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Unformatted text preview: Chapter 12 — Questions Question 1 The price of a stock is $46. The volatility of the stock is 35%. The stock pays a
continuously compounded dividend yield of 2%. The continuously compounded riskfree rate of return is 3%. A European call option has a strike price of $45 and expires in 3 mouths.
Calculate the price of the European call option. A 3.35 B 3.23 C 3.22 D 4.12 E 4.22 Question 2 The price of a stock is $46. The volatility of the stock is 35%. The stock pays a
continuously compounded dividend yield of 2%. The continuously compounded riskfree rate of return is 3%. A European put option has a strike price of $45 and expires in 3 months. Under the ElackScholes framework. calculate the price of the European put option.
A 1.53. E 2.43 C 2.36 D 3.23 E 4.12 Question 3 The price of a stock is $45. The volatility of the stock is 35%. The stoclt pays a dividend
of $5 in 1 month. The volatility of the prepaid forward maturing in 3 months is 39.24%. The continuoust compounded riskfree rate of return is 3%. A European call nption has a strilte price of $45 and expires in 3 months. Under the BlackScholes framework, calculate the price of the European call option.
A 2.37 E 3.45 C 4.13 D 5.41 E 733 Question 4 The spot exchange rate is $1.25JE. The dollar interest rate is 5%. The eurovdenominated
interest rate is 3.3%. The volatility is 11%. A dollardenominated European call option expires in 3 months and has a strike price of
$1.31]. Under the BlackScholes framework, culoulate the price of the European call option.
A 50.3153 E 20.13253 C 30.0345 D $0.3335 E $23461 IE! Actuariallirewrom 201i}  Page 131121 Exam MFEI’EF Questions Ghapler 12 — The BlackScholar: Formula Question 5 The spot exchange rate is $1.25J'JE. The dollar interest rate is 6%. The euro—denominated
interest rate is 3.5%. The volatility is 11%. A dollardenominated European put option expires in E months and has a strike price of
$1.31]. Under the ElaclrScholes framework. calculate the price of the European put option. A $03451 E 530.0455 [1 $ﬂ.ﬂ585 D $D.U'i'ﬂﬂ E $D.DEUD Question '5 The spot exchange rate is $1.25l€. The dollar interest rate is 5%. The euro—denominated
interest rate is 5%. The T.rolatility is 15%. A11 atthenionegl,r European put option is eurodenominated and expires in 1 year.
Under the Black—Scholes framework, calculate the price of the European put option.
A ED.U2ﬂD E 310312 U EULU425 I} 450.0531 E Eﬁﬂﬁﬁfi Question 7 The 1year futures price for oil is $Eﬂl’harre1. The volatility of oil is 25%. The continuously compounded risk‘free rate of return is 8%. A 1—year European call option on the futures contract has a strike price of $50.
Under the BIackScholes framework. calculate the price of the European call option.
A 3.55 E 5.94 G 5.7'3 I} 5.15 E 8.55 Question 3 The 1—year futures price for oil is $Eﬂfharrel. The volatility of oil is 25%. The continuously compounded riskrfree rate of return is 8%. A 1year European put option on the futures contract has a strike price of 551].
Under the Black—Scholes framework, calculate the price of the European put option.
A 3.94 I E 5.?3 C 5.19 D 3.2? E 8.55 t: Actuarislﬂrew.mrn coio Page {21122 Question 9 The price of a stock is 37”]. The 1eolutilitg,r of the stock is 33%. The stock pays continuously
compounded dividends at a rate of 3%. The continuoule compounded riskfree rate of return is 3%. A 3month European call option on a 3rInontl'L Futures contract has a strike price of $33.
Under the BlackrScholee framework, calculate the price of the European call option. A 2.34 B 3.35 C 3.33 D 13.31 E 12.33 Question Ill The price of a stock is $73. The volatility of the stock is 33%. The stock pays contiuuously
compounded dividends at a rate of 5%. The continuouslyT compounded riskfree rate of return is 3%. A 3month European put option on a ivyear futures contract hae a strike price of $35. Under the BlackScholee Eranlettrorlt+ calculate the price of the European put option on the
futures contract. A 2.54 B 2.32 C 3.34 D 3.33 E 13.33 Question 1 1 The table below lists the prices and Greek measures of two European call options on
Stock X. The current price of Stock III is $43. Option 1 Option 2 Price 11.3333 3.5333
Delta 3.2333 3.3235
Gamma 3.3133 3.3222
Vega 3.1323 3.1343
Rho 3.2431 3.2233
Theta 43.3113 —U.Dl23
Psi 43.3323 43.3123 A bull spread is constructed from the two calls. Determine the value of Vega for the call
hull spread position. A 43.3333 E —D.[}317 C 3.331? D 3.3335 E lIC}.143.EI IE! Actuarialﬂrewnom 2cm  Page Q12}! Exam MI‘EJEI" Questions Chapter 12 — The BlackScholea Formula lQuestion 12
assume that the Blackﬂcholes framework holds.
The price of a stock is $35. The volatility of the stock is 35%. The stock pays contiouously _ compounded dividends at a rate of 3%. The continuouslyr compounded riskfree rate of return is 3.5%. A. 3month European pnt option on the stock has a strike price of $33.
Calculate the delta of the European put option.
1'51 ﬂ.573 E 43.553 C 41172 D 41.449 E 43.427 l[E‘iuestion 13
assume that the ElackScholes framevvork holds. The price of a stock is $33. The volatility of the stock is 35%. The stock pays continuously
compounded dividends at a rate of 3%. The continuously compounded riskfree rate of return is 3.5%. A 3month European call option on the stock has a strike price of $33. A. 3month
European put option on the stock also has a strike price of $33. An investor owns in!) of the calls and 55 of the puts. Calculate the delta of the investor’s
position. A 2145 E 31.52 C 333?? D 35.55 E 75.35 IQuestion 14
ﬁssume that the BlacltScholes framework holds. The price of a stock is $35. The volatility of the stock is 35%. The stock pays cootlnuously
compounded dividends at a rate of 3%. The continuously compounded riskfree rate of return is 3.5%. A 3month European pnt option on the stock has a strike price of $33.
Calculate the elasticity of the European put option. 1"; —3.TQ E —3.'l'1 C —3.53 D —3.35 E —3.CIT E Actuarialﬂrevvnom 2U] CI I Page @124. Exam MFEFBF II:l'.uesl:ious Ghapter 12 — The BlackEcholes Formula Question 15 The table below lists the prices and Greek measures for 3 options. Option 1 Option 2 ' Option 3 Price 13.3 333 23.3333 3.3333
Delta asses 3.7371 ' —3.2354
Gamma 3.3143 3.3133 3.3124
Vega 3.231"? 3.1342 ‘ 3.2414
Rho 3.2154 3.364]. —3.238'ir
Theta —3.3241 —3.3194 —3.3131
Psi —3.3534 "3.5141 3.1T12 An investor creates a portfolio with a value of $53. The investor invests 43% of the
portfolio in l[Clptioo 1, 43% in lICIption 2, and 23% in Option 3. Calculate the value of rho for the investor's portfolio. _
A 3.214 E 3.25? C 3.238 D 3.431 E 3.433 Queation 1.3
Assume that the BlackScholee framework holds. The solid curved line bElDW depicts a GraeIt measure For a European option. ‘23 25 33 35 43 45 53 55 33 Stock Price ($) The underlying stock‘s Volatility is 33%. and it does not papr dividends. The strike price
of the European option is $43. The European option expires in 3 months. Determine which of the following Greek measures is desciibed by the graph.
A Delta for a call option B Vega for a put option C Rho for a put option D Psi for a call option E Theta for a put option El ﬁctuariﬁlﬂreureom 2313 Page {3125 Question 1'? An option has an elasticity of 4.5. The continuously compounded expected return on the underlying stock is 15%.
The continuously compounded riskfree rate of return is Tit. Calculate the risk premium of the option. A 51.5% E 55.5% C 43.5% D 55.5% E 57.5% Question 1 5
The curreut price of a stool: is $55. A European option on the stock has a strike price of $75. The value of the option is $4.11
The elasticity of the option is 43.55. An investor uses the stock and a riskfree asset to create a replicating portfolio to match
the performunce of the option. Calculate the amount that the investor invests in the rielofree asset.
A $15.57 B $14.95 5 $15.14 D $22.31 E $25.45 'Question 19
The continuously compounded expected return on Stock K is 15%.
The continuously compounded riskfree rate of return is 5%. The volatility of a European call option on Stock 1: is 145%. The elasticity of the op tion is
4.3T'l'. Calculate the Sharpe ratio of the call option.
A 25.14% E 31.55% C 35.35% D 42.51% E 45.55% Question 25 The table below describes the price, elasticity. and strike price of three call options. .511
three of the options have the same underlying asset. IIUptiou A Up tion E lOption C Price 5.555 1555 5.357
Elasticity 4.357 4. T54 5.22? Strike Price 55.555 55.555 T5555 An inyestor purchases one of lDption 3'1 and one of Option B. The investor writes one of
Option 5. Calculate the elasticity of the investor’s position.
A 2.25 E 3.53 C 4.15 D 4.73 E 4.55 ﬂﬁchmrialﬂrevrrom 251.5 Page 5125 Chapter 12  The BlackEchelon Formula Quentinn 21
Assume that the BlacltScholes Erarncwork holds. On January 1, EDDEI, the following currency information is given: I Spot exchange rate = $1.4Dfeuro I Dollar interest rate = 5.11% compounded continuously
I Euro interest rate = 2.5% compounded continuously
I Exchange rate volatility = {LID What is the price of LOUD dollardenominated euro put options with a stiilte exchange
rate of $1.1EUfeurc that expire on January 1, EDGE? A $12.95 B $30.26 C $85.17 D $91.15? E $144.19 Question 22 A put oplﬁcn is modeled using the BlackScholes formula 1with the fellhwing parameters:
' S = 25 ' K=26  r =ett  5 =19; I 0': coat I T :2. Calculate the put option elasticity, n. A —5.1. B —4.2 I3 —2.5 I} —2.5 E 43.3 Que sti on 23 The current price of a stock is $ED. The volatility of the stock is coat. The stoclt pays
dividends at a connhiuously compounded rate of 5%. The riskfree rate of return is 13%. A sixmﬂnth European call option and a sixvroonth European put option on the stock both
have a strike price of $62. An investor purchases one of the call options and writes one of the put options. Calculate the elasticity of the investor’s portfolio. A D E 1 . C 12 D 135 E 143 «El ActuaﬁalErcwmnl Zillﬂ Page (312? :.. thqhﬂmsvranxAu"ru .a...s.....,;.w... _.._..._......... no»... __i.... ._i .._... .....H. ...Jr“a:2.;sti;;t;1;:.ui..:;u.3;:m. L_..' i....':.‘....;..... cf. 5 . ._' .;.....i .. ._..:.'c:dir:ake=iﬁe::lim Exam MFEIBF Questions Chapter 12 — The BlackrScholca Formula
Question 2st The current price of a stock is $60. The volatility of the stock is 30%. The stock pays
dividends at a continuously compounded rate of 5%. The continuously compounded
expected return on the stock is 22%. The risk~Eree rate of retuin is 5%. An atthenioney European call option on the stock expires in 6 months. The current:
price of the call option is $5.1ﬁ and the delta of the call option is 0.52?7. An investor purchases two atthermoney European call options and one atthemoney
European put option. Calculate the continuously compounded expected return on the investor's portfolio.
A 33% B 4 it C 53% D 59% E 63% Question 25 An investor is deciding whether to buy a given stock or two Enropean call options on the
stock. The value of the call options is modeled using the BlackScholes formula and the
following assumptions: I Continuously compounded riskfree rate = 4%
I Continuously compounded dividend = 3% I Expected return on the stock = if: I Current stool: price = $41] I Strike price of call option = $27 I Estimated stock volatility = 25% I Time to expiration = 1 year Calculate the Sharpe ratio of the call options.
A $.34 B 1107 C 1111 D 13.161 E 1116 Question. 26
Determine which of the following statements is FALSE.
A The elasticity of a European call option increases as its strike price decreases. B If its underlying stock has a positive risk premium, then the expected return of a
European call option goes down as the stock price goes up. C If its underlying stock has a positive risk premium, then the expected return of a
European put option is less than the expected return of the stock. 13! The existence of volatility skew suggests that the BlackScholes model and its
assumptions are not an accurate description of the world. E The Sharpe ratio for a call equals the Sharpe ratio [or the underlying stock. Question 21' The table below hate the prices and Greek measures of two European call options on Stock X. The current price of Stock It is $411+ The only difference hetwcen the two options
is that the}:r mature on different dates. Option 1 Option 2' Price 1.5355 5.5772
Delta 5.5525 5.5751
Gamma [1.1575 13.5251
Vega c.0457 121.1455
Rho 5.5121 5.213112r
Theta 4.5293 4113115
Psi —ﬂ.0154 —U.2T54 An ilT‘lr'estﬂr believes that the price of stock X will not change over tbe next month. Based
on this belief, the investor enters into a calendar spread by selling one of the options and
buying the other one. Calculate tbe value of psi for the calendar spread position.
.131. 43.345 B —ﬂ.252 C 5.515 D 0.252 E 13.349 Question 213 The table below lists the prices of European pnt options on Stock 2 based on the price of Stock 2 and the time remaining until matnrity. All of the put options have a strike price
of $4151. Time to Expiration
Stock Price {$1} 12 Months 5 Months 3 Months 55 4.75 4.52 4.23
55 3.55 5.513 3.52
45' 5.25 2.5":= 2.55
42 2.55 2.115 1.35
44 2.15 1.45 5.55 The current price of Stock 2 is $412}. The continnously compounded riskfree rate is 5.5%. An investor purchases a 12—month option and Writes a 5—month option. Calculate the 5month holding period proﬁt if the stock price is $35 at the end of 5
months. :‘1. 5.55 B 5.55 C 1.55 D 2.11 E 2.55 o actuarinieremmm coin ' Page oiss Exam MFEI‘SF Questions Chapter 12 n The BlackEleholes Formula Question 20
Assume that the BlackScholes framework holds. The price of a stocl: is $40. The volatility .of the steel: is 30%. The steel: pays a
continuously compounded dividend yield of 2%. The continuously compounded riskfree rate of return is 10%.
A European call option has a strike price of $35 and expires in 1 year. An investor uses the binomial model with 1.000 stepa to calculate the value of the call
option. Determine the price calenlated by the investor. A 3.32 E 5.10 C 8.05 D I31.01 E 0.05 Question 30
Assume thot the BlackScholes framework holds. The price of a steel: is $T'l'. The volatility of the steel: is 25%. The steel: pays a dividend
of $7 in 3 months, and a dividend of $0 in 0 months. The volatility of a prepaid forward that matures in 0 months is 27.43%. The volatility of a
prepaid forward that matures in 0 months is 31.14%. The continuously compounded riskfree rate of return is 10%.
A European put option on the steel: has a strike price of $703 and expires in E' months. Calculate the price of the European put option.
A 1.30 E 4.03 C 5.30 D 5.12 E 9.43 Question 31 The table below lists the prices and Greek measures of two European put options on Steel:
)1. The current price of Steel: X is $100. Option 1 Option 2 Price 2.9 540 5.0 T3?
Delta 41.2542 0.4521
Gamma 0.0181 0.0225
vega 0.2257 0.2300
Rho ' —0.14l.0 43.2650
The ta —0.0073 —0.00=l 7
Pei 0.1271 0.2310 A put hear spread is constructed from the two puts. Determine the value of gamma for
the put hear spread position. A —0.025'l' E —0.0044 G 0.0044 D 0.0200 E 0.0.‘35ir @Aetuarialﬂrewmom 2010 Page l013210 Question 32
assume that the Black—Scholes framework holds. The current price of Stock 1: is 5536. Stock K pays continuously compounded dividends. at
a rate of 3%. a European call option on Stock H has a strike price of $75 and expires in 9 months. The
1.Talue of the European call option on Stock H isl$15.ﬂ5. The current price of Stock Y is $11545. Stock Y page continuouslyr compounded dividends
at a rate of 1.3%. The T..I'olai;il'1‘l‘.15.T of StoolL Y is equal to the volatility of StoolIL X. 131. European call option on
Stock Y has a strike price of $105 and expires in '3 months. Unlculate the value of the European call option on Stock Y.
A 19.26 E 22.119 C 22.92! D 23.2"? E 24.33 Question 3?.
Assume that the BIaclt—Sehcles framework holds. The current price of a stock is $55. The stock’s continuously compounded dividend yield is
5%. The continuously compounded riskfree interest rate is 8%. A 1year European put option on the stock has a strilre price of $35. The DhEEITFed price of
the put option is $5.55. The table below provides the values of o‘l and d2 for each poaeihlc stock volatihty level. a i fig 15% 13.2083 [1.0553
20% 0.2 DDU DJJD [I'D
25% 0.21351] —EI.ﬂ4 50
3W2”. 0.215“? —D.0333 35% 0.2321 43.1179 Determine the imphed volatility of the European put op tiou.
A 15% E 20% C 2595 D 30% E 35% ID Actuariallirewmom 2010 Page Q1241 Exam MFEIEF Questions Obap ter 12 — The BiacloScholes Formula lQuestion 34 The table below describes the price, strilte price. time until maturity (in years}, delta,
gamma, and theta for four European options on Stock X. Option .1. Option 2 QM Option 4
Price 3.55 0.05 12.30 0.37
Strilte Price T0 TE TU TE
Time to Matnrity 0.5 0.5 1. 1
Delta 0.0055 0.5407 0.6052 0.0105
lGamma 0.02 30 0.0 26 0.0 102 0.0 173
Theta 40.0230 43.0230 —0.0180 —0.018Ei An investor believes that Stock K‘s price will not change over the next 3 months. The
investor enters into a calendar spread based on this belief. Determine which of the following strategies best describes the calendar spread position
entered into by the investor. A Bell Option 1 and Eu],r Option 2
B Sell Option 2 and .‘Eiuﬂpr Option 1
C Bell Option 4 and Buy Option 2
D Sell Option 2 and For].T Option 4
E Bell Option 4 and Hug.r Option 3 Question 35
Assume that the Blacknﬁeboies framework holds. The exchange rate is ¥132!E. The yendenominated interest rate is 1%. The euro—
tlenominated interest. rate is 4%. The exchange rate volatility is 12%. lC'ralculate the price of a 12E—strike yendenominated euro put with 6 months to expiration.
A 1.40 E 1.08 O 2.43 D 3.05 E 4.31 lQuestion 313i
Assume that the Black—Sohoies framework holds. The exchange rate is E13205. The yen—denominated interest rate is 1%. The euro
denominated interest rate is 4%. The exchange rate volatility is 12%. Calculate the price of a 0.000strilLe enrordennnﬁnated yen call with 5 months to
expiration. it 0.00015 E 0.00010 l[;":10.00021 D 0.00024 E 0.00027 {3.} Actual‘ialBrewnoln 2010 Page {112—12 Question 3'? Assume that the BleekSoholes framework holds. 11 nondividendpeying stool: has 3.
ourrent priCE of $1110. The volatility of the steel! is 35%. The continuously compounded
riskfree interest rate is 7'94. ' Calculate the price of s. 1yeor lilostrike European call option. where the underlying,r
asset is a futures controot maturing st the some time as the option. A 5.91] E 8.38 C 11.113 D 14.82 E 19.41] Question 38 You are asked to determine the price of o. Europeon put option on a stock. Assuming the
EleckrScholes Ersmeworh holds1 you ore given: [i] The stock price is “5101]. (ii) The put option will expire in E months. {iii} The strike price is $1133. (in) The continuously compounded rishrfree interest rate is r = [1.013 .
(V) s = ones {vi} o = [1.512]
Calculate the price of this put option.
A $11.52 B $13.22 '3 $14.42 D $16.32 E $13.92 Question 39 You are considering the purchase ot'sn American call option on o nondividendpsying
stock. Assume the BleehSoholes fromeworh. You are given: {i} _The stock is currently selling for $413.
{ii} The strike price of the option is $42.
{iii} The option expires in 3 mouths. (is) o' = use [1?) The delta of the call option is 0.454. Determine the price of the cell option. .4. 15.336E2e'0'5x2dx —si.ss7
B 17.1so [EganMk: — sssso
c 21.537 E2345x2dx—1s.sso
n 23.7212}—1T.1EDID'ﬂe‘0'5x2olr —L"J .22
E 40.947 1: adjExam — 21sec [GI MtuarileIowmom L'Dll] I  Page {3:1213 Exam MFEFEF llamestions Chapter 12 — The BLachEchcles Formula Question nil}
Assume that the BlackScholes framework holds. The current price of a stock is $3. The stock does not pay dividends. The volatility of the
stock is 2T%. The continuously compounded risk...
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