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Ch%2012%20Q%202011

Ch%2012%20Q%202011 - Chapter 12 — Questions Question 1...

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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 risk-free 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 risk-free rate of return is 3%. A European put option has a strike price of $45 and expires in 3 months. Under the Elack-Scholes 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 risk-free rate of return is 3%. A European call nption has a strilte price of $45 and expires in 3 months. Under the Black-Scholes 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 dollar-denominated European call option expires in 3 months and has a strike price of $1.31]. Under the Black-Scholes 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 Black-Scholar: 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 dollar-denominated European put option expires in E months and has a strike price of $1.31]. Under the Elaclr-Scholes 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 at-the-nionegl,r European put option is euro-denominated 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 1-year 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 BIack-Scholes 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 1-year 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 {2112-2 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 risk-free rate of return is 3%. A 3-month 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 risk-free rate of return is 3%. A 3-month European put option on a ivyear futures contract hae a strike price of $35. Under the Black-Scholee Eran-lettrorlt+ 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 Black-Scholea 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 risk-free rate of return is 3.5%. A. 3-month 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 41-172 D 41.449 E 43.427 l[E‘iuestion 13 assume that the Elack-Scholes 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 risk-free rate of return is 3.5%. A 3-month European call option on the stock has a strike price of $33. A. 3-month 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 Blaclt-Scholes 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 risk-free rate of return is 3.5%. A 3-month 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 Black-Echoles 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 $53. The investor invests 43% of the portfolio in l[Clptioo 1, 43% in lICIption 2, and 23% in Option 3. Calculate the value of rho for the investor's portfolio. _ A 3.214 E 3.25? C 3.238 D 3.431 E 3.433 Queation 1.3 Assume that the Black-Scholee framework holds. The solid curved line bElDW depicts a GraeI-t measure For a European option. ‘23 25 33 35 43 45 53 55 33 Stock Price ($) 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 {312-5 Question 1'? An option has an elasticity of 4.5. The continuously compounded expected return on the underlying stock is 15%. The continuously compounded risk-free 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 risk-free 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 risk-free 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 512-5 Chapter 12 - The Black-Echelon Formula Quentinn 21 Assume that the Blaclt-Scholes 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 dollar-denominated euro put options with a stiilte exchange rate of $1.1E-Ufeurc 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 Black-Scholes 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 $E-D. The volatility of the stock is coat. The stoclt pays dividends at a connhiuously compounded rate of 5%. The risk-free rate of return is 13%. A six-mflnth 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-? :-.. thqhflmsv-ranx-Au-"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 at-the-nioney 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 at-thermoney European call options and one at-the-money 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 2-5 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 Black-Scholes formula and the following assumptions: I Continuously compounded risk-free 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 Black-Scholes 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 risk-free rate is 5.5%. An investor purchases a 12—month option and Writes a 5—month option. Calculate the 5-month 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 ois-s Exam MFEI‘SF Questions Chapter 12 n The Black-Eleholes Formula Question 20 Assume that the Black-Scholes 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 risk-free 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 Black-Scholes 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 risk-free 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 l0132-10 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 Stool-L Y is equal to the volatility of Stool-IL 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 BIacl-t—Sehcles framework holds. The current price of a stock is $55. The stock’s continuously compounded dividend yield is 5%. The continuously compounded risk-free interest rate is 8%. A 1-year European put option on the stock has a strilre price of $35. The DhEEIT-Fed 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] —E|I.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 yen-denominated 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 yen-denominated 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 0.000-stril-Le 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 Bleek-Soholes framework holds. 11 nondividend-peying stool: has 3. ourrent priCE of $1110. The volatility of the steel! is 35%. The continuously compounded risk-free interest rate is 7'94. ' Calculate the price of s. 1-yeor lilo-strike 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 nondividend-psying stock. Assume the Bleeh-Soholes 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 [Egan-Mk: — sssso c 21.537 E234-5x2dx—1s.sso n 23.7212}—1T.1EDID'fle‘0'5x2olr —L"J .22 E 40.947 1: adj-Exam — 21sec [GI MtuarileI-owmom L'Dll] I - Page {3:12-13 Exam MFEFEF llamest-ions Chapter 12 — The BLach-Echcles Formula Question nil} Assume that the Black-Scholes 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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