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Unformatted text preview: .""'\__ 1]., Exam MFEESF Questions Chapter 9 — Parity and Either Option Relationships Chapter 9 — Questions Question 1 The price of a nondividendpaping stock is $512}. a. 8month American call option on the
stock 1with a strike price of $88 has a premium ot"$3.48. The continuously compounded interest rate is 8%. Calculate the premium for a 8month European put option on the stock with a strike price
of $58. A 8.98 E 1.59 C 2.49 D 3.48 ' E 4.4?
Question 2
The price of a stock is $51]. The stock pays a. dividend of $5 in 3 months. A 8month European put option on the stock has a strike price of $48 and a premium of
$4.88. The continuously compounded interest rate is 8%. Calculate the premium for a 8—month European call option on the stock with a strike price
of $48. 1*: 1.82 E 8.88 C 3.48 D 4.38 E 5.48 Question. 3 The price of a stock is PETS. The stock pays a dividend of $4 in 4 months and auother
dividend of $8 in ’1’ months. A 8month European put option on the stock has a strike price of $88 and a premium off
$18.37. The continuously compounded interest rate is 8'34. Calculate the premium for a 8mouth Europeau call option on the stock with a strike price
of $88. A 0.56 D 3.41 C 8.98 D 11.27 E 13.15 Question 4 The price of a stock is €75. The stock pays continuously compounded dividends at an
annual rate of 4%. it 1year European put option on the stock has a strike price of E88 and a premium of
£18.87. A 1year European call option on the stock has a atiike price of E88 and a premium of
€153. Calculate the continuously compounded risk—free interest rate on euros.
A 0.75% B 5.70% U 5.9 “it D 7.24% E 14.04% DﬂctuarialErewcom 2011]  Page QQl Question ii
The price of a stock is 2T5. The steel: pave a $4 dividend in E! months. A 6—month European put option on the stock has a strike price of PETE: and a premium of
$3.02.  The continuouslyT compounded interest rate is 2%. Calculate the premium fer a 6month American call option on the stock with a. strilre price
of 55TH. A {3.61:} E 4.35 C 6.63 D 10.43 E 12:?5 Question 5
Stock X pays a $3 dividend in 5 months. A 9month atthemonels,r European put option on Stoolr. H has a premium that is $1.34
higher than the premium for a IE‘l~month at—thesmonev European call option on Stock K. The continuoule compounded rialefree rate of return is Tit.
Calculate the price of Stock III.
A 33.44 B 32.25 C 45.25 D 49.32 E 32.34 Question T
Stock It pays a $3 dividend in 6 months. A Bvlnonth European put option on Stock K has a premium of $2.3D. A Elimonth
European call option on Steel: K has a premium of $3.25. Both options have a strike price
of $28. The continuously compounded risk—free rate of return is 9%. Determine the amount of cash that must he lent at the riskEros rate of return in order to
replicate the stock. A 23.31:} B 26.1? C 28.08 D 29.114 E 30.130 Question 3
The current price of Stock K is $.52. Stock It pays dividends at continuous rate of 7%. A 9month European put option on Stool: K has a premium of $3.61. A Qsmonth European call option on Stock X has a premium of $5.56. Both options hnve a strilte price
of $50. Calculate the cost of creating a conversion for a Thill that matures for $1,0DD in 9
months. 9. cases a 924.84 Io 924.11 D 92131 a seam IE] Act11aria1Erew.com 22110 Page 9.9—2 f3 Question 0 Stock A pays a dividend of $4 in 5 months. The current price of Stock A. is $52. din nmonth European put option on Stock A has a premium of $5.57. An emonth
European call option on Stock A has a premium of $5.01. Both options have a strike price
of $50. Determine the amount of cash that must he lent at the riskvfree rate of return in order to
replicate the stock. A $9.55 B 50.00 C 51.?0 D 52.00 E 54.14 Question 10
The current exchange rate is 0.05 euros per dollar. The riskfree continuously compounded interest. rate for dollars is 5%. The riskfree
continuously compounded interest rate for euros is 4%. A dollardenomiuated European put option on one euro has a strike price of $0.04. The
dollardenominated European put option expires in 1 pear and has a premium of $0.005. Calculate the value of a dollardenominated European call option on one euro that has a
strike price of $0.04 and expires in 1 year. A $0.004 l3 $0.042 C $0.053 D $0.111 E $0.121 Question 11
The current exchange rate is $0.50 per Swiss franc. The riskvfree continuously compounded interest rate for dollars is 4%. The riskfree
continuously compouuded interest rate for francs is are A fi'uncsdenominated European call option on one dollar has a strike price of 1.15 francs. The francdenominated European call option expires in 1 pear and has a premium of
0.127 francs. Calculate the Twins ofa francdenominated European put option on one dollar that has a
strike price of 1.15 francs and expires in 1 year. A $0.00? B $0.000 C $0.011 D $0.055 E $0.552 Question 12
A South African rand is worth 200 Iraqi diners.
The continuously compounded riskfree rate of return on the rand is 0%. A dinarrdenominated European call option on one rand has a premium of 13.57 djnara. A
dinerdenominated European put option on one rand has a premium of 1.2? diners. Both
the call and the put option expire in 5 months and have a strike price of 105 diners. Calculate the contuiuousiy compounded riskfree rate of return on the diner.
A 0.05 B 0.00 C 0.10 D 0.23 E 0.28 E! Actuarielﬁrowrom 2010  Page {3103 Exam hﬂi‘Ei‘ﬂF Questions _ Chapter ‘3' — Parity and Other Option Relationships Question 13 a 15year hond pays 12% coupons at the end of each year. The par amount of the hond is
$1,UDD. The yield on the hond is equal to the continuously compounded riskﬁres rate of
return, which is 1U"/i. ' A lﬁnmonth ‘European call option on the hond has a strike price of $1,DDD and a premium
of$15U. Ealculote the value of a 15—month European put option on the hood with a strike price of
$1,DDU. A 31.54 E 53.88 E T104 D 141.03 E 149.134 Question 14 A 12~year hond pays semiannual coupons at an amino] rate of 9%. The par amount of
the hand is $1.3m. The yield on the bond is equal to the continuously compounded risk
free rate of return, which is 8%. ﬁne month after the hond is issued, a 1year put option ou the bond has a strike price of
$35!] and a premium of $25. Ealeulate the value of a 1year call option on the hood with a strike price of $3513, one
month after the hond is issued. a can a sale ' 0 mass D 132.44 E 13am Question 15 a iD—year hond pays semiaunual coupons at on annual rate of TEE. The par amount of
the hand is EELDDID. The price of the bond is equ s1 to its par amount. A lLitmonth call option on the hood has a premium that is $53.43 greater than the
premium for a 9—month put option on the bond. Both options have the same strike price. Calculate the strike price.
A 862.113 B 955.83 C 956.71 D 1,DZT.04 E LDTBET Question 16
Stock It pays a $3 dividend in 2 months. The current price of Stocit X is $50. Stock Y pays continuous dividends at an annual rate of 3%. The current price of Stock Y
is $51. A European option gives its owner the right to give up a share of Stock Y in exchange for
a share of Stock K at the end of 6 months. The premium for this option is $2.?D. The continnously compounded riskfree rate of return is 696. Calculate the value of a European option that gives its owner the right to give up a share
of Stock 15'. in exchange for a share of Stock Y at the end of E months. A 0.51 E 3.93 C 5.16 D 5.91 E 144 £1 Actuariallirewcom ZI‘JIU Page Q94 Exam bﬂ‘E‘EF Hues tious Chapter 9 — Parity and Either Option Relationships Question 17
Stock A has a current price of M9. Stock A does not pay dividends. Stock 13 has a current price of 559?. Steel: 13 pays continuous dividends at an annual rate
of 5%. It. European put option gives its owner the right to give up'a share of Stock E in exchange
for a share of Stock It. at the end of 1 year. The value of this option is $11.49. The continuously compounded riskFree rate of return is 14% Calculate the value of a European put option that gives its owner the right to give up a
share of Stock A in exchange for a share of Steel: 13 at the end of 1 year. Pl 5.22 E 11.99 C 11.99 D 14.97 E 1176 Question 19
The price of Stock X is $49.
Both Stock K sud Stool: Y pay dividends continnously at an annual rate of 4%. Option A gives its owner the right to exchange a share of Stock X for a share of Stock Y at
the end of 5 months. Dption E gives its owner the right to exchange a share of Stock Y for a share of Stock X at
the end of 5 months. The value of Dption A. is $1195 greater than the value of Option B.
Calculate the price of Stock Y. A 49.32 E 43.19 C 47.29 D 42.99 E 49.29 Question 19
The table below describes 4 stocks: A 1—year European call option gives its owner the right to obtain 1 share of Stock 151 and 2 shares of Slow]: B in exchange for 1 share of Steel: D and 1 share of Stock D. The value of
this call option is $19. Find the value of a 1—year European call option that gives its ovvner the light to obtain 1 share of Stock 9 and 1 share of Stock D in exchanga'for 1 share of Steeli A and 2 shares of
Stock 13. A 4.93 E 4.94 C 4.92 D 9.99 E 9.99 e Aemarial'ﬂrewpmu 2919 Page QHE Exam hIFEI'BF Questions _ Chapter 3 — Parity.r and Other Cption Relationships Question 20
The price of Stock K is $100. Stock K does not pa},r dividends. The price of Stock Y is 0100 Stock Y pays dividends continuously at an annual rate of
4%. An American option gives its owner the right to exchange a share of Stock Y for a share of
Stock X at any time during the next 'i' months. The value of this American option is
$10.22. Calculate the value of a European option that gives its owner the right to exchange a
share of Stock K for a share of Stock '1' at the end of T months. A 030 B T01 C 3.5? D 12.53 E 13.53 q. Question 21
The current exchange rate is $1.20 per euro. A European dollardenominated euro call has a strike price of 01.213 and a premium of
$0033. The call expires in 3 months. The continuouslyr compounded dollardenominated interest rate is Tit. The continuously
compounded euro—denominated interest rate is 5%. Calculate the value of a European euro—denominated dollar put that has a strike price of
€0.30 and expires in 0 months. A. E0055 E E0030 C €01.00 I] E0120 E E0125 Qu estion 22
The current exchange rate is €0.35 per dollar. A European euro—denominated dollar call has a strike price of €030 and a premium of
E00333. The call expires in 0 months. Calculate the value of c European dollardenominated euro put that has a strike price of
$1.25 and expires in 0 months. A 3003205 E 000345 C $00354 D $01123 E $01321 Question 23
The ClL'L'l'EﬂI: exchange rate is 1.05 Swiss ﬁraocs per euro. A European francdenominated put on one euro has a strike price of 1.0 trance and a
premium of 00313 francs. The put expires in 1 pear. Calculate the value of a European euro—dc nominated call ou one franc that has a strike
price of 0.025 euros and expires in 1 year. A €002.42 B E00343 C £00574 D E00330 E E0034? IE] actuarieJBrewrom 2010 Page 0100 Exam l'riFEu'BF Questions Chapter 9 — ParityT and Clthar Option Relationships Question 2.4
The current exchange rate is [3.42 British pounds per Australian dollar. 5. Enropean ponndndenominated put on one o‘iustralisn dollar has a strilce price of 0.4
pounds and a premium of 3.13133 pounds. The put expires in 1 veer. The eontinuonsly compounded interest rate. available on British pounds is 3%. The
continuously compounded interest rate available on Australian dollars is “ii/n. Calculate the value of a European ﬁustralian dollardenominated put on one British
pound that has a strike price of 2.5 Ans‘tralian dollars and expires in 1 year. The answer
choices halos.T are denominated in australian dollars. A 0.0356 E ﬂﬂ’lBZ C 113349 D [3.2123 E 1.1863 QUESHDH 25
The current exchange rate is [3.7 euros per Canadian dollar. A Enropean eurodenominated call on one Canadian dollar has a strike price of 0.625
euros and a premium of DDS euros. The call expires in 6 months. The continuously compounded interest rate available on nurse is 8%. The continuously
nompounded interest rate available on Canadian dollars is T%. Calculate the value of a Enropean Canadian dollardenominated call on one euro that has
a strike price of 1.6 Canadian dollars and expires in 6 months. 151 Eﬂﬂﬂdﬂ B €D.DDTB C Eﬂﬂlﬁd D €3,131:er E EELDEEU QIIEStiOn 26 The premium of a ICUstrike pandenominated put on the euro is ¥1.53. The put expires
in Tpears and is a European option. The current exchange rate is 111] EHE. Calculate the premium of lIIIIJIIIIlstrilca enro—denominated van call that expires in T years
and is a European option. A Eﬂﬂﬂﬂldl B €D.Dl}ﬂ144 C Eﬂﬂﬂﬁlﬁﬂ D Ellllﬂﬂl'ldr E Eﬂﬂﬁﬂdﬂ4 lQuestion 2'? The price of a 6—month dollardenominated call option on the sure with a $0.59 strike is
550.1347. The price of an otherwise equivalent put option is $ﬂ.l}11. The annual continuouslyr compounded dollar interest rate is 5%.
The annual continuously compounded euro interest rate is 3.5%. Calculate the spot exchange rate. _
A $43.332JE B $0.934IE C $0.92DIIE D $13.542J'E E $43.94WE ﬁActuarialﬂremoom sale Page 9.9? KN :‘T‘w Exam MFEIEF Questions Ghapter 9 — Parity and Other Dption Relationships Question 35 rI‘aro European put options expire in 1 year. The put options have the same underlying
asset, but they have different strike prices and premiums. A E Premium 4.01:} 8.7’5 The continuously compounded riskfree rate of return is 9%.
A profitm arimieing,r arbitrageur constructs an arbitrage strategy.
Arbitrage proﬁts are accumulated at the risk—free rate of return. If the stock price is $43 at the eud of the year, then the accumulated arbitrage profits are
SK. If the stock price is $52 at the end of the year, then the accumulated arbitrage proﬁts are
HEY. Calculate the ratio of X to Y.
A EIL'DQ E 13.53 C 1.130 I} 1.24 E 2.3? Question 35 Three European put options expire in 1 year. The put options have the same underlying
asset, but they have different strike prices and premiums. —E c The continuously compounded riskfree rate of return is 11%. A proﬁtmaximising erbitrageur constructs an arbitrage strategy.
Arbitrage profits are accumulated at the risk—free rate of return. If the stock price is $52 at the and of the year, then the accumulated arbitrage proﬁts are
H. If the stock price is $812} at the end of the year, then the accumulated arbitrage profits are
$Y. ' Calculate the ratio ofX to Y. H
A [1.42 E 1.30 C 1.74 D 2.4“}  E 3.69 '5'! ActuarialBrewmom 2010 Page QQll Exam treats]? euaaasng _ _ ' Chapter 9 — Parity and Other Option Relationships Question 3 'i' Three European call options expire in 1 year. The call options have the same underlying
asset, hut they have different strike prices and premiums. a B lace ass 4.25 The continuously compounded riskfree rate of return is THE. A profit—maximising arbitragenr constructs an arbitrage strategy.
Arbitrage profits are accumulated at the riskvfree rate of return. If, the stool.1: price is $52 at the end of the year, then the accumulated arbitrage profits are H. If the stock price is $60 at the end of the year, then the accumulated arbitrage proﬁts ara
$Y. Calculate the ratio of X to Y. a oao B are c ass _ D 11cc E 32.7? Question 33 Three European put options expire in ‘3 months. The put options have the same
underlying asset, but the}.r have different strike prices and premiums. Put Uption Premium Determiue which of the following strategies results in arbitrage proﬁts.
A Call Bnll Spread E Call Bear Spread 0 Put Bull Spread D Put Bear Spread E Asymmetric Butterﬂy spread _ ‘U ActuarialBrewemn 2010 Page CHE—12 Exam MFEIHF Questions Chapter Fl — Parity and Other ID'ption Relationships Question 35' Three European call options expire in 1 year. The call options have the same underlying
stock, but they have different strike prices and premiums. The continuously compounded riskfree rate of return is 11%.
a proﬁtmaximising arhitrageur constmcts an arbitrage strategy. Determine which of the following year—end prices for the underlying stock results in the
highest arhitrage proﬁts. 1‘5. $45 13 5545 U $50 D $52 E $55 Qu estion 4] The bid and ask prices for a stock. a European call option on the stock, and a European
put option on the stock are listed in the table below. The strike price for both options is
$95, and they both expire in 1 year. The stock does not pay dividends. Call Option 19.55 JEL'TE An arhitrageur can borrow at a continuously compounded rate of 6%. The arhitrageur can
lend at a con tinnously compounded rate of 5.9%. The arhitrageur constructs an arbitrage strategy that involves the sale or purchase of
exactly one share of stock. Determine the present value of the arbitrage proﬁts. a 0.156 a 0.241 5 uses :1 0.456 E 0.841 E? ActuarialBrewnom 2510 Page (19—13 Exam Iii—FEMF Questions  Chapter 9  Peiit],T and Other Option Relationships Question 41 An insurance company sells single premium deferred ennuit'jllr contracts with returns linked to a stock index, the time i value of one unit of which is denoted by Sift). The
contracts offer a minimum guaranteed return rate of 4%, At time O, a single premium of P is paid by the policyholder and P x 3.3% is deducted by the insurance company. Thue, nt
the contract metnrilrv date, T, the insurance oompenv will pa].r the policyholder: _ n so") T
Po yeixMux[S(m,1.c4 ] You are given the ibllowing information:
(i) The contract will mature in 2 years. (ii) Dividends are incorporated in the stock index. That is, the stock index is
constructed with ail stock dividends reinvested. [iii] sic} = so {iv} The price of a 2year European call option on the index with strike price of $54ﬂ3
is $10.15. {iv} The continuously componnded riskfree interest rate is 6%. Determine 3%, so that the insurance companyT does not make or lose moneyr on this
contract. A 12% B 8.3% O 14.3% D 15.9% E 22.2% Question 42 The cum—dividend price of a stock is $53 just before a dividend of $3 is to be paid. The
stock will also pa].r a dividend of $2 in 9 months. The continuousljir compounded riskfree
interest rate is 1D“ xi} per year. The table below describes the strilte prices and times until maturity [CO in years for 5
different American call options on the stock. You are given that it is optimal to exercise one of the options now. Determine which of
the options should be exercised now. a Option A B Option B O Option O D Option D E Option E El Actusrileremccm 2010 Page Oil14 Exam MFEI’BF Questions Chapter Fl  Parity and Uther Option Relationships Question 43
011 October 31. EDGE, a common stock is priced at $413.31}. You are given the following: (i) Dividends of equal amounts will be paid on December 31, EGGS and March 31,
23139. {ii} A European call option on the stock with strike price $42.06 expiring in 6
months sells for $2.55. (iii) A European pat option on the stock with strike price $411313 expiring in 6
months sells for $4.35. (iv) The continuously compounded risk—free interest rate is 5%. Calculate the amount of each dividend.
A $13.43 B $11.64 C $13.36 13‘ $1.41 E $2.44 Question 44
For a stock1 you are given:
(i) The current stock price is $5ﬂﬂﬂ.
(a) s = o.oo
(iii) The continuously oompoun tied risket'ree interest rate is r = [1.136. {iv} The prices for one—year European calls {C} under various strike prices {K} are
shown below: You own four special put options, each 1with one of the strike prices listed in (iv). Each of
these put op ticns can only be exercised immediately or one year Jfrom now. Determine the lowest strike price for which it is optimal to exercise one or more of these
special put options immediately. A $25 E $51] U $75 D $10G E It ia not optimal to exercise any of these pnt options. PE? ActuarialBreweoin Eﬂlﬂ ' Page $1915 Question =1 5 Consider a model with two stocks. Each stock pa_vs dividends continuously at a rate
proportional to its price. SJ (t) denotes the piice of one share of st...
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