cfa二級(jí)自編題150道衍生品

1、衍生品 EP 章節(jié)后題Reading 40 章節(jié)題題目I21802001Q1As the CSI 300 index will change the weights of the stockshe next year, Tiao,who is running an index fund, has to buy a large amount of stock A in 90 days. Inorder to hedge the riskt stock A will rise sharply, he enterso a longition in90-day forward contract on

2、the stock. It is knownt stock A will pay a 1 yuan and0.8 yuan per share dividend in 60 days and 180 days respectively. The stock price is currently at 50 yuan. The risk free rate is 3% and will not change. After 70 days, the stock is now trading at 55 yuan, what is the value of this forward contract

3、?A. 5.63670B. 5.7166C. 4.71575：B考點(diǎn)：指數(shù)遠(yuǎn)期合約價(jià)值計(jì)算：第一步，先求出分紅的現(xiàn)值。由于遠(yuǎn)期合約期限只有 90 天，所以 180天的分紅不用考慮，只需計(jì)算第 60 天的分紅現(xiàn)值：1PVD = .995261. 65第二步，計(jì)算 90 天期限的遠(yuǎn)期價(jià)格：FP = 5 .9952 1.9 65 = 9.6第三步，計(jì)算 70 天后多頭頭寸的價(jià)值：9.61.2 65V =55 = 5.7166I21802002(Q1 continued) Instead of buying forward, Tiao findst CSI futures are also題目Q2av

4、ailable which are now trading actively in CFFE. Supe Tiao bought two ninemonths IC futures at 3520. Two months passed, and the IC futures is now trading at 3450. No cash flow occurred during this period. What is the value of this IC futures after marking to market?A B C140700：C考點(diǎn)：指數(shù)合約價(jià)值計(jì)算實(shí)行結(jié)算制度。因此，I

5、C（滬深 300：注意，與遠(yuǎn)期不同，的。結(jié)算之后價(jià)值均為 0，故選 C，考生無(wú)需計(jì)算即縮寫）合I21802003When pricing a stock forward based on no arbitrage theory, which題目Q3of thefollowing changes will not decrease the forward price?A.B.C.A decrease An increasehe risk free rate.he stocks dividends.An adverse eventt causes the expected future stock

6、 price to fall.：C考點(diǎn)：遠(yuǎn)期合約定價(jià)的性質(zhì)：注意，無(wú)定價(jià)下對(duì)股價(jià)預(yù)期價(jià)格的變化是不會(huì)導(dǎo)致遠(yuǎn)期價(jià)格發(fā)生變化的，選 C。根據(jù)無(wú)定價(jià)公式，A 與 B 均會(huì)導(dǎo)致遠(yuǎn)期價(jià)格下降。I21802004A 9% Treasury bond is currently trading at 1035, and it will make a coupon題目Q4payment 55 days from now. Supe the annual risk free rate is 4.5%, what is theclosest price for a 150-day forward contract?

7、 A .1008.07B. 1008.38C. 1053.89：B考點(diǎn)：債券遠(yuǎn)期定價(jià)：本題較為簡(jiǎn)單，直接代公式即可。55 天后票息的現(xiàn)值為：1 92 = .755 651.5因此，150 天的理論遠(yuǎn)期價(jià)格應(yīng)為：1515 .7 1.565 = 1 . 題目Q5I21802005When valuing a shortition in a Euro bond forward, theyst neglectserests paid by underlying bond before expiration. Under this circumstan, thevalue of the shortiti

8、on will most likely:A.B.C.be undervalued by the future value of the be undervalued by the present value of the be overvalued by the present value of theerests. erests. erests.：B考點(diǎn)：債券遠(yuǎn)期合約的價(jià)值判斷：利息是標(biāo)的債券帶來(lái)的收益，在計(jì)算多頭遠(yuǎn)期價(jià)值時(shí)應(yīng)將收益現(xiàn)值扣除。然而，根據(jù)題設(shè)，分析師忘記將其扣除了，這會(huì)導(dǎo)致多頭價(jià)值被。多頭收益即意味著空頭損失，多頭價(jià)值被選 B。就意味著空頭價(jià)值被低估。因此這道題最終Readin

9、g 41 章節(jié)題I21802011題目Q1 John shorts 100,000 put options on Golden Education. Given the current delta of-0.45, the stock price has significantly increased by 20% because of an unexpecteditive information. How about the change of the value of Johns option exures?A.B.C.Largern 9%Equal to 9%Smaller：Cn 9%考

10、點(diǎn)：希臘字母 Gamma 的性質(zhì)：對(duì)于一個(gè)賣空的人，Gamma 是小于 0 的，根據(jù) 0.45 0.2=0.09 粗略估價(jià)格應(yīng)該變化 9%，但是由于價(jià)格變化幅度較大需要引入非線性修正計(jì)Gamma，又因?yàn)橘u空的 Gamma 小于 0，所以變化幅度是小于 9%。I21802012The stock price of Golden Education is currently $300. At each year, the price題目Q2can move up by 70% or move down by 3%. Given the current market risk-free rate o

11、f5%, which of the following priis the most approximaterinsic value of atwo-year American call option wi$350 exercise price based on the binomial treepricing m?A.B.C.$31.2458$32.1388$30.7083：A考點(diǎn)：二叉樹(shù)定價(jià)：根據(jù)公式計(jì)算得到如下參數(shù) = 1 = 1.5 .97 = .196 1.7 .97 = 5 = 517 = 5 = 1.7 = 5 = 1 1.5 = 5，= 176.6667 1 1.5 = 5 =

12、 15.12由于在期間節(jié)點(diǎn)，立可行權(quán)的價(jià)值均小于折現(xiàn)值所以均無(wú)需提前行權(quán) 1 C = 1.25 1.5I21802013The stock price of Sliver Forward is currently $15. At each year, the price can題目Q3move up by 7% or move down by 60%. Given the current market risk-free rate of 1%,which of the following pri American put option wiis the most approximayrinsi

13、c value of a two-year$9 exercise price based on the binomial tree pricingm A.B.C.?$0.4692$0.4722$0.4643：B考點(diǎn)：二叉樹(shù)定價(jià)：根據(jù)公式計(jì)算得到如下參數(shù)，需要特別注意在第一期判斷是否行權(quán)的時(shí)候，未來(lái)支付的折現(xiàn)值小于即刻行權(quán)的價(jià)值，如果忘記在第一期 down node 判斷是否可以提前行權(quán)，則會(huì)認(rèn)為此節(jié)點(diǎn)的價(jià)值為 2.9109，再進(jìn)行折現(xiàn)會(huì)錯(cuò)誤的選擇選項(xiàng) C。 = 1 = 1.1 . = .91 1.7 . = 9 = = 9 = 2.5 = 9 = 6.6 1 = 9 ，= .22 1.1 1

14、= 9 = 1.1P = 1 = .7221.1I21802014題目Q4Thelge, the FICC manager of Sliver Forward, decides to use anerest rateoption to hedge the portfolio exof the forward rate, she predicts anure of $75,000,000. According to her expecion erest rate binomial tree asfollowsShe also bevest the risk-neutral probability

15、 of up moving and down movingwould be the same. The current risk-free rate is 1%. How much should be paid for thebehavior of this hedging if she bought a European call option wi 4%?n exercise rate ofA.B.C.$2,513,462$2,614,422$2,325,000：B，需要注意的是對(duì)于利率考點(diǎn)：利率二叉樹(shù)定價(jià)： = .5并非使用無(wú)風(fēng)險(xiǎn)利率進(jìn)行折現(xiàn)。 = .1 . = .6= .= .2= .

16、 . = .6 . 1 1. = .6 1 = .2 1.6 1 C = .91.7V = C NP = .9 75 = 2 617 5題目Q5I21802015The stock price of Golden Education is currently $213.56. At each year, theprice can move up by 40% or move down by 2%. Given the current market risk-freerate of 3%, which of the following pri two-year European call opt

17、ion wiis the most approximaterinsic value of a$206 exercise price based on the binomial treepricing m?A.B.C.$20.7436$20.0414$20.6517：B考點(diǎn)：二叉樹(shù)定價(jià)：根據(jù)公式計(jì)算得到如下參數(shù)，需要特別注意在第一期判斷是否行權(quán)的時(shí)候，C。未來(lái)支付的折現(xiàn)值小于即可行權(quán)的價(jià)值，如果忘記判斷則會(huì)選擇 = 1 = 1. .9 = .119 1. .9 = 26 = 212.5776= 26 = 7. = 26 = 1 = = 9 .9 1. 1 = = 15.121. 1 C = 2.

18、11.5Reading 42章節(jié)題題目I218020211. An investor shorts a call option for $1.3 wistrike price of $25 and purchases astock for $23, what is theum profit and loss for thisition?TheTheTheum profit infinite and the um profit is $1.3 and the um profit is $3.3 and theum loss is $1.3 um loss is $23 um loss is $2

19、1.7：C考點(diǎn)：備兌認(rèn)購(gòu)：本題其實(shí)的計(jì)算covered call 策略，當(dāng)標(biāo)的資產(chǎn)價(jià)格上升時(shí)，買入的收益為 ST- S0=ST-23 而賣出看漲的損失為 X- ST +C=25-ST-1.3，因此 coveredcall 策略的最大收益為(ST- S0)+( X- ST +C)= X- S0+C= 25-23+1.3=3.3，最大損失為 S0-C0=23-1.3=21.7。I21802022題目2. A fund manager wants to establish Bear Call Spreosition based on his marketoutlook, he longs a cal

20、l option for $3 wistrike price of $65 and shorts another calloption for $5 wistrike price of $61. Ame the two options have the sameexpiration, the breakeven price is:A. $63B. $67C. $59：A考點(diǎn)：熊市價(jià)差：本題 策略的計(jì)算Bear Call Spread 策略， Bear Call Spread 盈虧平衡點(diǎn)為 XL+CL-CH=61+5-3=$63，首先基金經(jīng)理賣出執(zhí)行價(jià)格較低($61)的 call option

21、收益為-Max (0, ST - XL)+ CL，而買入執(zhí)行價(jià)格較低($65)的 call option 的收益為Max (0, ST - XH)- CH，因此總收益為 Max (0, ST - XH) - Max (0, ST - XL) - (CH - CL)盈虧平衡點(diǎn)為 XL + CL - CH=61+5-3=63。I21802023題目3. Wendy Wang, a portfolio manager, worries about the increasing volatilityheequity market, so she establishes a collar for his

22、 portfolio. Which sement is most appropriate for collar strategy？A collar strategy can be viewed as a combination of covered call and protective put.It is no costs to establish a collar strategy because the premium for purchasing the put option must be covered by the premium for selling the call opt

23、ion.The collar strategy has limited upside potential but unlimited downside potential.：A考點(diǎn)：衣領(lǐng)：策略的性質(zhì)collar 策略的以及風(fēng)險(xiǎn)敞口，在 collar 策略中持有標(biāo)的資產(chǎn)同時(shí)買入一個(gè) put option 再賣出一個(gè) call option，相當(dāng)于 covered call 和 protective put 的結(jié)合，因此選 A；在賣出 call option 時(shí)所獲得的收益不一定等同于 put option的付出,如果二者相等則成為 zero-cost collar，但只是一種特殊情況，故 B 錯(cuò)；最后 collar 的上行和下行的潛在收益都是有限的，故 C 錯(cuò)。題目4. AI21802024me a call option wistrike price of $40 is priced at $5 and a put option withthe same features costs $3. Using the options above, what is the profit for a straddle if the stock price at exp