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Final Exam 10 June 2013, questions and answers

Course

Applied Derivatives (FINM7041)

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Australian National University

Academic year: 2012/2013

Listed bookFundamentals of Futures and Options Markets

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Australian National University

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Australian National University THE AUSTRALIAN NATIONAL UNIVERSTTY RESEARCH SCHOOL OF FINANCE, ACTUARJAL STUDIES AND APPLIED STATISTICS Final Examination Semester 2, 2013 FTNMZOGZ Derivatives Study Time: 15 minutes Writing Time.“ 3 hours Permitted materials: Non-Programmable Caicut'ater Paper Based Dictionary INSTRUCTIONS: 1. 2. 3. This exam paper comprises a total of 6 pages. Please ensure your paper has the correct number of pages. The exam includes a total of 4 questions. The questions are of unequal value, with marks indicated for each question. You must attempt to answer all questions. Do not round calculations until providing your ﬁnal answer to each question. Final answers should be rounded to 4 decimal places. Include all workings for each question, as marks wilE not be awarded for answers that do not include workings. . Ensure you include your student number on your answer book. Total Marks = 60 This exam counts towards 60% of your ﬁnal assessment IN M2002 Derivatives: Final Exam, Semester 2, 2013 Question 1 (15 marks) Question 1 comprises two parts. Students are to answer ALL parts of this question: a) The ASX200 is currently trading at 5,450 points, and pays a dividend yield of 4% p. continuously compounded. The risk—free rate of interest is 2% pa. compounded weekly. The volatility of the index is 35% p. continuously compounded. Using the binomial option pricing model, calculate the value of a 1— year American call option on the index with a strike price of 5,300 points. In providing your answer, you can assume there are three time steps of four months each, and you must include a diagram of the binomial tree with all nodes clearly labelled. (12 marks) in) Using two portfolios, derive the lower bound for the price of a European futures put option. In doing this, detail the composition of each portfolio and draw a table illustrating the initial and terminal values of the portfolios. (3 marks) Question 2 (14 marks) Question 2 comprises three parts. Students are to answer ALL parts of this question: a) How would you create a reverse butterﬂy spread using puts? (2 marks) b) Suppose that a futures price is currently $29. The riskufree interest rate is 3% pa. compounded semi—annually. A threemmonth American put futures option with a strike price of $25 is currently selling for $1. Calculate the upper and lower bounds for the price of a three—month American call futures option with a strike price of $25? (8 marks) 0) What is the payoff for an average strike Asian put option? (4 marks) Question 3 (17 marks) Question 3 comprises three parts. Students are to answer ALL parts of this question: a) WJC Ltd is renowned as the number one intermediary for currency swaps in Europe. Their standard charge for arranging a swap is 28 basis points per annum. BO Ltd wishes to borrow US Dollars at a ﬂoating rate of interest. GB Ltd wishes to borrow Euros at a fixed rate of interest. After accounting for the 28 basis points per annum for WJ C Ltd, 60% of the remaining gains will go to B0 Ltd, and 40% of the remaining gains will go to GB Ltd. You must draw a diagram illustrating all cash flows, as well as show your calculations for how WJC Ltd receives its 28 basis points per annum. In drawing your diagram, you must pay the borrowed LIBOR rate all the way across the swap. BO Ltd and GB Ltd have been quoted the following rates per annum (adjusted for differential tax effects): (8 marks) BO Ltd GB Ltd US Dollars (ﬂoating rate) LIBOR + 2% LIBOR + 5% Euros (ﬁxed rate) 1% 6% Page 2 of 6Q\ h/ i: \ 31: wig;- 5:“ {13‘ {ﬂu/K M43; V (QR/“fl; {i : u.“ 1:;— an}? { Q/WE‘ 3&amp;quot;» LL“. 3: - ' L O£V . OU'ﬁ 1 ’J-ﬂq WM 5:: K ”H ‘ KW l‘e/ -. f 8/ I 1'1 8‘ w . f ,,,,, - PM U 01 ., ' .2» \ 5 1l% {R13 g; é“) g C T: C) 1 \A C, K ‘2‘ ’&amp;gt; ”A” ”V “L ﬁx W V 2-,: (:3 .. (71% k“l («53&amp;quot; W75 m a; .fgmﬁp’mﬁ? “.5:— Q} .UZDQH OIL—A337 ff. \rmqﬂ'“) {-96% &amp;quot; ‘3 e/mmt; emwﬁ A \é/ (A370 UN) WW QL‘W \/ \ 'agt—tq .ﬁ qqcr; . Hbﬂﬁs . \TL‘ F/ CO} W/é’b‘BA 1 f) m Ox wig/‘43 _.,_, 0a; \7 @7980Uahg. ck} Netti»; 6 “ €7ﬁh:ﬂg§v@;wﬂyég (;\W7o%:®_wa&amp;amp;) cm q$eﬁa2 _ n N 0T gxé’aycﬂ‘a’jc 6/? W5! 24:3 Lowe 7L 6’ 7’36“! 0F? . O ‘ U6 «Me 5| A‘AOLQQ Q) 2' 11%)] r 0 $ Gilt/{0117 (37 U (AKA-(L (IX, A’OQQ. (—J ,0 UA'DJVEFQ’KAS C, chb 563k 0 WM&amp;quot;)

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