000.000,00. The issuance rate is 5,4 %. After 45 days, the bank resells the CD at 5,44 %. What is the yield achieved during the holding period? QUESTION 8 : CP PRICE A EURO JPY CP is issued for 61 days at a rate of 7,125 % The Amount is JPY 110.000.000.000 What is the issuance price? QUESTION 9 : CP INVESTMENT DECISION A bank in New York has two choices (everything else equal) : Purchase a 152 days domestic USD CP at an issuance rate of 7,375 % or Purchase a 152 days euro USD CP at an issuance rate of 7,395 %. What is the best investment for a nominal amount of USD 100 Mio? QUESTION 10 CLASSIC REPO AND SELL&BUY BACK Classic repo : Value date is the 03/12/14, your bank repoes out a security maturing the 03/05/17 with a coupon of 2,125 % for a nominal amount of GBP 215.000.000,00 at a market price of 99,99. The security's day count basis is : 30/360. The repo period will mature on the 03/06/15 and the expected repo rate is 1,125 %. What will be the final consideration of this trade? The cash lender wants an initial margin of 3,00%. QUESTION 11 CLASSIC REPO AND SELL&BUY BACK Sell & Buy back Contract : Value date is the 03/12/14, your bank repoes out a security maturing the 03/05/17 with a coupon of 3,75 % for a nominal amount of GBP 130.000.000,00 at a market price of 94,52. The security's day count basis is : 30/360. The repo period will mature on the 03/06/15 and the expected repo rate is 5,25 %. What will be the theoritical price of the security at the repo maturity?
Chapter 3 In this chapter, we will consider the following data Value 03-12-14 The currency is USD Deposit Yield curve : Per Maturities days middle Bid - Ask IRS Ask 1 05-01-15 33 6,16 6,11-6,21 6,21 2 03-02-15 62 6,28 6,23-6,33 6,34 3 03-03-15 90 6,4 6,35-6,45 6,46 4 03-04-15 121 6,52 6,47-6,57 6,58 5 04-05-15 152 6,64 6,59-6,69 6,70 6 03-06-15 182 6,76 6,71-6,81 6,82 7 03-07-15 212 6,88 6,83-6,93 6,94 8 03-08-15 243 7 6,95-7,05 7,07 9 03-09-15 274 7,12 7,07-7,17 7,19 10 05-10-15 306 7,24 7,19-7,29 7,31 11 03-11-15 335 7,36 7,31-7,41 7,43 12 03-12-15 365 7,48 7,43-7,53 7,55 FRA Prices : Per days Bid - Ask 1/4 88 6,63-6,66 4/7 91 7,22-7,25 7/10 94 7,74-7,77 1/7 179 6,99-7,03 1/10 273 7,33-7,38 3/6 92 7,02-7,05 6/9 92 7,59-7,63 9/12 91 8,14-8,19 3/9 184 7,36-7,40 6/12 183 7,93-7,97 3/12 275 7,71-7,76 4/10 185 7,54-7,58 QUESTION 1 : FORWARD / FORWARD The spot value is the 03/12/14 We have the yield curve quoted as described in the chapter introduction What are the prices : A short 1/4 forward/forward? A long 3/6 forward/forward? A long 6/12 forward/forward? QUESTION 2 : FORWARD / FORWARD We use the data as described in the chapter introduction What is the value of a 6 Months long cash position built up from the compounding of the 3 Months cash and the 3/6 Months FRA?
QUESTION 3 : FRA SETTLEMENT We bought a 9/12 FRA for USD 40.000.000 The LIBOR fixing is 8,59 What amount do we have to pay or receive according to the fixing? QUESTION 4 : FRA POSITION AND SETTLEMENT Value the 03/12/2014, we make the following deals with the same counterparty : Sold a 1/7 USD FRA at 7,03 for USD 40.000.000 Bought a 2/5 USD FRA at 7,08 for USD 60.000.000 Sold a 1/7 USD FRA at 7,05 for USD 80.000.000 Bought a 1/7 USD FRA at 7,01 for USD 50.000.000 Value the 05/01/2015, what is the amount to be paid or received? we have a netting agreement with our counterparty The 179 days USD Libor fixing is 6,97 QUESTION 5 : PLAYING THE CURVE WITH FRA Value the 03/12/2014 We anticipate a steepening of the yield curve What is our strategy and at what price? After one month, we have the following prices in the market : 2/5 FRA : 6,97-7 8/11 FRA : 8,24-8,29 We want to close our position (according to the suitable strategy) What is our profit or loss (expressed in pips)? QUESTION 6 : FRA AND CASH HEDGING Value the 03/12/2014 : we have lent the 10 months at 7,295 % We want to try to hedge our position (including by using FRA). We are limited to use the following FRA's The 4/7 FRA, the 7/10 and the 4/10 FRA At what price would be the best possible 10 months long position? QUESTION 7 : FUTURE PROFIT OR LOSS A bank anticipates a rate cut in the EUR. The bank takes position in the morning in 100 JUNE EUR 3 Months Future contracts. The dealing price is 93,60-62 in the Euronext Liffe exchange In the evening, the closing price of the future contract 93,68 What is the daily profit or loss of the bank? QUESTION 8 : IRS FLOWS The 1 Y IRS/3 month USD quotes 7,52-7,55. The spot date is on the 03-12-14 The bank wants to have a short position in the 1 year for USD 40.000.000,00 We have the following fixings in the three months Fixing1 : 6,43458 Fixing2 : 7,03929 Fixing3 : 7,71356 Fixing4 : 8,19555 What are the flows of this IRS?
QUESTION 9 : OIS SETTLEMENT Value the 03-12-14, the EONIA 1 week is quoted 6,00 % - 6,02 % Bank A wants to take the 1 week EONIA for EUR 40.000.000,00 from bank B The two banks have a bilateral netting agreement We have the following O/N fixings : - O/N 03-12-14 to 04-12-14 has been fixed at 5,97 - O/N 04-12-14 to 05-12-14 has been fixed at 6,01 - O/N 05-12-14 to 08-12-14 has been fixed at 5,975 - O/N 08-12-14 to 09-12-14 has been fixed at 6,0175 - O/N 09-12-14 to 10-12-14 has been fixed at 6,005 What is the amount to paid or received by bank A? What does it represent in term of rate (in %)? When is the settlement date? QUESTION 10 ZERO COUPON CALCULATIONS Long Term Calc positive yield curve Here are the Mid Prices EUR Bond Basis. Per IRS (Bd B) 1 7,53 2 7,88 Please, calculate the Fwd/Fwd Prices of the straight 1 against 2 years Calculate the 2 years Zero Coupon Rates (APR) Calculate the semi, quarterly Bond rate and the equivalent euro rates for each period QUESTION 11 ZERO COUPON CALCULATIONS Long Term Calc negative yield curve Here are the Mid Prices EUR Bond Basis. Per IRS (Bd B) 1 15,06 2 14,21 Please, calculate the Fwd/Fwd Prices of the straight 1 against 2 years Calculate the 2 years Zero Coupon Rates (APR) QUESTION 12 STRIPPING Value the 03-12-14 we have the STIR EuroUSD quoted Future DEC14 97,810 MAR15 97,755 JUN15 97,505 SEP15 97,200 The deposit price up to the 1st future is 1,62 % What are the strips for the 3/9 and 6/12 USD FRA
PART 2 Chapter 4 Spot Main/Sub : 1,7084 1/12/2014 PER Maturity Days T/N 3/12/2014 1 1W 10/12/2014 7 1 5/01/2015 33 2 3/02/2015 62 3 3/03/2015 90 6 3/06/2015 182 9 3/09/2015 274 12 3/12/2015 365 Basis 360 Basis 365 PER MAIN DEPOSIT SUB DEPOSIT FX SWAP PRICES T/N 7,06 7,09 11,37 11,40 1,977 1,982 1W 7,07 7,12 11,38 11,43 13,91 13,98 1 7,14 7,24 11,45 11,55 64,6 64,9 2 7,26 7,36 11,60 11,70 120,3 121,5 3 7,38 7,48 11,75 11,85 178 181 6 7,74 7,84 12,20 12,30 360 365 9 8,10 8,20 12,65 12,75 531 536 12 8,46 8,56 13,10 13,20 718 727 QUESTION 1 : SPOT POSITION A bank buys 80 M CHF/JPY at 115,295 and then buys 75 M CHF/JPY at 115,215 and then buys 95 M CHF/JPY at 115,275 and finally sells 110 M CHF/JPY at 115,335 and What's its final position? QUESTION 2 : CROSS CALCULATION What is the cross price AUD/SGD provided by a Market Maker combining the AUD/USD at 0,8723 to 0,8728 and the USD/SGD at 1,275 to 1,2755 QUESTION 3 : CROSS CALCULATION What is the cross price CAD/JPY provided by a Market Maker combining the USD/CAD at 1,149 to 1,1495 and the USD/JPY at 109,612 to 109,662
QUESTION 4 : CROSS FORWARD CALCULATION What are the Cross Forward Points AUD/CHF provided by a Market Maker combining the AUD/USD having a mid spot price of 0,8723 and a FX Forward points of 23 / 18 with the USD/CHF having a mid spot price of 0,9512 and a FX Forward points of 8 / 13 QUESTION 5 : CROSS FORWARD CALCULATION What are the Cross Forward Points CAD/JPY provided by a Market Maker combining the USD/CAD having a mid spot price of 1,149 and a FX Forward points of 24 / 19 with the USD/JPY having a mid spot price of 109,612 and a FX Forward points of 9 / 14 QUESTION 6 : FORWARD BROKEN DATE CALCULATION Calculate the ASK Outright 4 and 5 months (linear interpolation) using the data of this chapter QUESTION 7 : SWAP PRICES FROM CASH Using the Deposit data of this chapter, What are the 3 Mth FX forward Main/Sub calculation (left-right) QUESTION 7 BIS : FX FORWARD? My customer wants to play lower FX in 3 months They are not allowed to deal FX Forward 3 months They don't want to use the main currency at all in this trade What type of trade can you propose them? Explain! Case 1 : if the real FX after 3 months is 1,7242 then the profit for your customer will be : Case 2 : if the real FX after 3 months is 1,7272 then the loss for your customer will be : QUESTION 8 : ARBI VIA FX SWAP The FX Swap 9 Mth (274 days) Main(360) / Sub(365) are 531 / 536 (Mid Spot 1,7084 ) Your bank wants to know how to produce (borrow) the 9 months Main By using the offer 9 months Sub at 12,75 % for 10.000.000,00 Precise the exact amounts involved in this package if we do 9 Mth Sub currency QUESTION 9 : ARBI VIA FX SWAP The FX Swap 1 Mth (33 days) Main(360) / Sub(365) are 64,6 / 64,9 (Mid Spot 1,7084 ) Your bank wants to know how to lose (lend) the 1Mth Sub By using the 1 Mth Main deposit Bid at 7,14 % for 10.000.000,00 Precise the exact amounts involved in this package if we do 1M Main currency
QUESTION 10 : FORWARD/FORWARD CALCULATION ON FX SWAPS Using our Chapter data What are the 3 against 6 Forward/Forward Fx Swap Prices Main/Sub What are the 6 against 12 Forward/Forward Fx Swap Prices Main/Sub QUESTION 11 : ANTE SPOT QUOTES Using our Chapter data But let's consider here the spread Bid-Ask on spot : 1,7084-1,7089 Calculate the value-tomorrow FX Rate for Main/Sub QUESTION 12 : PRECIOUS METAL We have the following information in the gold market : Spot gold price = 1.728 $ / oz Forward gold price = 1.734 $ / oz (62 days) The USD Libor is 3,73 % (62 days) What is the gold lease rate (according to the usual market approximation)? QUESTION 13 : PRECIOUS METAL We have the following information in the silver market : Spot gold price = 1.440 $ / oz Forward gold price = 1.430 $ / oz (121 days) The USD Libor is 3,95 % (121 days) What is the gold lease rate (according to the usual market approximation)?
Day Finder Copy from 2012 Oct, 16
Chapter 5 EUR/USD 1,2691 PER Days EUR Mid % USD Mid % FX FwD 1 33 0,00700% 0,15400% 1,26927 2 62 0,04200% 0,19940% 1,26944 3 90 0,08200% 0,23310% 1,26958 4 121 0,11567% 0,26553% 1,26974 5 152 0,14933% 0,29797% 1,26990 6 182 0,18300% 0,33040% 1,27004 7 212 0,20633% 0,37162% 1,27033 8 243 0,22967% 0,41283% 1,27067 9 274 0,25300% 0,45405% 1,27104 10 306 0,28233% 0,49527% 1,27139 11 335 0,31167% 0,53648% 1,27175 12 365 0,34100% 0,57770% 1,27214 QUESTION 1 : CALL / PUT PARITY What is the price for the 5 Months Call EUR/USD strike 1,2789? Put price, same strike (1,2789) on 152 days = 1,81 cts / QUESTION 2 : CALL / PUT PARITY What is the price for the 11 Months Put EUR/USD strike 1,2618? Call price, same strike (1,2618) on 335 days = 2,45 cts / QUESTION 3 : PREMIUM What is the value of the premium of this Option :? With a nominal amount of 15.000.000,00 on EUR/USD The price is expressed in cts per nominal of main : 1,43 (Put on 2 Months Strike 1,2794) QUESTION 4 : RISK PROFILE A trader has bought an European Call EUR/USD 152 days for 20.000.000,00 EUR Strike 1,2399, premium = 3,3 cts / EUR What is position and at what break-even? QUESTION 5 : RISK PROFILE A trader has sold an European Put EUR/USD 243 days for 10.000.000,00 EUR Strike 1,2857, premium = 2,51 cts / EUR What is position and at what break-even?
QUESTION 6 : DELTA HEDGING Still using our current data A trader is long of 40.000.000,00 EUR/USD forward 10 Mth He wants a neutral delta hedging "at the money" forward What is the type of option (Put or Call) he has to sell or buy to have is neutral delta hedging position? What is the amount of EUR/USD option he has to do? The Call premium such a period ATM is 1,84 cts/eur Illustrate the P&L around the FX Fwd 1,27139 QUESTION 7 : DELTA HEDGING Still using our current data A trader is long of a CALL 5.000.000,00 EUR/USD forward 12 Mth at 1,2521 The DELTA is : 0,62 Is this option OUT, AT or IN the money? To have a Delta hedging, what amount of EUR/USD should he sell or buy? The PUT premium 365 days strike 1,2521 is 1,15 cts/eur Illustrate the P&L around the FX Fwd 1,27214 QUESTION 8 : SYNTHETIC POSITION A trader has a long European Call EUR/USD (274 days), Strike 1,27104, premium = 1,75 cts / EUR He has a short forward EUR/USD position at 1,27104 (274 days) The actual Fx Forward for that maturity is at 1,27104 What is position and at what break-even? QUESTION 9 : SYNTHETIC POSITION A trader has a long European Put EUR/USD (121 days), Strike 1,26974, premium = 1,17 cts / EUR He has a long forward EUR/USD position at 1,26974 (121 days) The actual Fx Forward for that maturity is at 1,26974 What is position and at what break-even? QUESTION 10 : Synthetic Position We have the following informations in the market : Fx Spot is : 1,2691 and Fx Forward EUR/USD 1,27175 Call EUR/USD, strike 1,2691, 335 days, Premium = 2,06 cts Call EUR/USD, strike 1,30175, 335 days, Premium = 0,81 cts Put EUR/USD, strike 1,2691, 335 days, Premium = 1,8 cts A) What is the options combination to use if a trader anticipates an increase in the EUR/USD value but doesn t want to pay the full 2,06 cts premium of the call strike 1,2691? B) What is the options combination to use if a trader anticipates a strong volatility in the EUR/USD parity? we will assume no spread bid / ask in option prices and we will not take into account the financing costs over the period
WEDNESDAY 3 DECEMBER 3 12 2014 17 1 31 MON TUE WED THU FRI SAT SUN 1 2 3 4 5 6 7 1 2 3 4 8 9 10 11 12 13 14 5 6 7 8 9 10 11 15 16 17 18 19 20 21 12 13 14 15 16 17 18 22 23 24 25 26 27 28 19 20 21 22 23 24 25 29 30 31 26 27 28 1 JANUARY 2015 2 FEBRUARY 2015 3 MARCH 2015 5 1 2015-29 31 3 2 2015-60 28 3 3 2015 18 88 31 MON TUE WED THU FRI SAT SUN MON TUE WED THU FRI SAT SUN MON TUE WED THU FRI SAT SUN 1 2 3 4 1 1 29 30 31 32 60 88 5 6 7 8 9 10 11 2 3 4 5 6 7 8 2 3 4 5 6 7 8 33 34 35 36 37 38 39 61 62 63 64 65 66 67 89 90 91 92 93 94 95 12 13 14 15 16 17 18 9 10 11 12 13 14 15 9 10 11 12 13 14 15 40 41 42 43 44 45 46 68 69 70 71 72 73 74 96 97 98 99 100 101 102 19 20 21 22 23 24 25 16 17 18 19 20 21 22 16 17 18 19 20 21 22 47 48 49 50 51 52 53 75 76 77 78 79 80 81 103 104 105 106 107 108 109 26 27 28 29 30 31 23 24 25 26 27 28 23 24 25 26 27 28 29 54 55 56 57 58 59 82 83 84 85 86 87 110 111 112 113 114 115 116 30 31 117 118 4 APRIL 2015 5 MAY 2015 6 JUNE 2015 3 4 2015-119 30 4 5 2015-149 31 3 6 2015 17 180 30 MON TUE WED THU FRI SAT SUN MON TUE WED THU FRI SAT SUN MON TUE WED THU FRI SAT SUN 1 2 3 4 5 1 2 3 1 2 3 4 5 6 7 119 120 121 122 123 149 150 151 180 181 182 183 184 185 186 6 7 8 9 10 11 12 4 5 6 7 8 9 10 8 9 10 11 12 13 14 124 125 126 127 128 129 130 152 153 154 155 156 157 158 187 188 189 190 191 192 193 13 14 15 16 17 18 19 11 12 13 14 15 16 17 15 16 17 18 19 20 21 131 132 133 134 135 136 137 159 160 161 162 163 164 165 194 195 196 197 198 199 200 20 21 22 23 24 25 26 18 19 20 21 22 23 24 22 23 24 25 26 27 28 138 139 140 141 142 143 144 166 167 168 169 170 171 172 201 202 203 204 205 206 207 27 28 29 30 25 26 27 28 29 30 31 29 30 145 146 147 148 173 174 175 176 177 178 179 208 209 7 JULY 2015 8 AUGUST 2015 9 SEPTEMBER 2015 3 7 2015-210 31 3 8 2015-241 31 3 9 2015 16 272 30 MON TUE WED THU FRI SAT SUN MON TUE WED THU FRI SAT SUN MON TUE WED THU FRI SAT SUN 1 2 3 4 5 1 2 1 2 3 4 5 6 210 211 212 213 214 241 242 272 273 274 275 276 277 6 7 8 9 10 11 12 3 4 5 6 7 8 9 7 8 9 10 11 12 13 215 216 217 218 219 220 221 243 244 245 246 247 248 249 278 279 280 281 282 283 284 13 14 15 16 17 18 19 10 11 12 13 14 15 16 14 15 16 17 18 19 20 222 223 224 225 226 227 228 250 251 252 253 254 255 256 285 286 287 288 289 290 291 20 21 22 23 24 25 26 17 18 19 20 21 22 23 21 22 23 24 25 26 27 229 230 231 232 233 234 235 257 258 259 260 261 262 263 292 293 294 295 296 297 298 27 28 29 30 31 24 25 26 27 28 29 30 28 29 30 236 237 238 239 240 264 265 266 267 268 269 270 299 300 301 31 271 10 OCTOBER 2015 11 NOVEMBER 2015 12 DECEMBER 2015 5 10 2015-302 31 3 11 2015-333 30 3 12 2015 16 363 31 MON TUE WED THU FRI SAT SUN MON TUE WED THU FRI SAT SUN MON TUE WED THU FRI SAT SUN 1 2 3 4 1 1 2 3 4 5 6 302 303 304 305 333 363 364 365 366 367 368 5 6 7 8 9 10 11 2 3 4 5 6 7 8 7 8 9 10 11 12 13 306 307 308 309 310 311 312 334 335 336 337 338 339 340 369 370 371 372 373 374 375 12 13 14 15 16 17 18 9 10 11 12 13 14 15 14 15 16 17 18 19 20 313 314 315 316 317 318 319 341 342 343 344 345 346 347 376 377 378 379 380 381 382 19 20 21 22 23 24 25 16 17 18 19 20 21 22 21 22 23 24 25 26 27 320 321 322 323 324 325 326 348 349 350 351 352 353 354 383 384 385 386 387 388 389 26 27 28 29 30 31 23 24 25 26 27 28 29 28 29 30 31 327 328 329 330 331 332 355 356 357 358 359 360 361 390 391 392 393 30 362
Chapter 3 Extra QUESTION 7 bis : FUTURE HEDGING Value the 10/05/16 The bank takes position in buying 100 USD USD JUN16 3 Mth Future contracts. The dealing price is at 97,455 in the Euronext Liffe exchange The bank wants to hedge in trading FRA same rate, same period What is the approprate FRA trade? What is the amount to be applied? Please develop step by step QUESTION 7 ter : FUTURE HEDGING The bank buys 10 EUR 3 Mth Contracts at 96,59... 6 days before fixing. The initial margin is 945 EUR per contract and the minimum reserve at 700 EUR per contract Describe the successive balance at each closing day 1 96,590 2 96,670 3 96,630 4 96,680 5 96,560 6 96,510
(c) Ver. 01-12-14 521 CZK
PART 1 Chapter 1 SOLUTION 1 : INTEREST RATE CALCULATION 1st flow of interest rate payment after 1 year : 366 days The annual basis for money market deposit on GBP is 365!!! So the Interest calculation is : GBP 71.000.000 * 5,125 * 366 / 365 = GBP 3.648.719 2nd flow of interest rate payment after 155 days (reimbursement of the nominal + residual interests): So the Interest calculation is : GBP 71.000.000 * ( 1 + (5,125 * 155 / 365 ) ) = GBP 72.545.223 spot 1 year ( 366 days ) Maturity ( 521 days ) 71.000.000 3.648.719 72.545.223 SOLUTION 2 : DATES VALUES If we are in DECEMBER 2014 trading value the last day of the month The spot value is the 31/12/14 Per Maturities Euro Days 1 30/01/2015 30 2 27/02/2015 58 3 31/03/2015 90 4 30/04/2015 120 5 29/05/2015 149 6 30/06/2015 181 7 31/07/2015 212 8 31/08/2015 243 9 30/09/2015 273 10 30/10/2015 303 11 30/11/2015 334 12 31/12/2015 365 SOLUTION 3 : CHANGES IN INTEREST CALCULATION METHODS From To Euro Days Bond Days Euro Rate Bond Rate Euro APR 5/01/2015 27/05/2015 142 142 5,625 5,625 5,803 10/02/2015 11/05/2015 90 91 2,591 2,563 2,653 27/03/2015 15/05/2015 49 48 8,188 8,358 8,606 3/08/2015 26/11/2015 115 113 13,081 13,313 13,875
SOLUTION 4 : BROKEN DATE CALC From 275 days to 366 days we have 91 days Full spread in rate is : 2,75-2,5625 = 0,1875 From 275 days to 305 days we have 30 days Proporata is : 32,967% So 32,967% of 0,1875 = 0,0618 10 Months rate approximation is = 2,5625 + 0,0618 = 2,6243 From 275 days to 336 days we have 61 days Proporata is : 67,033% So 67,033% of 0,1875 = 0,1257 11 Months rate approximation is = 2,5625 + 0,1257 = 2,6882 9 275 2,5625 10 305 2,6243 11 336 2,6882 12 366 2,7500 SOLUTION 5 : CASH POSITION The bank QPRFC borrows SEK 71.000.000 at 2,5625 % The weight of the trade is + 71.000.000 * 2,5625 = 181.937.500 (+ because the Bank borrowed) and after SEK 35.500.000 at 2,75 % The weight of the trade is + 35.500.000 * 2,75 = 97.625.000 (+ because the Bank borrowed) Finally the bank lends SEK 26.625.000 at 2,6875 % The weight of the trade is - 26.625.000 * 2,6875 = -71.554.688 (- because the Bank lent) Final position is the global weighted average Long of 71.000.000 + 35.500.000-26.625.000 = 79.875.000 The global weight = (71.000.000 * 2,5625) + (35.500.000 * 2,75) - (26.625.000 * 2,6875) The global weight = SEK 79.875.000 Final position is 208.007.813 / 79.875.000 Final position is = 2,6042 % in the Swedish Krona book Chapter 2 SOLUTION 1 : US TREASURY BILL PRICE As we have a US TBILL, we must apply our formula 3 of the PURE RATE OF DISCOUNT The issuance price = Nominal * ( 1 - ( PRD% * MMDays to Maturity / Annual Basis ) The issuance price = 35.500.000 * ( 1 - ( 2,75 % * 366 / 360 ) The issuance price = 34.507.479,17 The amount of discount = Nominal - Issuance Price = 992.520,83
SOLUTION 2 : UK TREASURY BILL AMOUNT OF DISCOUNT The amount of discount is the Nominal (maturity amount) * the PRD * remaining days/annual Basis (for GBP) The amount of discount is GBP 170.000.000,00 * 5,375 % * 214 / 365 = GBP 5.357.328,77 SOLUTION 3 : YIELD / PURE DISCOUNT RATE To transform a PRD into a yield, we can apply the formula (available at the exam) PRD / (1 - ( PRD % * DAYS / Annual Basis )) 4,125 / (1 - ( 4,125 % * 183 / 360 ) = 4,2133 Yield Rate = 4,2133 % SOLUTION 4 : PURE DISCOUNT RATE / YIELD For example, an final amount of 100.000.000,00 GBP having a yield of 1,375 % on 122 days means : Initial Amount = Final Amount / ( 1+ ( Yield % * Days / Annual Basis ) ) Initial Amount = 100 / ( 1+ ( 1,375 % * 122 /365 ) ) Initial Amount = 99,543 Amount of discount = 0,457 Pure Rate of Discount = ( Amt of disc / Nominal ) * Annual Basis / Days Pure Rate of Discount = ( 0,457 / 100 ) * 365 / 122 Pure Rate of Discount = 1,3687 % SOLUTION 5 : PURE DISCOUNT RATE / YIELD Initial discount amount : = 250.000.000,00 * ( 1 - ( 5,1 * 244 / (360*100) ) ) = 241.358.333,33 Secondary discount amount : = 250.000.000,00 * ( 1 - ( 5,14 * 183 / (360*100) ) ) = 243.467.916,67 Yield during the holding period = ((243.467.916,67 / 241.358.333,33) 1 ) * 36000 / 61 = 5,1583 % SOLUTION 6 : CD SECONDARY MARKET VALUE Originally, the CD had 182 days ( from 03/12/14 to 03/06/15 ) The bank holds it for 62 days, the remaining number of days is 120 The maturity proceed for a CD is : Nominal * ( 1 + (Yield% * Days / Annual Basis ) ) 350.000.000,00 * ( 1 + (4,88 % * 182 /360 ) ) = 358.634.888,89 We apply the new discounting yield to find the secondary market value : 358.634.888,89 / ( 1 + (4,92 % * 120 /360 ) ) = 352.848.178,76 Yield during the holding period = ((352.848.178,76 / 350.000.000,00) 1 ) * 36000 / 62 = 4,725 % SOLUTION 7 : CD YIELD ACHIEVED Maturity amount : = 500.000.000,00 * ( 1 + ( 5,4 * 183 / (365*100) ) ) = 513.536.986,30 Secondary discount amount : = 513.536.986,30 / ( 1 + ( 5,44 * 138 / (365*100) ) ) = 503.187.589,39 Yield during the holding period = ((503.187.589,39 / 500.000.000,00) 1 ) * 36500 / 45 = 5,1710 %
SOLUTION 8 : CP PRICE The EURO JPY CP is issued on a PV calculation (Formula 2) The issuance price = Nominal / ( 1 + Rate% * Days / Annual Basis ) The issuance price = 110.000.000.000 / ( 1 + 7,125 % * 61 / 360 ) The issuance price = 108.687.820.994 SOLUTION 9 : CP INVESTMENT DECISION 2 different approaches 1st : What would it cost me in both cases? And of course I 'll choose the cheapest USD Domestic CP is computed on PRD basis (formula 3) The price = Nominal * ( 1 - ( PRD% * MMDays to Maturity / Annual Basis)) The price = 100.000.000,00 * ( 1 - ( 7,375 % * 152 / 360 ) ) The price = 96.886.111,11 USD Euro CP is computed on present value basis (formula 2) The price = 100.000.000,00 / ( 1 + (7,395 % * 152 / 360 ) ) The price = 96.972.204,53 2nd : Which investment has the highest yield? USD Domestic CP is computed on PRD basis (formula 3) To transform a PRD into a yield, we can apply the formula PRD / (1 - ( PRD % * DAYS / Annual Basis )) 7,375 / (1 - ( 7,375 % * 152 / 360 ) = 7,612 Yield Rate = 7,612 % USD Euro CP is computed on present value basis (formula 2) Yield Rate = CP rate Yield Rate = 7,395 % SOLUTION 10 CLASSIC REPO AND SELL&BUY BACK The clean amount is equal to the nominal of GBP 215.000.000,00 x 99,99 % = GBP 214.978.500,00. For the Interest accrued, (30/360), we use 210 days :( from the 03/05/14 to the 03/12/14 ) So we have as interest accrued : GBP 215.000.000,00 x 2,125 % x 210 / 360 = GBP 2.665.104,17. The full (dirty) value of the security is : 214.978.500,00 + 2.665.104,17 = GBP 217.643.604,17. As the lender wants an initial margin of 3,00%., we compute : 217.643.604,17/(1 + 3,00%. ) ARR Simulating a cash trade, the maturing amount of the repo must be : 211.304.500,00 x ( 1 + (1,125 %. x 182 / 365 ) ) = GBP 212.506.294,34 SOLUTION 11 CLASSIC REPO AND SELL&BUY BACK The clean amount is equal to the nominal of GBP 130.000.000,00 x 94,52 % = GBP 122.876.000,00. For the Interest accrued, (30/360), we use 210 days :( from the 03/05/14 to the 03/12/14 ) So we have as interest accrued : GBP 130.000.000,00 x 3,75 % x 210 / 360 = GBP 2.843.750,00. The full (dirty) value of the security is : 122.876.000,00 + 2.843.750,00 = GBP 125.719.750,00. Simulating a cash trade, the maturing amount of the repo must be : 125.719.750,00 x ( 1 + (5,25 %. x 182 / 365 ) ) = GBP 129.010.851,95 Knowing the final consideration, we have to find out the forward price of the SBB At the maturity, part of the dirty amount will be due to the last Interest accrued at Maturity GBP 130.000.000,00 x 3,75 % x 30 / 360 = GBP 406.250,00 If the lender keeps the full coupon during the remaining period, he will make interest on the recapitulazation 4.875.000,00 x 5,25 % x 31 / 365 (from the 03/05/15 to the 03/06/15) = GBP 21.737,16 The principal will be 129.010.851,95-406.250,00-4.875.000,00-21.737,16 = GBP 123.707.864,79 Theoretical Forward Price = 123.707.864,79 / 130.000.000,00= 95,15990 %
Chapter 3 SOLUTION 1 : FORWARD / FORWARD 1/4 (88 days) is computed as 6,5303 to 6,7049 3/6 (92 days) is computed as 6,8538 to 7,1465 6/12 (183 days) is computed as 7,7788 to 8,0717 Descrition for the short 1/4 forward/forward : I'm short on Forward/Forward when I give the longest period by taking the shortest I must give the 4 months at 6,47 by taking the 1 month at 6,21 So I'm short 1/4 months at 6,530326 SOLUTION 2 : FORWARD / FORWARD To get a long position during the full period, I'll have to borrow the 3 months and the 3/6 The ask price on 3 months is at 6,45 % The offer of the 3/6 months FRA is at 7,05 % We have 90 days in the 3 months deposits And 92 days in the 3/6 FRA So the 6 months period will count 182 days The currency is the USD so the annual basis calculation is 360 The synthetic 6 months is equal to = ( ( 1 * ( 1 + 6,45 % * 90 / 360 ) * ( 1 + 7,05 % * 92 / 360 ) ) - 1 ) * 360 / 182 = 6,81076195054941 SOLUTION 3 : FRA SETTLEMENT As We bought a 9/12 FRA for USD 40.000.000 The period is 91 days at the FRA rate of 8,19 % The fixing being 8,59 %, we know that we made a profit The profit is : USD 40.000.000* ( 8,59-8,19 ) % * 91 / 360 on present value basis USD 40.444,44 / ( 1 + ( 8,59% * 91 ) / 360 ) USD 39.584,91 SOLUTION 4 : FRA POSITION AND SETTLEMENT Trading value the 05/01/2015, we have exactly 1 months later We just need to evaluate the former FRA 1/7 Having a netting agreement, it is easier to compute the position USD- 40.000.000 * 7,03 = - 281.200.000 USD- 80.000.000 * 7,05 = - 564.000.000 USD 50.000.000 * 7,01 = + 350.500.000 Total Short of 70.000.000 on a global weight of 494.700.000 The average rate (short position) is - 494.700.000 / - 70.000.000 = 7,067 % The fixing being 6,97 %, we have a profit because in average we sold at the higher price of 7,067 % The profit is : USD 70.000.000* ( 7,067 % - 6,97 % ) * 179 / 360 on present value basis USD 33.811,11 / ( 1 + ( 6,97 % * 179 ) / 360 ) USD 32.678,59
SOLUTION 5 : PLAYING THE CURVE WITH FRA Value the playing a steepening of the curve, We 'll sell the short and buy the long For instance, we'll sell the 3/6 FRA at 7,02 and buy the 9/12 FRA at 8,19 After one month, we'll close our position The 3/6 FRA is now a 2/5. So to cover my position I'll buy at 7 The 9/12 FRA is now a 8/11. So to cover my position I'll sell at 8,24 We made a profit of 2 pts in the new 2/5 and We made a profit of 5 pts in the new 8/11 SOLUTION 6 : FRA AND CASH HEDGING We have 4 differents possibilities in this limited context : (1) Either we consider to simply borrow the 10 months deposit (2) Either we borrow the 4 month deposit combined with buying a 4/10 FRA (3) Either we borrow the 4 month deposit combined with buying a 4/7 FRA and a 7/10 FRA (4) Either we borrow the 7 months deposit combined with buying a 7/10 FRA Please note that each FRA trade must be made "cash" by borrowing the cash amount at the fixing Sol 1 : The straight 10 months deposit at 7,29 % Sol 2 : 4 month at 6,57 % accumulated at the 4/10 FRA Rate : 7,58 % ( 1 + ( 6,57 % * 121 /360 ) ) * ( 1 + ( 7,58 % * 185 /360 ) ) = ( 1 + ( Rate 10 M % * 306 /360 ) ) Synthetic 10 Months is : 7,2818179403595 Sol 3 : 4 month at 6,57 % accumulated at the 4/7 FRA Rate : 7,25 % % and accumulated at the 7/10 FRA Rate : 7,77 % ( 1 + ( 6,57 % * 121 /360 ) ) * ( 1 + ( 7,25 % * 91 /360) ) * ( 1 + ( 7,77 % * 94 /360 )) = ( 1 + ( Rate 10 M % * 306 /360 )) Synthetic 10 Months is : 7,28587697038278 Sol 4 : 7 month at 6,93 % accumulated at the 7/10 FRA Rate : 7,77 % ( 1 + ( 6,93 % * 212 /360 ) ) * ( 1 + ( 7,77 % * 94 /360 ) ) = ( 1 + ( Rate 10 M % * 306 /360 ) ) Synthetic 10 Months is : 7,28544708431371 The cheapest solution is the Sol 2 with the rate of 7,2818179403595 %
SOLUTION 7 : FUTURE PROFIT OR LOSS Anticipating a rate cut in EUR I'll buy the Future Contract (opposite of the rate) Here we buy at 93,62 As the closing price is 93,68 we make a profit of 6 points On EUR, the value of 1 point per contract is 25 EUR Our closing day profit is equal to 100 * 6 * 25 EUR = EUR 15.000,00 SOLUTION 8 : IRS FLOWS Short position 1 Year means selling the fixed leg at 7,52 Value the 03-12-14 we have 365 days in the year On the fixed leg, the bank will receive USD 40.000.000,00 * 7,52 % * 365 / 360 = 3.049.777,78 on the 03-12-15 On the floating leg, the bank will pay USD 40.000.000,00 * 6,43458 % * 90 / 360 = 643.458,00 on the 03-03-15 On the floating leg, the bank will pay USD 40.000.000,00 * 7,03929 % * 92 / 360 = 719.571,87 on the 03-06-15 On the floating leg, the bank will pay USD 40.000.000,00 * 7,71356 % * 92 / 360 = 788.497,24 on the 03-09-15 On the floating leg, the bank will pay USD 40.000.000,00 * 8,19555 % * 91 / 360 = 828.661,17 on the 03-12-15 SOLUTION 9 : OIS SETTLEMENT Bank A wants to take the 1 week EONIA for EUR 40.000.000,00 from bank B at 6,02 Bank A will have to pay as fixed interest amount at the maturity : 40.000.000,00 * 6,02 % * 7 / 360 = EUR 46.822,22 Against it, the Bank A will receive the accumulation of interest amount on rolling O/N : 40.000.000,00 * ( 1 + ( 5,97 % * 1 / 360 ) ) = 40.006.633,33 40.006.633,33 * ( 1 + ( 6,01 % * 1 / 360 ) ) = 40.013.312,22 40.013.312,22 * ( 1 + ( 5,975 % * 3 / 360 ) ) = 40.033.235,51 40.033.235,51 * ( 1 + ( 6,0175 % * 1 / 360 ) ) = 40.039.927,18 40.039.927,18 * ( 1 + ( 6,005 % * 1 / 360 ) ) = 40.046.606,06 Total Interest Amount accumulated is 46.606,06 The balance is a loss of EUR -216,16 It represents in term of rate (in %) = ((40.046.606,06 / 40.000.000,00 ) - 1 )* 36000 / 7 = 5,992 % The settlement date for an OIS is always after the maturity (for EONIA 1 day after) so on the 11-12-14
SOLUTION 10 ZERO COUPON CALCULATIONS Long Term Calc positive yield curve Let's consider the flows step by step I want to create a 1 against 2 years forward/forward position I'll for instance give the 1 year by taking the 2 years PER G 1 year T 2 years Balance Flows SPOT -100 100 0 1 107,53-7,88 99,65 2 0-107,88-107,88 From year 1 to year 2, the initial amount is 99,65 And the maturing amount is -107,88 We can compute the 1 Year Rate againt the 2 years as = ((107,88/ 99,65) - 1 ) * 100 So the 1 Ag. 2 years Rate is 8,25890617160059 % If we compound the 1 year with the 1 Ag 2 years, we will compute the maturing zc amount Maturing amount = ( ( 1 *( 1 + 7,53 % ) * ( 1 + 8,259 %) = 1,16410801806322 Maturing amount = ( ( 1 *( 1 + ZC R 2Y % ) ^ 2 ) = 1,16410801806322 ZC R 2Y = ( 1,16410801806322 ^ 0,5 ) - 1 ) *100 = 7,89383754706388 ZC R 2Y = 7,89383754706388 Per IRS (Bd B) Fw Fw ZCR IRS (Euro) IRS (semi) IRS (quar) 1 7,53 7,53 7,53 7,427 7,393 7,326 2 7,88 8,259 7,894 7,772 7,731 7,657 Note that the ZCR is above the IRS while the curve is positive SOLUTION 11 ZERO COUPON CALCULATIONS Long Term Calc negative yield curve Let's consider the flows step by step I want to create a 1 against 2 years forward/forward position I'll for instance give the 1 year by taking the 2 years Per G 1 year T 2 years Balance Flows 0-100 100 0 1 115,06-14,21 100,85 2 0-114,21-114,21 From year 1 to year 2, the initial amount is 100,85 And the maturing amount is -114,21 We can compute the 1 Year Rate againt the 2 years as = ((114,21/ 100,85) - 1 ) * 100 So the 1 Ag. 2 years Rate is 13,2473971244423 % If we compound the 1 year with the 1 Ag 2 years, we will compute the maturing zc amount Maturing amount = ( ( 1 *( 1 + 15,06 % ) * ( 1 + 13,247 %) = 1,30302455131383 Maturing amount = ( ( 1 *( 1 + ZC R 2Y % ) ^ 2 ) = 1,30302455131383 ZC R 2Y = ( 1,30302455131383 ^ 0,5 ) - 1 ) *100 = 14,1501008021383 ZC R 2Y = 14,1501008021383 Per IRS (Bd B) Fw Fw ZCR 1 15,06 15,06 15,06 2 14,21 13,247 14,150 Note that the ZCR is under the IRS while the curve is positive
SOLUTION 12 ZERO COUPON CALCULATIONS 1st of all, we must compute the ZC on every IMM maturities USD From To Rate 30/360 Edays Rate Act/360 ZC Rate Cash 3/12/2014 17/12/2014 14 1,6200 1,6200 DEC14 17/12/2014 18/03/2015 2,1900 91 2,1659 2,0943 MAR15 18/03/2015 17/06/2015 2,2450 91 2,2203 2,1591 JUN15 17/06/2015 16/09/2015 2,4950 91 2,4676 2,2661 SEP15 16/09/2015 16/12/2015 2,8000 91 2,7692 2,3993 Then we calculate the broken dates for the maturities of the deposit fixed dates DEC14 17/12/2014 14 1,6200 1,620 1 5/01/2015 33 calc 1,719 2 3/02/2015 62 calc 1,870 3 3/03/2015 90 calc 2,016 MAR15 18/03/2015 105 2,0943 2,094 4 3/04/2015 121 calc 2,106 5 4/05/2015 152 calc 2,128 6 3/06/2015 182 calc 2,149 JUN15 17/06/2015 196 2,1591 2,159 7 3/07/2015 212 calc 2,178 8 3/08/2015 243 calc 2,214 9 3/09/2015 274 calc 2,251 SEP15 16/09/2015 287 2,2661 2,266 10 5/10/2015 306 calc 2,294 11 3/11/2015 335 calc 2,336 12 3/12/2015 365 calc 2,380 DEC15 16/12/2015 378 2,3993 2,399 Now we just have to calculate the forward forward 3 2,016 6 2,149 9 2,251 12 2,380 3/9 2,353774563 6/12 2,582055968
PART 2 Chapter 4 SOLUTION 1 : SPOT POSITION We compute the weighted average position 1 80 115,295 9.223,60 2 75 115,215 8.641,13 3 95 115,275 10.951,13 4-110 115,335-12.686,85 140 16.129,00 The bank has a long position of 140.000.000 CHF Average rate : 16129 / 140 = 115,207142857143 SOLUTION 2 : CROSS CALCULATION Combining AUD/USD and USD/SGD As the USD is in the middle, we simply compute Left * left and right * right The LEFT cross price AUD/SGD : 0,8723 * 1,275 The RIGHT cross price AUD/SGD : 0,8728 * 1,2755 Cross price AUD/SGD : 1,1122 to 1,1133 SOLUTION 3 : CROSS CALCULATION Combining USD/CAD and USD/JPY As the USD is NOT in the middle, we have to adapt CAD/USD at 0,8699 to 0,8703 and USD/JPY at 109,612 to 109,662 The LEFT cross price CAD/JPY : 0,869943453675511 * 109,612 The RIGHT cross price CAD/JPY : 0,870322019147084 * 109,662 Cross price CAD/JPY : 95,3562 to 95,4413 SOLUTION 4 : CROSS CALCULATION Combining AUD/USD and USD/CHF As the USD is in the middle, we simply compute Left * left and right * right On spot time : The cross price AUD/CHF : 0,8723 * 0,9512 Cross price SPOT AUD/CHF = 0,82973176 On forward time : Fwd prices are AUD/USD: 0,87 to 0,8705 and USD/CHF: 0,952 to 0,9525 The LEFT cross price AUD/CHF : 0,87 * 0,952 The RIGHT cross price AUD/CHF : 0,8705 * 0,9525 Cross price FWD AUD/CHF : 0,8282400 to 0,829151 Fx Fwd Points are : Left : 0,82824-0,82973176 Fx Fwd Points are : Right : 0,82915125-0,82973176 Fx Fwd Points are : -14,92 to -5,81
SOLUTION 5 : CROSS CALCULATION Combining USD/CAD and USD/JPY As the USD is NOT in the middle, we have to adapt On spot time : CAD/USD at 0,8703 and USD/JPY at 109,612 The cross price CAD/JPY : 0,870322019147084 * 109,612 Cross price SPOT CAD/JPY = 95,39773716 On forward time : Fwd prices are USD/CAD: 1,1466 / 1,1471 and USD/JPY: 109,702 / 109,752 But we use CAD/USD at 0,8718 / 0,8721 and USD/JPY at 109,702 / 109,752 The LEFT cross price CAD/JPY : 0,871763577717723 * 109,702 The RIGHT cross price CAD/JPY : 0,872143729286586 * 109,752 Cross price FWD CAD/JPY : 95,6342080 to 95,719519 Fx Fwd Points are : Left : 95,6342080027896-95,3977371627502 Fx Fwd Points are : Right : 95,7195185766614-95,3977371627502 Fx Fwd Points are : 23,65 to 32,18 SOLUTION 6 : FORWARD BROKEN DATE CALCULATION spot 1,7084 0 0 Fx Outright 3 90 181 181 1,72650 4 121 33,70% 243,0 1,73270 5 152 67,39% 305,0 1,73890 6 182 365 365 1,74490 We add the same percentage as the day percentage move The FX outright = FX Spot + FWD Points SOLUTION 7 : SWAP PRICES FROM CASH 1 BID Main after 90 days will be = 1 + ( 7,38 * 90 / (360 * 100 ) = 1,01845 1 ASK Main after 90 days will be = 1 + ( 7,48 * 90 / (360 * 100 ) = 1,0187 1,7084 BID Sub after 90 days will be = 1 + ( 11,75 * 90 / (365 * 100 ) = 1,75789679452055 1,7084 ASK Sub after 90 days will be = 1 + ( 11,85 * 90 / (365 * 100 ) = 1,75831804383562 Left Fx Fwd = Sub Fwd Amount BID / Main Fwd Amount ASK Left Fx Fwd = 1,75789679452055 / 1,0187 = 1,72562755916418 Right Fx Fwd = Sub Fwd Amount ASK / Main Fwd Amount BID Right Fx Fwd = 1,75831804383562 / 1,01845 = 1,72646476885033 Fx Swap Points for 3 Mth Main/Sub are the difference between Spot and FX Forward 3 Mth Fx Swap Points : 172,3 / 180,6 SOLUTION 7 bis : FX Forward? The price 3 months FX Swap is 178 to 181 so Fx forward should be 1,7262 to 1,7265 You can propose your customer to sell a NDF 3 Mths at 1,7262 Value 03-03-15 for a nominal of 100.000.000 Main 2 open days before the 03-03-15, we 'll check the offical price (fixing of the day) Case 1 : if the real FX after 3 months is 1,7242 then the profit for your customer will be : Nominal x (S-F) = - 100.000.000 x ( 1,7242-1,7262 ) = 200.000,00 Sub Case 2 : if the real FX after 3 months is 1,7272 then the loss for your customer will be : Nominal x (S-F) = - 100.000.000 x ( 1,7272-1,7262 ) = -100.000,00 Sub
SOLUTION 8 : ARBI VIA FX SWAP As my original goal is to receive Main in my book, in my FX Swap trade, I must buy this Main on the spot and consequently sell it on the forward. But as I ll take the Sub instead in the cash market, I ll rather prefer to do Sub amount on the swap. So I ll sell & buy the 10 mio Sub on the Fx Swap (so the left side 531 pts) Note that as the left value is smaller than the right, we have a ' + ' before our Fx Swap Pts values (+ 531) After 9 Mth, I ll have to repay the Sub (capital + interest) the exact amount of : 10.000.000 *( 1 + ( 12,75% * 274 / 365 ) = 10.957.123,29 Sub Using my Forward Exchange rate (second leg of my FX Swap Trade), I ll exchange my Sub against Main I ll exchange (buy) my Sub against Main So I'll buy 10.957.123,29 Sub at 1,7084 + (( +531 )/ 10.000) So I'll buy 10.957.123,29 / 1,7615 = 6.220.336,81 Main Using my Spot Price (first leg of my FX Swap Trade), selling my Sub, I bought the main amount of : 10.000.000 / 1,7084 = 5.853.430,11 Main The yield of our Main long position is :((Final Amount / Initial Amount) -1)*(Basis* 100) / days = ((6.220.336,81 / 5.853.430,11) -1)*( 360 * 100 )/ 274= 8,23563599498228 10.000.000,00 1,7084 5.853.430,11 12,750 % + 531 pts 8,2356 % 10.957.123,29 1,7615 6.220.336,81 SOLUTION 9 : ARBI VIA FX SWAP As my original goal is to lend the Sub from my book, in my FX Swap trade, I must sell this Sub on the spot and consequently buy it on the forward. But as I ll lend the Main instead in the cash market, I ll rather prefer to do Main amount on the swap. So I ll buy & sell the 10M Main on the Fx Swap (so the left side 64,6 pts) Note that as the left value is smaller than the right, we have a + before our Fx Swap Pts values (+64,6) After 1 Mth, I ll receive the Main back (capital + interest) the exact amount of : 10.000.000 *( 1 + ( 7,14% * 33 / 360 ) = 10.065.450,00 Sub Using my Forward Exchange rate (second leg of my FX Swap Trade), I ll exchange my Main against Sub I ll exchange (sell) my Main against Sub So I'll sell 10.065.450,00 Main at 1,7084 + (( +64,6 )/ 10.000) So I'll sell 10.065.450,00 * 1,71486 = 17.260.837,59 Sub Using my Spot Price (first leg of my FX Swap Trade), buying my Main I sold the sub amount of : 10.000.000 * 1,7084 = 17.084.000,00 Sub The yield of our Sub short position is :((Final Amount / Initial Amount) -1)*(Basis* 100) / days = ((17.260.837,59 / 17.084.000,00) -1)*( 365 * 100 )/ 33= 11,4489049385213 10.000.000,00 1,7084 17.084.000,00 7,140 % + 64,6 pts 11,4489 % 10.065.450,00 1,71486 17.260.837,59
SOLUTION 10 : FORWARD/FORWARD CALCULATION ON FX SWAPS The spot Price is 1,7084 The 3 months ASK FX Forward is : 1,7262 (1,7084 + (178 / 10.000) ) The 3 months ASK FX Forward is : 1,7265 (1,7084 + (181 / 10.000) ) The 6 months ASK FX Forward is : 1,7444 (1,7084 + (360 / 10.000) ) The 6 months ASK FX Forward is : 1,7449 (1,7084 + (365 / 10.000) ) The 12 months ASK FX Forward is : 1,7802 (1,7084 + (718 / 10.000) ) The 12 months ASK FX Forward is : 1,7811 (1,7084 + (727 / 10.000) ) FX Swap Pts 3/6 are (1,7444-1,7265) to (1,7449-1,7262) FX Swap Pts 3/6 are 179 pts to 187 pts FX Swap Pts 6/12 are (1,7802-1,7449) to (1,7811-1,7444) FX Swap Pts 6/12 are 353 pts to 367 pts SOLUTION 11 : ANTE SPOT QUOTES Spot = 1,7084-1,7089 Fx Swap from tomorrow to the Spot date is the T/N : 1,977 to 1,982 The ante spot value is the result of the crossing subtraction of the swap points at the spot value. Here we have 1,7084 - (1,982 /10.000) to 1,7089 - (1,977 /10.000) 1,7082018 to 1,7087023 TOMORROW 1,7082018 1,7087023 T/N 1,977 1,982 - - SPOT 1,7084 1,7089 SOLUTION 12 : PRECIOUS METAL We have a Contango situation (gold forward price > gold spot price) First we need to find the gold GOFO : GOFO = ((1734-1728) / 1728) * (360 / 62) = 2,0161 % Then doing the LIBOR GOFO (Contango), we obtain : Lease rate = 3,7300-2,0161 = 1,7139 % SOLUTION 13 : PRECIOUS METAL We have a Backwardation situation (silver forward price < silver spot price) First we need to find the silver GOFO : GOFO = ((1430-1440) / 1440) * (360 / 121) = -2,0661 % Then doing the LIBOR GOFO (Deport), we obtain : Lease rate = 3,9500 - -2,0661 = 6,0161 %
Chapter 5 SOLUTION 1 : CALL / PUT PARITY Call = Put + ( Fx FWD STRIKE ) / (1 +( (Sub IR % * Days /360 ))) Call = 0,0181 + ( 1,2699-1,2789 ) / (1 +( (0,297966666666667 % * 152 / 360 ))) Call = 0,0091 The result is logical: our Put was in the money (right to sell at 1,2789 what is 1,2699 forward) and our Call is out of the money (right to buy at 1,2789 what is 1,2699 forward) Our Call must be cheaper SOLUTION 2 : CALL / PUT PARITY Put = Call + ( STRIKE Fx FWD ) / (1 +( (Sub IR % * Days /360 ))) Put = 0,0245 + ( 1,2618-1,27175 ) / (1 +( (0,536483333333333 % * 335 / 360 ))) Put = 0,0146 The result is logical: our Call was in the money (right to buy at 1,2618 what is 1,27175 forward) and our Put is out of the money (right to sell at 1,2618 what is 1,27175 forward) Our Put must be cheaper SOLUTION 3 : PREMIUM So here we have, on a quotation Main/Sub, the price expressed in cents of the sub per unit of the main EUR / USD Put for 15.000.000,00 EUR Price = 1,43 cts / EUR Premium cost = 15.000.000,00 * 0,0143 = 214.500,00 USD QUESTION 4 : RISK PROFILE The trader has bought THE RIGHT to BUY EUR/USD up to 152 days, As long as the FX is lower than 1,2399, his max loss is 3,3 cts / EUR Which means 20.000.000,00 * 0,033 = 660.000,00 USD Between 1,2399 and 1,2729 the trader reimburse the cost of the premium After (over) 1,2729 the trader makes a profit equivalent to the increase of pips Ex. : If the EUR/USD is quoted 1,2739 the trader makes 10 points profit Which means 20.000.000,00 * 0,0010 = 20.000,00 USD SOLUTION 5 : RISK PROFILE The trader has sold THE RIGHT to SELL EUR/USD up to 243 days, As long as the FX is higher than 1,2857, his max profit is 2,51 cts / EUR Which means 10.000.000,00 * 0,0251 = 251.000,00 USD Between 1,2857 and 1,2606 the trader will spend part of the premium Before (under) 1,2606 the trader makes a loss equivalent to the decrease of pips Ex. : If the EUR/USD is quoted 1,2586 the trader makes 20 points loss Which means 10.000.000,00 * 0,0020 = 20.000,00 USD
SOLUTION 6 : DELTA HEDGING Being long, he needs to be protected against lower rates The type of option to stick to this strategy is to buy a PUT Option To have a NEUTRAL hedge position, the PUT must be strike ATM ( Δ = 0,5 ) As we are ATM Fwd (Strike=FX Fwd), Call Premium = Put Premium so the cost of the PUT is :1,84 The amount of PUT Option ATM he has to buy is :(Amount of Fx FwD Position) / Delta = 40.000.000,00 / 0,5 = 80.000.000,00 EUR Development : FX Forward LG FX Fwd Put Prem P&L Put 1,27039 40000 0,0179-40000 1,27139 0 0,0184 0 1,27239-40000 0,0189 40000 SOLUTION 7 : DELTA HEDGING The Delta is 0,62 : the option is in the money (Delta > 0.50) I have the right to buy only at 1,2521 something which worths 1,27214 forward Being long, he needs to be protected against lower rates To cover this position in neutral Delta, the trader should sell a FX Forward: As the DELTA is 0,62, the amount of FX Forward must be : Amount of Option * Delta 5.000.000,00 * 0,62 = 3.100.000,00 Illustration : First we need to know the price of the CALL Call = Put + ( Fx FWD STRIKE ) / (1 +( (Sub IR % * Days /360 ))) Call = 0,0115 + ( 1,27214-1,2521 ) / (1 +( (0,5777 % * 365 / 360 ))) Call = 0,0314 Development : FX Forward Call Prem P&L Put LG FX Fwd 1,27114 0,03078-3100 3100 1,27214 0,0314 0 0 1,27314 0,03202 3100-3100 QUESTION 8 : SYNTHETIC POSITION Let's face the successive P&L of the 2 combined positions EUR/USD Long Call Sh FX Fwd Synthetic 1,23604-0,0175 0,035 0,0175 1,24479-0,0175 0,02625 0,00875 1,25354-0,0175 0,0175 0 1,26229-0,0175 0,00875-0,00875 1,27104-0,0175 0-0,0175 1,27979-0,00875-0,00875-0,0175 1,28854 0-0,0175-0,0175 1,29729 0,00875-0,02625-0,0175 1,30604 0,0175-0,035-0,0175
Graphically 0,04 0,03 0,02 Long Call Sh FX Fwd Synthetic 0,01 0-0,01 1,23604 1,24479 1,25354 1,26229 1,2710 1,2798 1,2885 1,2973 1,3060-0,02-0,03-0,04 SOLUTION 9 : SYNTHETIC POSITION Let's face the successive P&L of the 2 combined positions EUR/USD Long Put Lg FX Fwd Synthetic 1,24634 0,0117-0,0234-0,0117 1,25219 0,00585-0,01755-0,0117 1,25804 0-0,0117-0,0117 1,26389-0,00585-0,00585-0,0117 1,26974-0,0117 0-0,0117 1,27559-0,0117 0,00585-0,00585 1,28144-0,0117 0,0117 0 1,28729-0,0117 0,01755 0,00585 1,29314-0,0117 0,0234 0,0117 0,03 0,02 0,01 Long Put Lg FX Fwd Synthetic 0 1,24634 1,25219 1,25804 1,26389 1,2697 1,2756 1,2814 1,2873 1,2931-0,01-0,02-0,03
SOLUTION 10 : Synthetic Position A) a trader anticipates an increase in the EUR/USD value but doesn t want to pay the full 2,06 cts premium A solution is to buy that Call strike 1,2691 at 2,06 cts and sell at the same time another Call cheaper (so OTM) like the Call strike 1,30175 at 0,81 cts per EUR So my full maximum lost will be reduce from 2,06 to 1,25 ( = 2,06-0,81 ) Against that my maximum profit is not unlimited anymore and will capped after 1,30175 Maximum loss is 1,25cts per EUR and maximum profit is 2,02 cts per EUR This strategy is called : "The Bullish vertical spread" Let's face the successive P&L of the 2 combined positions EUR/USD Lg Call ATM Sh Call OTM Synthetic 1,261-0,0206 0,0081-0,0125 1,2691-0,0206 0,0081-0,0125 1,2816-0,0081 0,0081 0 1,2897 0 0,0081 0,0081 1,30175 0,01205 0,0081 0,02015 1,30985 0,02015 0 0,02015 1,31795 0,02825-0,0081 0,02015 1,32605 0,03635-0,0162 0,02015
B) a trader anticipates a strong volatility A solution is to buy that Call strike 335 days at 0,81 cts and buy at the same time a Put (same strike) at 1,8 cts As long as the EUR/USD stays close to the strike, we lose money So if the SPOT is out of the range from 1,26315 to 1,34035 then the bank makes money EUR/USD Lg Call ATM Lg Put ATM Synthetic 1,24255-0,0206 0,0412 0,0206 1,26315-0,0206 0,0206 0,0000 1,28375-0,0206 0,0000-0,0206 1,30175-0,0206-0,0180-0,0386 1,32235 0,0000-0,0180-0,0180 1,34035 0,0180-0,0180 0,0000 1,36095 0,0386-0,0180 0,0206 0,05000 0,04000 0,03000 Lg Call ATM Lg Put ATM Synthetic 0,02000 0,01000 0,00000-0,01000 1 2 3 4 5 6 7-0,02000-0,03000-0,04000-0,05000