CHAPTER 7 FUTURES AND OPTIONS ON FOREIGN EXCHANGESUGGESTED ANSWERS AND SCX.UTIONS TO END-OF-CIIAPTERQUESTIONS AND PROBLEMSQUESTIONS1 ・ Expl ain the basi c dificrcnces between the operation of a ciurcncy ibrward market and a fiitures market. Answer: Tlie forward mark巩is an OTC market where the forward contract for purchase or sale of foreign currency is tailor-made between the client and its international bank・ No money cliangess hands miti l tlie maturity d^:e of the contract when deliveiy and receipt are typically made. A fijtiues contract is ail exchaiige-tiaded instniment with standaidized featuies specifying contiact size and deliveiy date. Futiues coohacts aie m aiked-to-iiiarket daily to reflect chaiig es in tlie settlement pii ce. Delivery i s seldom made in a futures market. Rather a l^versi ng trade is made to close out a long or short position.2.In order for a derivatives market to fimetion most cfFio cntly, two types of economic agetits are needed: hedgers atid speculdtors・ Explain・Answer: Two types of niarket paiticipants arc ncccssaiy for the 巴尸五ci ent operat on of a derivatives market：speculators and hedgers. A speculator attempts to profit fiom a ijiange in the futures price・ To do this, the speculator wi 11 take a long or sliort position iti a futures contract depending upon his expectations of iuture price movern ent. A hedger, on- tlie-otlier- han d, desir es to avoid price var iation by locking in a purchase pri ce of die wide dying asset thiougli a long position in a liitures ccutract ci a sales price through a short positi on. hi effect, the hedger passes off the iisk of price vai iation to the speculator who is better able, or al I ea?t more willing, to bear this risk.3.Wliy are most fiitiu es positions cl os ed out th rough a reversing trade rath er than held to deliveiy? Answer: In forward markets，approximately 90 percent of all cont「勺cts that 前e initially establishucl result in the short making deliveiy to the long of the asset underlying the contract. This is natural because tlie term s of forward contracts ai e tailor — ni ade between th c long and s hort ・ By contrast, only about one percent of CIUTCIICV fiitiwcs cotit roots result in del i very ・ While futures contracts arc useful for speculation and hedging, their standardized delivery dates make them unlikely to correspond to the actual future dates wiicti forogii cxdiange transactions will occur. Tlius, they are genet'al closed out in arcs z ei^ing trade. In fact, the commission that buyers mid sell ers pay to transact hi the futures maket is s singl c amount that covei^ the round-trip tiTais actio ns of initiating and closing out the position・4.How can the FX firtut es maiket be used for pH cc discovery?Answer: To the extent tliat FX forward pri oes are ail unbiased predictor of fiiture spot exchange rates, tlie market anticipates whether one cuiyenoy will appreciate or depreciate versus another・ Because FX Eitiires conti-acts trade in an expi ration cycle, cliflerent c onto acts expire at diHeient peiiDclic dates into tlie iiiture ・Tlie patteiri of the prices of these contacts provides information as to tlie mai kefs ciin ent belief about th巴rd ative fiiture value of one ciui ency versus anothei at the scheduled expiration dates of the contracts. One will genially see a steadily appreci ating or depreciating pattern; howevei; it may be mixed at times. TTius, the fiitures market is usefill for price dscovery. i.e., obtaining the market's forecast of the spot exchange rate at different future：d“tES・5・ What is tlie major di fFerenoe in the obligation of one with a long positi on in a fijturcs (or fonvaid) contract in comparison to an options confraot?Answer: A futures (or forwaid) contract is a vehicle for buying or sei ing a staled amount of foreign exchange at a stated price per unit at a specified time in tlie fiitiue・ If the long holds the contract to the delivery date, he pays tlie effective contractual fiitures (or foiwat'd) price, regardless; of whether i t is an advantageous pti ce in oompaiiscn to tlie spot price at the delkeiy date. By oontiasf, ail option is a contiact giving the loris tlie riglit to buy ci sell a given quantity of an asset at a specified price at some time in the fiihn e? but not enforcing any obligation on him if the spot pti ce is more favorable tliaii the exercise prize. Because th巴opti on ownei* does not have to exercise t he option if it i s to his disadvaiit^e, the option has a price, or premium, whereas no price is p已id at inception to enter into a futures (orforward) contract6. Wliat is nieait by the terminology that an option is in-, at-, or oiit・of— the-money?Answer： A call (put.) option with St >E (E> S^) is refetred to as trading in-thc-monej r・ If E tlie option is hading at-tlic-money. If Sf< E (E<§) the call (put) option is trading out-ofithe- JYiOYie^ ・7 List the arguments (variables) of which an FX call or put oj^tion model price is a function ・ How does tiic call and put preininm change with respect to s change in the ai'guments?Answer: Botii call mid put options are fiinctions of only six variables：£, E, r讣讣 T an de When all else remains tlic same、the price of aEuicpcaii FX call (put) option w 11 incressc:1・ tlic lai'gei'(smaller) isS,2. the small曰(larged is E、3・ tlie smaller (larger) is r n4・ tlie i aiger (smalleij is r t>5.the laiger (smaller) is relative to r f, arid6.the gj eater is aWhen and are not too niucli different in size, a European FX call and put will increase in price when the option term-to-matiirity increases・ Howe、曰；when 飞 is very mu ch laigei than a European FX cal I will increase in price, but the put premium wil I decrease, whe厂i the option tenn-to-m increascs. The opposite i s tme when i s vety much greater than r$. ForAmerican 二X opti oils tlic analysis is I傑s complicated Since a longer tenn American option can be exercised on any date that a shorter tenn opti on can be exercised or □ some later date, it follows tliat tlie all else remaining the sarne. tlie longer tenn Americen opti on will sell at a price at least as laige as tlie shorter tenn option.PROBLEMS1. Assiunc toda>r，s settlement price on a CME EUR futures contract is S1.314O/EUR. Yon have a short position in one contract. Your performaiicc bond accoimt ciurcntly has a balance of $L 700. The next tlii'cc days, scttleincnt prices ETC $1.3126, $1.3133, arid S1.3049. Calculate the changes in tlic perfonnaiicc bond account from d已ily marking-to-market andthe balance of tlie perfotTnance bond accoiuit after the third day. Solution: $1, 700 +[〔$1.314 O・ S1.3126) + ($1.3126 -Si. 3133)+ (Sl.3133 - SI.3049)]XEUR125,000= $2,837.50,where EUR125, 000 is the contractual size of one EUR contract.2- Do problem 1 again assuming you have a long position in the futures conti act・Solution： $1,700+ [($1.3126 ・ $1.3140)+($ 1 ・ 31 33 ・S1・3126)十($L3(Mg • $1 .3133)] xEUR125,0OO= $562.50,where EUR125, OOO istlie contrachial sizeuf one EUR contract.With only $562・ 50 in your petfonnancc bond account, you would experience a tnargiti call requesting that additional fijnds be added to youipeiionnance bond account to bring tlic balance back up to tlie initial petdonnaiice bond level・3・ Using the quotations in Exlubit 7.3、cal cul ate the face value of the open interest in the June 2005 Swiss franc fiitures contiact ・Solution： 2401 contracts x SF125Q00 二SF262, 625JD00.vvhei'e SF125, 0C0 is tlie couti actnal size of one SF contract ・ing tlie quotations in Exliibit 7. 3, note that the June 2005 Mexican peso Mur es contract has a price of SO. 08845. You believe tlie spot piice in June wil be $ 0. 09500. WhM speculative position would you enter into to attempt to profit frotn your beliefs ? Calculate your anticipated profits, assuming you taP；e aposition in tlwee contracts ・ Wliat is the size of your profit (loss) if the fhtures price is indeed an unbiased predictor of the fiitii re spot price and this price materializes?Solution： If you expect the Mexi can peso to li se from SO.08845 to SO. 09500, you would take a long position in fiitiucs since the fiitiires price of $ 0.08845 is less than your expected spot price.Your anticipated profit from a I ong position in tiirec contracts is: 3 x ($0.09 500 -$0・ 08845)xMP500.0C'0= $9, 825.00. where MP500.00C1 isthe contractual size of one MP contrast.If the fiitures price is sn unbiased predictor of the expected spot price, the expected spot price is tlic iutca cs price of $0.08845///MP・ If tliis spot price materializes, you will not hsrs r e any profits or losses from your short position in three futures contracts: 3 x ($O・ 08845 -$0.08845) XMP500.000 =0.5.Do problem 4 again assuming you believe the Jiuie 2005 spot price will be $0.08500. Solution: If you expect tlie Mexi can psso to depieci ate fi-oni $ 0.08&15 to $ 0.07500, you wou d take a short position in fiitures since the futures price of $0.08845 is greater tliaii your expected spot price・Yciu anticipated p io fit from a sh or t pos ition in three contract s is： 3 x i, $ 0 ・ 08845 ・ $0.07500) xXlP500,000= $20,175.00 ・If tlie fiitiues price is an unbiased predictor of the Future spot price and this price materializes? you will not profit or lose from your long futwes pzisiti on.6.George Johnson is considering a possible ax-motith SI 00 million LJBClR-bascd, floating-ratebank loan to Hind a project 址terms shown in the tabic below. Johnson fears a possible ti ss in the LIBOR rate by December mid wants to use the December Eurodollar fiitures contrast to hedge thi s risk・ Tlie contract expires December 20< 1999. has a US$ 1 mi Ilion contract size,and a discount yield of 7. 3 pei cent・Joints on will ignore the cash flow implications of marking to market、i nitial margin requirements, and any timing niisinatch between ex change-ti'aded fiitures contiact cash flows and tlie interest payments due in March. Loan TermsaLoan First loan payment (9%) Second paynie nto initiated and fiitures contract expires and principal•••5 9/20/99 町2/20/933/20/00a・ Fonnulatc Jolmsotrs September 20 floating-to-f xed-ratc sti ategy using the Eurodollai futui c contracts discussed in tlie text above. Showthat tliis strategy would result in a fixed-rate Icaih assiuning ail increase in tlieLIBOR rate to 7・ 8 percent by December20, which remains at 7.8 peicent tbrougli March 2O・ Show all calculations.Johnson is considering s 1 2 — moutli loan as aii alternatiue・Ihi $ approach wi II result in two additional unceilain cash flows, as follows:I.oaricFii sbSecond Tliii(UFoin1li pa^nnento initiated payment (9%) s>payin ent payment a and principal9/20/99 12/20/99 码/20/00 6/20/009/20/00b. Describe tlie strip hedge that Johnson could use and explain how it liedges the 12-month loan (spec 迅'number of contracts). No calculatious are needed.CFA Guidel ine Answer孔Tlie basis point value (BPV) of a Eiu odollai' fiihu es cxDiiti act can be found by substituting the contract specifications into the following money m aiket relationship：a BPV FUI = Ciiange in Value = (face value) x (days to maturity / 360)x (change in yield)a q尸$(1 milion) x (90 / 360)x (.0001 )$25Tlie nimibcr of contract, N. can be found by:N = (BPV spot) / (BPV fiitiires)x($2,500)/($25)3 = 100aORo N = (value of spot position) f (face value of each Futures contract)尸($ 100 million) / (SI million)a =1CO(value of spot position) / (value of iutiucs position)b □ S(1 OO, 000, 000) / ($ 981,750)where value of fiitiires position = $1,000,000 x [1-(0.073/4)]« 102 contractsTlicreforc on September 20, Johnson would sell ICO (or 102) December Eurodollar futures contracts at the 7.3 percent yield. The imp： iedL1BOR rate in December is 7・3 percent as indicated by the December Eiuofiitiu'es discount yield of 7.3 percent・ fhus a boniowing rate of 9・3 percent (7.3 percent + 200 basis points) can be locked in if tlie hedge is cciTcctly implemented.A rise in the rate to 7.8 percent represents a 50 basis point (bp) increase over tlie implied LIBOR rate. For s 50 basis point increase in LIBOR, the cash flow on the short futures position is:o = ($25 per basis point per contract) x 50 bp x 100 contractsx$125,000.However, the cash flow on die floating rate liabi lity is:x -0.098x ($100,000,000/4)=・ S2,45O, 000.Combining the cash flow fiom tlie hedge with the cash flcwfi-om the loan results in a net outflow of S2?325,GOO, which translates into an annual rate of 9.3 percent：=($2,325,000x4) / $100,000,030 = 0.093This is precisely the implied bor rowii^ rate that Johnson locked in on September 2(). Regardless of the LIBOR rate on December 20. the net outflow will be $ 2,325,000, which translates into ail annualized rate of 9.3 percent. Consequently, tlie floating rate liability 1ms been converted to a fixed rate liabil ity i n the sense tliat tlie interest rate imcertaintv associated with tlie March 20 payine nt (using tlie December 20 contiact) has been removed as of Sepzember 20・ b・【1】a strip hedge, Johnson would sell 100 December futiues (for the March payment), 100 March fiitiires (lor the June payment)、and 100 June firtiu'es (for the September payment)・ The objective is to hedge each interest rate psynient sepaiately using tlie appropriate muiiber of contiacts. The probl em is the same as in Pai! A except here tlii ee cash flows sie subject to rising rat es and a strip of fiitu res is used to hedge this interest rate risk. Tliis pi obi em is simplified somewhat because the cash flow mismatch behveen the fiitiires and the loan payment is ignored ・ Therefore, in ord er to hedge each cash flow, Johnson simply sells 100 contracts far each payment・The strip hedge traiisfbrrns the floating rate loan into a strip of fixed rWc payments・As was done in Part A、the f xed rates are found by adding 200 basis points to tlie imp I icd Foiwar d LIBOR rate indicated by tile dis count yield of the tlirce diiFcrcnt Eiu^odollar fiitiires contracts・ Tlic fixed pajments will be equal wlicn the LIBOR temi structure is flat for the first year ・7.Jacob Bower has a liability that:•has a pnncipal balance of S1 DO million on June 30,1998,•accrues interest quarterly stalling on June 30. 1998.•pf^s interest quarterly、•has a one-yeai' tenn to maturity, end•calculates interest due based on 90-day LIBOR (die London Intel bank Offeredo Rate.)Bower wishes to hedge hi s remaining i nterest payments against changes in interest rates・Bower has coircctly cal cul ated that he needs to sell (short) 300 Eurodollar fhturcs contracts to accomplish the hedge ・ He is considei*ing the altemative hedging strategies out I inedin the following table.Initial Position(6/30/98) in90 Day LlBOR Eurodollai- Contracts曰Explanwhy strategy B is a more effective hedge than strategy A when the yield curve undergoes em instant aiieous iionparallel shift.b・ Discuss ail interest rate scenario in which strategy A would be superior to strates^/ B・CFA Guide! ine Answei*a.^Strategy, B's SuperiorityStrategy B is a strip hedge that is constructed by selling (shoiiiiig) 1 OO Bjtures contracts m aturiiig in each of the next three quailers. With tlie strip liedge in place, each qiiaiter of the coming year is hedged against shifts in interest rates for th at qnailei*. The r eason Strategy B will be a more effective hedge than Strategy A for Jacob Bower is that Strategy B is likely to work well whether a parallel shift or a nonpai'allcl shift occurs over th ㊁onc-yeat' term of Bow er 7s liability. That is, regardless of what happens to the term structiwc, Strategy B structures the fiihires hedge sc that the rates reflected by the Einodollar fiihwcs cash price match the applicable fates forthe undciiying liability-tlic 90day LIBOR-based rate on Bower's liability. The same is net true forStrategy A. Because Jacob Bowers liability cemcs a floating interest rate that resets quaitcrly ・ he needs a sti ategy that provides a series of th rec-month hedges ・ Strategy A will need to be re^triictm'ed when tlie three -montii September contract expires. In particular, if the yield curve twists upward (fijtures yields rise more for distant expirations than for neai' expirstious), Strategy A will produce iiife ioi hedge results・b. Scenaiio in Which Stiategy A is SuperiorStrategy A is a stack hedge stiategy that initially involves selling (sliortirig) 300 September contracts・ Strategy A is raiely better than Stiategy B as a hedging orrisk-nediiction strategy. Only from the perspecti ve of faxorable cnsh flows is Strategj r A better than Strategy B. Such cash flows occur only in certain interest rate scenarbs・For example Strategy A wil 1 work aswclI ss Strategy B for Bowct^s liability if interc^z rates (inst antatieously) change in parallel fashion. Another interest rate scenario where Sfratcgy A outpctioniis Strategy B is one in which tlie yield ciuve rises but witli ahvist so that futures yields rise more for neai' expi rations than for distant expirations. Upon expiration of the September co厂tract. Bower will have to rol 1 out his hedge by selling 200 December contracts to hedge the remaining interest payments. Tliis action will have the effect tliat tlie cash flow from Stiat 已gy A wi 11 be larger than the cash flow from Strategy B b©cause tlie appreciation ou the 300 slioi! September fiitures contracts will be larger tliaii the cumulative appreciation in the 300 contracts shorted in Strategy B (i.e., 100 Septem ber, 100 Deceinber, and 100 Mauch). Consequently, the cash flow fi-oni Strategy A will more thai offset the increase in the intei est payment on the liability, whereas the cash ilowfi-om Strategy B wil I exactly offset the increase in the interest payment on the I lability・e the quotations in Exliibit 7.7 to calcinate the intrinsic value and the time value of the 97 September Japanese yen Amet iceii call arid put options.Solution: Premium- Intrinsic Value = Time Value97 Sep Call 2.08 -Max [95.80 -97.00= - 1.20. o] =2.08 cents per 100 yen97Sep Put 2.47 - Ma>c[97.C0 - 95.80 =1. 20, 0] = 1.27 cents per 1 OOyen9.Assume spot Swiss franc is $ 0.7000 and the six-month fbrwaid rate is $0.6950. What is tlie minitnuni price that a six-month Ametican call option with a striking price of SO.6800 should sellFor in a rational market f Assume the aimualizcdsix-niontii Ewodollar rate is 3 % percent・ Solution:Note to Instnictor: A complete solution to this problem relies on the boiindaiy expressions presented in footnote 3 of the text 济Chapter 7.C a>Mzx[(70 — 68)、(6950 - 68)/(1.0175), O]>Zl4zx[ 2. 1.47. 0] = 2 cents10・ Do problem 9 again assimiing ail American put option instead of a call option・Solution：心必4(68 -70), (68-69. 50)/(1.0175), 0]-2, -1.47. 0] = 0 cents1 1 ・ Use tlie European option-pii ci ng models developed in tlie chapter to value the cal 1 of probl an 9 and tlie put of problem 1 0・ Assume the aimualized volatility of the Swiss fi*anc is 14.2 percent. This problem can be solved using tlie FXOPM.xJ s spreadsheet・Solution:^ = [/n(69.50/68)+.5(. 142)2(.50)]/(.142)心O=.2675<4= £・.142*50 =・ 2765 ・.1004 = .1671N(di) = .6055N(d^ =・ 5664M呦= .3945N(-d^) = .4336Q 二[69.50(.6055)・ 68(・5664)]e"3%j°)= 3.51 centsP. - [68(.4336)-69.50(. 3945张心珈刘=2.03 cents12. Use the binomial option-pricing model developed in the chapter to value the call of problem 9・ Tlie volatility of tlie Swissiiaiic is 14.2 percent・Solut ion: Tlie spot rate at T will be either 77.390 = 70・00c(l・ 1056) or 63.32 0 = 70.00^(.9045), where u = &*灼=1. 1056 and a? = 7血=・©045. At the exerci se price of E =6& the option wi II only be exercised at time T if the Swi ss franc appreciates; its exercise value would be C u f= 9.390 = 77.39^ - 68. If tlie Swiss franc depreciates it would not be rational to exercise the opti on ； its value woul cl be C dT = O.TVie hedge ratio is% = (9.39 一0)/(7739-63 J2)=・ 6674・Thus, the call premium is:=?k^{[69.50(.6674)-68((70/681 (. 6674 - 1)+])]/(1.0175), 70 -68}= Max[l. 64, 2] = 2 cctits per SF.国际财务管理课后习题答案chapter 711/11GMINI CASE ： THE OPTIONS SPECULATORA speciil at or is ccnsid ering the purchase of five three - month Japanese yen call options with a strikingprice of 96 cents per 100 yeti. Tlie premium is 1.35 cents per 100 yen ・ Tlie spot price is 95.28 cents per 100 yen and tlie 90・day forward rate is 95.71 cents. The speculator believes tlie yen will ^Jpreciate to $ 1.00 per 1 00 yen ovei the next du es months. As tlie speculator's assistant, you liavebeen asked to prepare the following ：1 ・ Graph the call option cash flow schedule.2. Det 已 rmine the speculator's profit if the yen appreciates to $1. 00/100 yen.3. Det 曰 Triine the speculators profit if the yen only appreciates to the fonvaid rate.4. Determine the fiitiu c spot price at which the speculator will only break wen.Suggested Solution to tlie Options Speculator:2. (5 x¥6,250000) x [(1 00 - 96)- 1. 35]/1 0000 = $&281・25・3. Sin c e the oprj on expi res out — of-the — money, the -s p ec u lator will let the opt ion expi leworthless ・ He uvill only lose tlie option pi emium ・4. = E +C=96 + 1.35 = 97.35 ceiitsper 100 yen.。
