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Unformatted text preview: Exam MFEFBF Questions Chapter 19  Binomial Option Pricing: I Chapter 19 — Questions Question 1 The price of a share of stock is $51. The stock ,does not pay dividends. In 1 year, the stock
price will either he $75 or $49. The continuously compounded risktree interest rate is 7%.
Compute the price of a $59strike, 1year, European call option on the stock.
A 5.49 E 9.49 C 9.79 D 19.59 E 13.52 Question 2 The price of a share of stock is $51. The stock does not pay dividends. In 1 year, the stock
price will either be $25 or $49. The continuously compounded riskfree interest rate is 7%.
Compute the price of a $59*strike, 1year, European put option on the stock.
A 3.92. E 5.41 C 5.99 D 5.95 E 9.22 Question 3 The price of a share of stock is $51. The stock pays dividends at a continuously
compounded rate of 3%. In 1 year, the stock price pill either he $TE or $49. The continuously compounded riskfree interest rate is 7%. Calculate the nuniher of shares of stock that must he purchased to replicate a 1year
European call option on the stock with a strike price of $59. A 9.425 B 9.592 C 9.596 D 9.593 E 9.?14 Question 4. The price of a share of stock is $51. The stock pays dividends at a continuously
compounded rate of 3%. In 1 year, the stock price will either he $75 or $49. The continuously compounded riskfree interest rate is. 7%. Calculate the amount that must he borrowed to replicate a 1year European call option on
the stock with a strike price of $59. ' A $25.54  13 $2173 C $25.57*r D $32.53 E $49.95 Eilﬂctuarialﬂrow.mni 291.9 Page Qlﬂul Question 5 The price of a share of stock is $51. The stock pave dividends at a continuously
compounded rate of 3%. In 1 year. the stock price will either be $75 or $412!. The
continuously compound ed riskfree interest rate is Tit. on exotic option pave the square of the stock price at the end of the pear. Galculste the
value of the exotic option. A EEEJQTJE. 13 $2,334.48 C 53.061553. D $3,134.34 E $3,842ﬂ’l Question E The price of a share of stock is $65. Ellie stock page dividends at a continuously
compounded rate of 5%. The stock’s volatility,r is 2T%. The price evolution of the stock
follows the textbooh’s binomial pricing model with each period being 1 pear in length. The continuously compounded riskfree interest rate is 5%. A 1—year European put option
on the stock has a strilte price of $63. The market price of the put option is $6.00. An srhitragcur constructs a strategy involving the pinchase or sale of exactly one of the
European put options. Determine which of the following is a component of that strategy. A Buy 0.3242 shares of stock 33 Sell 0.3084 shares of steel:
C Sell the put option for $6.013
D Lend $28,446 E Borrow $26259 Question 1' The graph helovr describes the payoffs of a European call option expiring in 1 year. The
price evolution of the underlying stock thllovvs a hinomial tree with each period being 1
gear in length. The underlying stock does not pager dividends. Option
Pavoﬂ' o. = 21.35 .____,.,_._.... ....................................  Stock price after
T If So. one period Determine the value at" the option‘s delta. A (1.525 13 0.539 (3 [1.555 D U.T5D E £1.83? ﬂActusrislBrewcom 2010 _ Page Gilli—2 Exam MFEJBF lQuestions Chapter 19 — Binomial Option Pricing: I Question II] The variahles used in a hinomial pricingmodel are deﬁned helow: u. = Factor applied to stock price in the optimistic scenario
o' = Factor applied to the stock price in the pessimistic scenario
: = Continuously compounded riskafree rate of return
a = Continuously compounded dividend yield
ft = Length of each period in the model
Determine which one of the models helov.r gives rise to an arhitrage opportunity.
it u. = 1.175 d. = case r = one a = coco a = c.25
B II.=1.23CI d = [1.305 r = CLUE E." = 0.061] h. = [1.5
C u. = LDDB d = [3.996 r = CLUE d' = D.D45 h. = {t4
1) u. = 1.27s d. = {1.733 r = c.12 a = c.12o h. = 1.5 E u. = 1.1100 d = [1.920 r = 11.06 .5 = {LDDD It — 2i) Question 11 The price of a stock is $50 per share. The stock pays dividends at a continuously
compounded rate of 2%. In 6 months, the price of the stock wiJl either he SEX or $41.51
The continuously compounded risk—Eree interest rate is 3%. A 6month European call option on the stock has a strike price of $55. The premium for
the call option is $2.55. Calculate the premium for a 6month European put option on the stock with a strilte price
of $55. A 4.34 E 5.92 C 6.36 D 7.118 E TBS Question 12 The price of a stock is 5T2. The stock pays dividends at a continuously compounded rate
of 3%. The price evolutiou of the stock foﬂows the texthook’e standard hinomial pricing
model with each period heing 1 year in length. The volatility of the stock is 23%. The continuously compounded risk—free interest rate is it. 11 2year American call option on the stock has EL strike price of $74. Calculate the
premium for the American call option. ' A GIFT E 11.134 C 11.96 D 12.95 E 14.41 lEIActqu'iaIEretmorn 2010 Page @104 Question 13 The price of a stool: is $72. The stock pays dividends at a continuously compounded rate
of 3%. The price evolution of the stock follows the textbooks standard binomial pricing
model with each period being 1 year in length.‘ The volatility of the stools is 23%. The continuously compounded riskfree interest rate is 3%. A Ziyear American call option on the stock has a strike price of $74. At the end of the ﬁrst
year, the stock price is greater than its initial price. Calculate the number of shares of stoclt that an investor must hold at the end of 1 year in
order to replicate the American call option. A 3.134 13 3.334 C 3.322 D 3.373 E 1.333 Qu estion 14 The price of a stock is “572. The stock pays dividends at a continuously compounded rate
of 3%. The price evolution of the stock follows the textbooks standaid binomial pricing
model with each period being 1 year in length. The volatility of the stock 1s 23% The continuously compounded risk—Eco interest rate is 3%. A 2~year European put option on the stock has a strike price of $74. Calculate the
premium for the put option. A 5.47 B 3.23 C 3.31 D 7.13 ' E 7.33 Question 13 The price of a stock is $72. The stock pays dividends at a continuously compoUnded rate
of 3%. The price evolntion of the stock follows the textbooks standard binomial pricing
model with each period being 1 year in length. The volatility of the stock is 23%. The continuously compounded riskfree interest rate is 3%. A 2year American put option ou the stock has a strilte price of $74. Calculate the
premium for the American put option. A 5.47 E 3.13 C 3.23 D 7.13 E 7.33 Question 13 The current price of a stock is $113. The stock pays dividends at a continuously
compounded rate of 3%. The volatility of the stock is 32%. The price evolution of the
stock followe the textbooks standard binomial pricing model. The continuously compounded risk—free interest rate is 13%. A 3month European call option on the stock has a strike price of $133. Use a 3period
binomial model to calculate the price of the option. A 13.53 E 17.14 C 17.53 D 13.43 E 21.11 D Actuarislllrew.co1n 2313  Page 1113—5 Exam MIi‘Ea'BF Questions ' Chapter 10  Binomial ﬂpticn Pricing: I Qu estinn 17 The current price of a stock is $110. The stock pays dividends at a continuously
compounded rate of 6%. The volatility of the stock is 62%. The price evolution of the
stool1' follows the textbook’s standard binomial pricing model. The continuously compounded riskrfree interest rate is 10%. A Sumonth American call option on the stock has a strilre price of 6100. Use a drperiod I
binomial model to calculate the price of the American option. A 1T.25 E 1166 C 16.1w!r D 16.46 E 21.11 Question 16 The current price of a stock is $110. The stock pays dividends at a continuously
compounded rate of 6%. The volatility of the steel: is 32%. The price evolution of the
stock follows the textbools‘s standard binomial pricing model. The continuously compounded rialsfree interest rate is 10%. A 6month European put option on the stock has a strike price of $100. Use a 6period
binomial model to calculate the price of the option. A 6.62 E 6.46 C' 6.56 D 6.66 E 6.61. Question 19 The current price of a. stock is $110. The stock pays dividends at a. continuously
compounded rate of 6%. The volatility of the stock is 62%. The price evolution of the
stoclt follows the texthoolt’s standard binomial pricing model. The continuously compounded riskfree interest rate is 10%. A 6month American put option on the stock has a strike price of $100. Use a 6period
binomial model to calculate the price of the American option. A 6.62 E 6.46 C 6.56 D 6.66 E 6.61 Question 20 The current price of a stock is $116. The stock pays dividends at a continuously
compounded rate of 6%. The volatility of the stock is 62%. The price evolution of the
stock follows the textboolr‘s standard binomial pricing model. The continuously compounded riskfree interest rate is 10%.
A 6—month American pnt option on the stock has a strike price of $100.
The option is priced using a 3—period binomial model. After 6 monthsT the stock has moved up once and down once in price. Calculate how
much an investor most have invested in the risk—free asset at the end of 6 months in
order to replicate the American put option. A 6.66 E 12.54 C 1126 D 16.66 E 3664 Q Ac1:un.rialErew.eo1n 2010 Page {HID6 A, Question 21 The current price of a stock is $90. The stock pays dividends at a continuously
compounded rate of 3%. The volatility of the stock is 3111's]. The price evolution of the
stock follows the textbooks standard binomial pricing model. The continuously compounded riskfree interest rate is 4%. A 1year American put option on the stock has a strilte price of $33. The option is priced
using a 3period binomial model. During the ﬁrst period, the stoclt moves dowo. Calculate the price of the American option at the end of the ﬁrst period.
A 12.33 E l3.'i"'3 C 14.33 D 14.25 E 14.44 Question 22 The current price of a stool: is $91.“). The stool: pays dividends at a continuously
compounded rate of 3%. The volatility of the stock is 33%. The price evolution of the
stock follows the textbook’s standard binomial pricing model. The continuously compounded riskfree interest rate is 4%. A 1year american put option on the stoclt has a'strilte price of $33. The option is priced
using a 3period binomial model. During the ﬁrst period, the stock moves down. Calculate the value of delta at the end of the first period. A A 41333 E 41.32"? C 43.333 D —ﬂ.3Eiﬁ E 41343
Question 23
The current price of a stock is $90. The stock does not pay dividends. The volatilityJ of the
stock is 33%.
The continuously compounded riskfree interest rate is Th3.
A 1year American call option on the stock has a strike price of $131. The option is priced
using the texthoolr’s binomial model with 4 periods.
Calculate the value of the American call option.
A 1.43 B 1.92 C 2.35 D 2.33 E 4.14
Question. 24
The current price of a stock is 343. Each month, the stock either increases in price by
23% or declines in price by 13%. The stock pays dividends at a continuoualy compounded
rate of 5%.
Tbs continuously compounded riskFree interest rate is 3%.
A 3month European call option on the stool: has a strike price of $33. The option is
priced using a 3period binomial model.' i "\ Calculate the value of the European call option. A as? E as? cars D cos B 7.91 'L‘J hetuarialldrewnom 2010 Page (.1191; Exam tracer Questions  Chapter is — Binomial Option Pricing: I Question 25 The current price of a stock is $4.13. Each month, the stock either increases in price by
2U% or declines in price hy 113%. The stock pays dividends at a continuously compounded
rate of 5%. ‘ The continuously compounded risk—free interest rate is 3%. A. 3month American call option on the stock has a strike price of $33. The option is priced using a Iiiperiod hinomial model. Calculate the value of the American call option. A 7.72 E 7.22 C 7.97 D 3.131 E 5.21 Question 26 The current price of a stock is $130. The volatility of the stock is 35%. The stock pays
dividends at a oontinuoualy compounded rate of 2%. The continuously compounded riskfree interest rate is 7%. An 3month European call option on the stock has a strike price of $247. The option is priced using the textboolt’s standard binomial model with El periods.
Calculate the value of the European call option. PL [LID E [1.11 C [1.12 D [3.13 E {1.15 Qu esti on 2 7 The current price of a stock is $13G. The volatility of the stock is 35%. The stock pays
dividends at a continuously compounded rate of 2%. The continuously compounded riskfree interest rate is 7%. An Eamouth European put option on the stock has a strike price of $247. The option is priced using the texthook‘s standard binomial model with 3 periods.
Calculate the value of the European put option. A 1135.11 B 1U7.4E C 107.59 D 112.73 E 117.00 Question 23 The current price of a stock is $13G. The volatility of the stock is 35%. The stock pays
dividends at a continuously compcuuded rate of 2%. The price evolution of the stock
follows the texthook‘s standard hinom'ial pricing model. The continuously compouuded riskfree interest rate is 7%. A 4—month European put option on the stock has a strike price of $20!]. The option is priced using a 4—period binomial model. Calculate the value of the European put option. A 5.9.05 B 63.25 C 70.131] D 71.67 E 73.85 '13] ActuarisIErermom 2211] Page 131108 Exam MFEI'3F Questions Chapter llilI — Binomial Option Pricing: 1 Question 23 The current price of a stool: is $133. The volatility of the stock is 35%. The stool: pays
dividends at a coutinuously compounded rate ,of 2%. The continuously compounded risk—free interest rate is T%. A 4month European put option on the stool: has a strike price of $233. The option is
priced using the tettbook’s standard binomial model with 4 periods. If the stool: price increases in each of the ﬁrst 3 mouths of the life of the option, then $37
must be invested at the riskfree rate of return at the end of 3 months in order to replicate
the option. CalculateX.
A 195.53 B 133.53 C 193.84 E 230.30 E 2131.15 Question 30 The current price of a stock index is 5133. The index page continuous dividends at a rate
of 4%. The solstilitv of the stock index' is 34%. The continuously compounded riskfree interest rate is 5%. A 3year European call option on the stoolr index has a strike price oi" 335. The option is
priced using the textboolr’a standard binomial model with 3 periods. lCalculate the price of the European call option.
A 11.83 E 16.13 C 24.33 D 25.54 E 23.39 Question 3 1 The current price of n stoolr index is $101]. The index pays continuous dividends at a rate
of 4%. The volatility of the stoolr iodex is 341%. Tbs continuoule compounded riskfree interest rate is 5%. A 3—year European put option on the stock index has a strike price of $35. The option is
priced using the textbooks standard binomial model with 3 periods. Calculate the price of the European put option. _
A 13.35 E 13314 C BELTS D 24.11 E 24.79 Question 32 The current price of a stock index is $13!]. The index page continuous dividends at a rate
of 4%. The volatility of the stock index is 34%. The continuoule compounded riskfree interest rate is 5%. A 3—year American put option on the stock index has a strilre price of $35. The option is
priced using the textboolr’s standard binomial model with 3 periods. Calculate the price of the American put option.
A 18.67 B 13.52 C 23315 D 24.11 E 24.?3 SI ActuarialEIewnom 2010 Page {1133 Exam MFEI’BF Questions Chapter It] — Binomial Option Pricing: I Question 33
The exchange rate is $1.2IUJ'E. Exchange rate volatility,T is 15%. The dollar interest rate is 5%. The euro interest rate is 9%. The price evolution of the
euro follows the texthoolt's standard binomial pricing model. A 9month European call option on the euro has a strike price of $1.1ﬂ and is valued using
a 3period binomial model. Calculate the price of the European call option.
A Ct'UErﬁi B 41.0612 U [1.13893 D [3.13912 E {3.0924 Question 34
The exchange rate is 551.2(11‘5. Exchange rate volatilityT is 15%. The dollar interest rate is 5%. The euro interest rate is 9%. The price evolution of the
euro follows the textbook‘s standard binomial pricing model. A 9month American call option on the sure has a strike price of $1.11] and is valued using
a 3period binomial model. Calculate the price of the American call option.
A ﬂﬂﬂﬁl E EIGHTH: U UJUUU D 13.11335 E 13.1344 Question 35 The exchange rate is 118 given per dollar. Exchange rate volatility is 11%. The dollar interest rate is 6%. The pen interest rate is 1%. The price evolution of the
dollar follows the textboolt’s standard binomial pricing model. A 1vesr attl'lenioneg,T American option is a dollar call that is yendenominated and is.
valued using a iiiperiod binomial model. Calculate the price of the American call.
A 2.58 E 2.97 C 3.33 D 3.03 E 3.2? Question 36
The exchange rate is 113 yen per dollar. Exchange rate volatility is 11%. The dollar interest rate is 6%. The yen interest rate is 1%. The price evolution of the
dollar follows the textbook’s standard binomial pricing model. A lvear atthemonev American option is a dollar put that is yendenominated and is
valued using a 3 period binomial model. Calculate the price of the American putl
A 2.58 H 3.138 C 3.14 D 3.22 E 8.27 IE] ActuarialErewnom coio Page QIDlﬂ ﬂue.5 tion 3'? the exchange rate is 2.35 Swiss francs per British pound. Exchange rate volatility is
12%. The franc interest rate is 5%. The pound interest rate is Tit. A 2year American call option is a pound call that is francdenominated. The strike price
is 2.35 francs. The call is valued using the textbdolt’s standard binomial model with 2
periods. Calculate the price of the American call option.
A 5.121 E 5.13’i C 5.142 D 5.145 E 5.252 Question 35 A call option has a gold futLu'es contract as its underlying asset. The current 1year gold
futures price is $555foz., and the strike price is $525. liolatilitp is 12%. The time to
expiration is 1 year. The continuously compounded lease rate on gold is 4%. The option is priced using the textbook's standard binomial model with 1 period.
The continuouslyr compounded risk—free rate of return is 7%. Calculate the price of the call option. A 15.55 E 1545 C 1115 D 24.?5 E 53.7'5 fﬁuestion 35 The futures price for an index is $1,555. The volatilityT of the index is 35%. The
continuoust compounded dividend rate of the index is 5%. The continuoule compounded riskfree rate of return is 7%. A 1year American call option on the futures contract has a strike price of $1,555. The
option is priced using the texthook’s standard binomial model with 3 periods. Calculate the price of the American call option. A 122.42 B 131.35 C 14155 D 155.55 E 151.55 Question 45 The futures price for an index is $1,555. lThe 1Iiolatilitrg,T of the index is 35%. The
continuously compnuuded dividend rate of the index is 5%. The continuouslyr compounded riskfree rate of return is “lit. A 1year American call option on the futures contract has a strilte price of $1,555. The
option is priced using the textbook's standard binomial model with 5 periods1 Determine the number of futures contracts an investor must huy at time 5 toreplicate the
call optiou. on. use n are c use 13 use E Loo lﬁActuariaIBrew.com 2515 Page l[51511 Exam MFEIBF Questions Chapter 13  Binomial Option Pricing: I Qn eation 41 _. [.3 For a twoperiod binomial model, you are given:
“g‘ a} Each period is one year.
i (ii) The current price [or s nondividend paying steel: is $43. 1;.I (iii) H = 1.2333. where u. is one plus the rate of capital gain on the stock per period ii?
’ the stock price goes up. i (iv) d = 3.3334 . where d is one minus the rate of capital loss on the stock per period if
‘ the stock price goes down...
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