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# Ch%2010%20Q.%202011 - Exam MFEFBF Questions Chapter 19...

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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 risk-tree interest rate is 7%. Compute the price of a \$59-strike, 1-year, 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 risk-free interest rate is 7%. Compute the price of a \$59*strike, 1-year, 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 risk-free interest rate is 7%. Calculate the nuniher of shares of stock that must he purchased to replicate a 1-year 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 risk-free interest rate is. 7%. Calculate the amount that must he borrowed to replicate a 1-year 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 risk-free 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 risk-free 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 pricing-model 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 6-month 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 6-month 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. 1-1 2-year 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'iaIEret-morn 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 risk-free 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 risk-free interest rate is 3%. A 2-year 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 3-month European call option on the stock has a strike price of \$133. Use a 3-period 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 stool-1' 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 rials-free interest rate is 10%. A 6-month European put option on the stock has a strike price of \$100. Use a 6-period 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 risk-free interest rate is 10%. A 6-month American put option on the stock has a strike price of \$100. Use a 6-period 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 risk-free 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.rialE-rew.eo1n 2010 Page {HID-6 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 risk-free interest rate is 4%. A 1-year American put option on the stock has a strilte price of \$33. The option is priced using a 3-period 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 risk-free interest rate is 4%. A 1-year american put option on the stoclt has a'strilte price of \$33. The option is priced using a 3-period 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 risk-free interest rate is Th3. A 1-year 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 risk-Free interest rate is 3%. A 3-month European call option on the stool: has a strike price of \$33. The option is priced using a 3-period 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. 3-month American call option on the stock has a strike price of \$33. The option is priced using a Iii-period 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 oont-inuoualy compounded rate of 2%. The continuously compounded risk-free interest rate is 7%. An 3-month 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 risk-free 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 risk-free 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] ActuarisIErer-mom 2211] Page 13110-8 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 4-month 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 risk-free 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 risk-free interest rate is 5%. A 3-year European call option on the stool-r 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 stool-r index is \$101]. The index pays continuous dividends at a rate of 4%. The volatility of the stool-r iodex is 341%. Tbs continuoule compounded risk-free 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 risk-free 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 ActuarialEI-ewnom 2010 Page {113-3 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 9-month European call option on the euro has a strike price of \$1.1ﬂ and is valued using a 3-period binomial model. Calculate the price of the European call option. A Ct'UErﬁ-i 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 9-month American call option on the sure has a strike price of \$1.11] and is valued using a 3-period 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 1-vesr at-tl'le-nioneg,T American option is a dollar call that is yen-denominated and is. valued using a iii-period 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 l-vear at-the-monev American option is a dollar put that is yen-denominated 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 QID-lﬂ 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 2-year American call option is a pound call that is franc-denominated. 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 1-year 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 risk-free rate of return is 7%. A 1-year 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 risk-free rate of return is “lit. A 1-year 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 to-replicate the call optiou. on. use n are c use 13 use E Loo lﬁActuariaIBrew.com 2515 Page l[515-11 Exam MFEIBF Questions Chapter 13 - Binomial Option Pricing: I Qn eation 41 _. [.3- For a two-period binomial model, you are given: “g‘ a} Each period is one year. i (ii) The current price [or s non-dividend 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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