(c) Ver CZK

Transcription

1 (c) Ver CZK

2 PART 1 Chapter 1 QUESTION 1 : INTEREST RATE CALCULATION What are the flows of payment for a loan of 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/ /05/2015 5,625 10/02/ /05/2015 2, /03/ /05/2015 8,1875 3/08/ /11/ ,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 at 2,5625 % After borrows again SEK at 2,75 % And finally the bank lends SEK 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 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?

3 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 ,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 ,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 ,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 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 ,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 ,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?

4 Chapter 3 In this chapter, we will consider the following data Value The currency is USD Deposit Yield curve : Per Maturities days middle Bid - Ask IRS Ask ,16 6,11-6,21 6, ,28 6,23-6,33 6, ,4 6,35-6,45 6, ,52 6,47-6,57 6, ,64 6,59-6,69 6, ,76 6,71-6,81 6, ,88 6,83-6,93 6, ,95-7,05 7, ,12 7,07-7,17 7, ,24 7,19-7,29 7, ,36 7,31-7,41 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/ ,74-7,77 1/ ,99-7,03 1/ ,33-7,38 3/6 92 7,02-7,05 6/9 92 7,59-7,63 9/ ,14-8,19 3/ ,36-7,40 6/ ,93-7,97 3/ ,71-7,76 4/ ,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?

5 QUESTION 3 : FRA SETTLEMENT We bought a 9/12 FRA for USD 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 Bought a 2/5 USD FRA at 7,08 for USD Sold a 1/7 USD FRA at 7,05 for USD Bought a 1/7 USD FRA at 7,01 for USD 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 The bank wants to have a short position in the 1 year for USD ,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?

6 QUESTION 9 : OIS SETTLEMENT Value the , the EONIA 1 week is quoted 6,00 % - 6,02 % Bank A wants to take the 1 week EONIA for EUR ,00 from bank B The two banks have a bilateral netting agreement We have the following O/N fixings : - O/N to has been fixed at 5,97 - O/N to has been fixed at 6,01 - O/N to has been fixed at 5,975 - O/N to has been fixed at 6, O/N to 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, ,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 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

7 PART 2 Chapter 4 Spot Main/Sub : 1,7084 1/12/2014 PER Maturity Days T/N 3/12/ W 10/12/ /01/ /02/ /03/ /06/ /09/ /12/ 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, ,74 7,84 12,20 12, ,10 8,20 12,65 12, ,46 8,56 13,10 13, 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

8 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 ,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 ,00 Precise the exact amounts involved in this package if we do 1M Main currency

9 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 = $ / oz Forward gold price = $ / 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 = $ / oz Forward gold price = $ / oz (121 days) The USD Libor is 3,95 % (121 days) What is the gold lease rate (according to the usual market approximation)?

10 Day Finder Copy from 2012 Oct, 16

11 Chapter 5 EUR/USD 1,2691 PER Days EUR Mid % USD Mid % FX FwD ,00700% 0,15400% 1, ,04200% 0,19940% 1, ,08200% 0,23310% 1, ,11567% 0,26553% 1, ,14933% 0,29797% 1, ,18300% 0,33040% 1, ,20633% 0,37162% 1, ,22967% 0,41283% 1, ,25300% 0,45405% 1, ,28233% 0,49527% 1, ,31167% 0,53648% 1, ,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 ,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 ,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 ,00 EUR Strike 1,2857, premium = 2,51 cts / EUR What is position and at what break-even?

12 QUESTION 6 : DELTA HEDGING Still using our current data A trader is long of ,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 ,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

13 WEDNESDAY 3 DECEMBER MON TUE WED THU FRI SAT SUN JANUARY FEBRUARY MARCH MON TUE WED THU FRI SAT SUN MON TUE WED THU FRI SAT SUN MON TUE WED THU FRI SAT SUN APRIL MAY JUNE MON TUE WED THU FRI SAT SUN MON TUE WED THU FRI SAT SUN MON TUE WED THU FRI SAT SUN JULY AUGUST SEPTEMBER MON TUE WED THU FRI SAT SUN MON TUE WED THU FRI SAT SUN MON TUE WED THU FRI SAT SUN OCTOBER NOVEMBER DECEMBER MON TUE WED THU FRI SAT SUN MON TUE WED THU FRI SAT SUN MON TUE WED THU FRI SAT SUN

14 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, 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, , , , , ,510

15 (c) Ver CZK

16 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 * 5,125 * 366 / 365 = GBP nd flow of interest rate payment after 155 days (reimbursement of the nominal + residual interests): So the Interest calculation is : GBP * ( 1 + (5,125 * 155 / 365 ) ) = GBP spot 1 year ( 366 days ) Maturity ( 521 days ) 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/ /02/ /03/ /04/ /05/ /06/ /07/ /08/ /09/ /10/ /11/ /12/ SOLUTION 3 : CHANGES IN INTEREST CALCULATION METHODS From To Euro Days Bond Days Euro Rate Bond Rate Euro APR 5/01/ /05/ ,625 5,625 5,803 10/02/ /05/ ,591 2,563 2,653 27/03/ /05/ ,188 8,358 8,606 3/08/ /11/ ,081 13,313 13,875

17 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, Months rate approximation is = 2, ,0618 = 2,6243 From 275 days to 336 days we have 61 days Proporata is : 67,033% So 67,033% of 0,1875 = 0, Months rate approximation is = 2, ,1257 = 2, , , , ,7500 SOLUTION 5 : CASH POSITION The bank QPRFC borrows SEK at 2,5625 % The weight of the trade is * 2,5625 = (+ because the Bank borrowed) and after SEK at 2,75 % The weight of the trade is * 2,75 = (+ because the Bank borrowed) Finally the bank lends SEK at 2,6875 % The weight of the trade is * 2,6875 = (- because the Bank lent) Final position is the global weighted average Long of = The global weight = ( * 2,5625) + ( * 2,75) - ( * 2,6875) The global weight = SEK Final position is / 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 = * ( 1 - ( 2,75 % * 366 / 360 ) The issuance price = ,17 The amount of discount = Nominal - Issuance Price = ,83

18 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 ,00 * 5,375 % * 214 / 365 = GBP ,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 ,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 : = ,00 * ( 1 - ( 5,1 * 244 / (360*100) ) ) = ,33 Secondary discount amount : = ,00 * ( 1 - ( 5,14 * 183 / (360*100) ) ) = ,67 Yield during the holding period = (( ,67 / ,33) 1 ) * / 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 ) ) ,00 * ( 1 + (4,88 % * 182 /360 ) ) = ,89 We apply the new discounting yield to find the secondary market value : ,89 / ( 1 + (4,92 % * 120 /360 ) ) = ,76 Yield during the holding period = (( ,76 / ,00) 1 ) * / 62 = 4,725 % SOLUTION 7 : CD YIELD ACHIEVED Maturity amount : = ,00 * ( 1 + ( 5,4 * 183 / (365*100) ) ) = ,30 Secondary discount amount : = ,30 / ( 1 + ( 5,44 * 138 / (365*100) ) ) = ,39 Yield during the holding period = (( ,39 / ,00) 1 ) * / 45 = 5,1710 %

19 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 = / ( 1 + 7,125 % * 61 / 360 ) The issuance price = 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 = ,00 * ( 1 - ( 7,375 % * 152 / 360 ) ) The price = ,11 USD Euro CP is computed on present value basis (formula 2) The price = ,00 / ( 1 + (7,395 % * 152 / 360 ) ) The price = ,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 ,00 x 99,99 % = GBP ,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 ,00 x 2,125 % x 210 / 360 = GBP ,17. The full (dirty) value of the security is : , ,17 = GBP ,17. As the lender wants an initial margin of 3,00%., we compute : ,17/(1 + 3,00%. ) ARR Simulating a cash trade, the maturing amount of the repo must be : ,00 x ( 1 + (1,125 %. x 182 / 365 ) ) = GBP ,34 SOLUTION 11 CLASSIC REPO AND SELL&BUY BACK The clean amount is equal to the nominal of GBP ,00 x 94,52 % = GBP ,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 ,00 x 3,75 % x 210 / 360 = GBP ,00. The full (dirty) value of the security is : , ,00 = GBP ,00. Simulating a cash trade, the maturing amount of the repo must be : ,00 x ( 1 + (5,25 %. x 182 / 365 ) ) = GBP ,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 ,00 x 3,75 % x 30 / 360 = GBP ,00 If the lender keeps the full coupon during the remaining period, he will make interest on the recapitulazation ,00 x 5,25 % x 31 / 365 (from the 03/05/15 to the 03/06/15) = GBP ,16 The principal will be , , , ,16 = GBP ,79 Theoretical Forward Price = ,79 / ,00= 95,15990 %

20 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, 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, SOLUTION 3 : FRA SETTLEMENT As We bought a 9/12 FRA for USD 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 * ( 8,59-8,19 ) % * 91 / 360 on present value basis USD ,44 / ( 1 + ( 8,59% * 91 ) / 360 ) USD ,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 * 7,03 = USD * 7,05 = USD * 7,01 = Total Short of on a global weight of The average rate (short position) is / = 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 * ( 7,067 % - 6,97 % ) * 179 / 360 on present value basis USD ,11 / ( 1 + ( 6,97 % * 179 ) / 360 ) USD ,59

21 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, 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, 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, The cheapest solution is the Sol 2 with the rate of 7, %

22 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 ,00 SOLUTION 8 : IRS FLOWS Short position 1 Year means selling the fixed leg at 7,52 Value the we have 365 days in the year On the fixed leg, the bank will receive USD ,00 * 7,52 % * 365 / 360 = ,78 on the On the floating leg, the bank will pay USD ,00 * 6,43458 % * 90 / 360 = ,00 on the On the floating leg, the bank will pay USD ,00 * 7,03929 % * 92 / 360 = ,87 on the On the floating leg, the bank will pay USD ,00 * 7,71356 % * 92 / 360 = ,24 on the On the floating leg, the bank will pay USD ,00 * 8,19555 % * 91 / 360 = ,17 on the SOLUTION 9 : OIS SETTLEMENT Bank A wants to take the 1 week EONIA for EUR ,00 from bank B at 6,02 Bank A will have to pay as fixed interest amount at the maturity : ,00 * 6,02 % * 7 / 360 = EUR ,22 Against it, the Bank A will receive the accumulation of interest amount on rolling O/N : ,00 * ( 1 + ( 5,97 % * 1 / 360 ) ) = , ,33 * ( 1 + ( 6,01 % * 1 / 360 ) ) = , ,22 * ( 1 + ( 5,975 % * 3 / 360 ) ) = , ,51 * ( 1 + ( 6,0175 % * 1 / 360 ) ) = , ,18 * ( 1 + ( 6,005 % * 1 / 360 ) ) = ,06 Total Interest Amount accumulated is ,06 The balance is a loss of EUR -216,16 It represents in term of rate (in %) = (( ,06 / ,00 ) - 1 )* / 7 = 5,992 % The settlement date for an OIS is always after the maturity (for EONIA 1 day after) so on the

23 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 ,53-7,88 99, ,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, % 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, Maturing amount = ( ( 1 *( 1 + ZC R 2Y % ) ^ 2 ) = 1, ZC R 2Y = ( 1, ^ 0,5 ) - 1 ) *100 = 7, ZC R 2Y = 7, 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, ,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 ,06-14,21 100, ,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, % If we compound the 1 year with the 1 Ag 2 years, we will compute the maturing zc amount Maturing amount = ( ( 1 *( ,06 % ) * ( ,247 %) = 1, Maturing amount = ( ( 1 *( 1 + ZC R 2Y % ) ^ 2 ) = 1, ZC R 2Y = ( 1, ^ 0,5 ) - 1 ) *100 = 14, ZC R 2Y = 14, Per IRS (Bd B) Fw Fw ZCR 1 15,06 15,06 15, ,21 13,247 14,150 Note that the ZCR is under the IRS while the curve is positive

24 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/ /12/ ,6200 1,6200 DEC14 17/12/ /03/2015 2, ,1659 2,0943 MAR15 18/03/ /06/2015 2, ,2203 2,1591 JUN15 17/06/ /09/2015 2, ,4676 2,2661 SEP15 16/09/ /12/2015 2, ,7692 2,3993 Then we calculate the broken dates for the maturities of the deposit fixed dates DEC14 17/12/ ,6200 1, /01/ calc 1, /02/ calc 1, /03/ calc 2,016 MAR15 18/03/ ,0943 2, /04/ calc 2, /05/ calc 2, /06/ calc 2,149 JUN15 17/06/ ,1591 2, /07/ calc 2, /08/ calc 2, /09/ calc 2,251 SEP15 16/09/ ,2661 2, /10/ calc 2, /11/ calc 2, /12/ calc 2,380 DEC15 16/12/ ,3993 2,399 Now we just have to calculate the forward forward 3 2, , , ,380 3/9 2, /12 2,

25 PART 2 Chapter 4 SOLUTION 1 : SPOT POSITION We compute the weighted average position , , , , , , , , ,00 The bank has a long position of CHF Average rate : / 140 = 115, 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, * 109,612 The RIGHT cross price CAD/JPY : 0, * 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, 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, to 0, Fx Fwd Points are : Left : 0, , Fx Fwd Points are : Right : 0, , Fx Fwd Points are : -14,92 to -5,81

26 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, * 109,612 Cross price SPOT CAD/JPY = 95, 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, * 109,702 The RIGHT cross price CAD/JPY : 0, * 109,752 Cross price FWD CAD/JPY : 95, to 95, Fx Fwd Points are : Left : 95, , Fx Fwd Points are : Right : 95, , Fx Fwd Points are : 23,65 to 32,18 SOLUTION 6 : FORWARD BROKEN DATE CALCULATION spot 1, Fx Outright , ,70% 243,0 1, ,39% 305,0 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, 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, ,7084 ASK Sub after 90 days will be = 1 + ( 11,85 * 90 / (365 * 100 ) = 1, Left Fx Fwd = Sub Fwd Amount BID / Main Fwd Amount ASK Left Fx Fwd = 1, / 1,0187 = 1, Right Fx Fwd = Sub Fwd Amount ASK / Main Fwd Amount BID Right Fx Fwd = 1, / 1,01845 = 1, 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 for a nominal of Main 2 open days before the , 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) = x ( 1,7242-1,7262 ) = ,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) = x ( 1,7272-1,7262 ) = ,00 Sub

27 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 : *( 1 + ( 12,75% * 274 / 365 ) = ,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 ,29 Sub at 1, (( +531 )/ ) So I'll buy ,29 / 1,7615 = ,81 Main Using my Spot Price (first leg of my FX Swap Trade), selling my Sub, I bought the main amount of : / 1,7084 = ,11 Main The yield of our Main long position is :((Final Amount / Initial Amount) -1)*(Basis* 100) / days = (( ,81 / ,11) -1)*( 360 * 100 )/ 274= 8, ,00 1, ,11 12,750 % pts 8,2356 % ,29 1, ,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 : *( 1 + ( 7,14% * 33 / 360 ) = ,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 ,00 Main at 1, (( +64,6 )/ ) So I'll sell ,00 * 1,71486 = ,59 Sub Using my Spot Price (first leg of my FX Swap Trade), buying my Main I sold the sub amount of : * 1,7084 = ,00 Sub The yield of our Sub short position is :((Final Amount / Initial Amount) -1)*(Basis* 100) / days = (( ,59 / ,00) -1)*( 365 * 100 )/ 33= 11, ,00 1, ,00 7,140 % + 64,6 pts 11,4489 % ,00 1, ,59

28 SOLUTION 10 : FORWARD/FORWARD CALCULATION ON FX SWAPS The spot Price is 1,7084 The 3 months ASK FX Forward is : 1,7262 (1, (178 / ) ) The 3 months ASK FX Forward is : 1,7265 (1, (181 / ) ) The 6 months ASK FX Forward is : 1,7444 (1, (360 / ) ) The 6 months ASK FX Forward is : 1,7449 (1, (365 / ) ) The 12 months ASK FX Forward is : 1,7802 (1, (718 / ) ) The 12 months ASK FX Forward is : 1,7811 (1, (727 / ) ) 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, (1,982 /10.000) to 1, (1,977 /10.000) 1, to 1, TOMORROW 1, , T/N 1,977 1, 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 = (( ) / 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 = (( ) / 1440) * (360 / 121) = -2,0661 % Then doing the LIBOR GOFO (Deport), we obtain : Lease rate = 3, ,0661 = 6,0161 %

29 Chapter 5 SOLUTION 1 : CALL / PUT PARITY Call = Put + ( Fx FWD STRIKE ) / (1 +( (Sub IR % * Days /360 ))) Call = 0, ( 1,2699-1,2789 ) / (1 +( (0, % * 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, ( 1,2618-1,27175 ) / (1 +( (0, % * 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 ,00 EUR Price = 1,43 cts / EUR Premium cost = ,00 * 0,0143 = ,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 ,00 * 0,033 = ,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 ,00 * 0,0010 = ,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 ,00 * 0,0251 = ,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 ,00 * 0,0020 = ,00 USD

30 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 = ,00 / 0,5 = ,00 EUR Development : FX Forward LG FX Fwd Put Prem P&L Put 1, , , , , , 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 ,00 * 0,62 = ,00 Illustration : First we need to know the price of the CALL Call = Put + ( Fx FWD STRIKE ) / (1 +( (Sub IR % * Days /360 ))) Call = 0, ( 1, ,2521 ) / (1 +( (0,5777 % * 365 / 360 ))) Call = 0,0314 Development : FX Forward Call Prem P&L Put LG FX Fwd 1, , , , , , 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, ,0175 0,035 0,0175 1, ,0175 0, , , ,0175 0, , ,0175 0, , , , ,0175 1, , , ,0175 1, ,0175-0,0175 1, , , ,0175 1, ,0175-0,035-0,0175

31 Graphically 0,04 0,03 0,02 Long Call Sh FX Fwd Synthetic 0,01 0-0,01 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, ,0117-0,0234-0,0117 1, , , ,0117 1, ,0117-0,0117 1, , , ,0117 1, , ,0117 1, ,0117 0, , , ,0117 0, , ,0117 0, , , ,0117 0,0234 0,0117 0,03 0,02 0,01 Long Put Lg FX Fwd Synthetic 0 1, , , , ,2697 1,2756 1,2814 1,2873 1,2931-0,01-0,02-0,03

32 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 0,0081 1, , ,0081 0, , , , , , ,0081 0, , , ,0162 0,02015

33 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, ,0206 0,0412 0,0206 1, ,0206 0,0206 0,0000 1, ,0206 0,0000-0,0206 1, ,0206-0,0180-0,0386 1, ,0000-0,0180-0,0180 1, ,0180-0,0180 0,0000 1, ,0386-0,0180 0,0206 0, , ,03000 Lg Call ATM Lg Put ATM Synthetic 0, , , , , , , ,05000