**Unformatted text preview: **Student Number: Seat Department of Finance Faculty of Economics and Commerce SAMPLE EXAM SUBJECT NUMBER: FNCE30007 SUBJECT NAME: Derivative Securities EXAM DURATION: 3 HOURS READING TIME: 15 minutes TOTAL MARKS: 70 Authorised Materials: 1. This is a CLOSED BOOK exam. Students are not permitted to have any materials in their possession. 2. Non‐programmable calculators are permitted. Calculators with the ability to enter and/or retrieve text are not permitted. 3. Students are not permitted to use a foreign language dictionary. Instructions to Invigilators: 1. Students should be provided with this booklet. 2. This booklet MUST be COLLECTED at the end of the exam. Instructions to Students: 1. Write your student number in the box at the top of this cover page. 2. Answer ALL questions. 3. Writing is NOT permitted during reading time. 4 You may detach the formula sheets and the normal distribution tables (last pages of this booklet). Do NOT
detach any other pages. Examination booklets with missing pages will NOT be marked. 1 QUESTION 1 [7 MARKS] A 9‐month American option allows an Italian investor to purchase 1 million USD at the rate of 0.85 euros per USD. The current spot FX rate is 0.90 euros/US, the FX rate volatility is 15% p.a., the risk‐free rate in the US is 1% p.a. and in Europe it is 2.5% p.a. a) Use a three‐period binomial model to assess the total premium paid by the investor (round to 4 decimal places) 2 3 b) What position does a financial intermediary writing the option need to take in FX to delta‐hedge its position? 4 QUESTION 2 [5 marks] A stock price is currently $30. During each two-month period for the next four months it is expected
to increase by 8% or reduce by 10%. The risk-free interest rate is 5%.
a) Use a two-step tree to calculate the value of a derivative that pays off max[(30 ST ) 0]2
where ST is the stock price in four month.
b) If the derivative is American-style, should it be exercised early? 5 6 QUESTION 3 [6 marks] A bank offers you to take a short position in a stock through a forward contract. You decide to
take the offer and ask for a 6-month forward. The stock is currently trading at $50 and it is
expected to pay a dividend of $1 per share in two months and in five months. The risk-free
rate of interest is 8% per annum with continuous compounding for all maturities.
a) What are the forward price and the initial value of the forward contract? Ignoring
transactions costs, how much do you owe the bank at the time you open your forward
position?
b) Three months later, the price of the stock is $48 and the risk-free rate of interest is still
8% per annum. What are the forward price and the value of the short position in the
forward contract?
c) If you want to liquidate your forward position at that point (i.e., when the stock is at
$48) what cash flow ($ amount and direction) do you face? 7 8 Question 4[6 Marks] It is now October 2013. A company anticipates that it will purchase 1 million pounds of
copper in February 2014 and August 2014. The company has decided to use the futures
contracts traded in the COMEX division of the CME Group to hedge its risk. One contract is
for the delivery of 25,000 pounds of copper. The initial margin is $2,000 per contract and the
maintenance margin is $1,500 per contract. The company’s policy is to hedge 80% of its
exposure. Contracts with maturities up to 13 months into the future are considered to have
sufficient liquidity to meet the company’s needs. Assume the market prices (in cents per
pound) today and at future dates are as follows. Date
Spot Price
Mar 2014 futures price
Sept 2014 futures price Oct 2013
372.00
372.30
372.80 Feb 2014
369.00
369.10
370.20 Aug 2014
365.00
364.80 a) Devise a hedging strategy for the company.
b) What is the impact of the strategy you propose on the price the company actually pays
for copper in Feb 2014? 9 10 QUESTION 5 [Multiple Choice, 2 marks each, Total 16 marks] Please circle only one answer for each question 1. You have made your portfolio gamma neutral and delta neutral by using 3‐month options in conjunction with the underlying asset. Which of the following statements is true? a) Your portfolio is riskless until the options you have included in your portfolio expire regardless of what happens to the price of the underlying asset b) Your portfolio will not change in value regardless of what happens to the price of the underlying asset c) Your portfolio may change in value even if you keep it delta and gamma neutral through weekly rebalancing d) The less frequently you rebalance your portfolio the more effective the hedging strategy will be e) None of the above is true 2. An investor is expecting the Australian equity market to undergo a period of low volatility over the next few weeks: however, he is not willing to take a bet on the direction of market movements over such period. The ASX 200 index is currently at 5400. Given the investor’s view, which one of the following strategies makes the most sense? a) A short (or, reverse) butterfly spread with strikes of 5300, 5400 and 5500 b) A short deep‐in‐the‐money put c) A long straddle with a strike of 5400 d) A long strangle with a strikes of 5200 and 5600 e) A short strangle with strikes of 5200 and 5600 3. Which one of the following statements about options trading strategies is NOT true: a) In a diagonal spread the options have different strikes and different maturities b) A bull spread with calls requires an initial outflow c) In a short straddle the trader faces potentially unlimited losses d) In a box spread with European options the payoff is highly uncertain e) In a long strip combination more puts then calls are purchased 4. Which of the following is true? a) The theta of a derivative portfolio can be changed by trading in the underlying asset b) The vega of a derivative portfolio can be changed by trading in the underlying asset c) The delta of a derivative portfolio can be changed by trading in the underlying asset d) None of the Greeks of a derivative portfolio can be changed by trading in the underlying asset e) None of the above is true 11 5. A trader betting on an increase in equity market volatility should: a) Take a long position on the spot VIX b) Write call options on the VIX c) Buy call options on the VIX d) Buy put options on the VIX e) Do none of the above 6. The Black Scholes and Merton model assumes that returns on the underlying asset are independent and identically distributed (i.i.d.) over time. Which of the following statements is NOT consistent with the i.i.d. assumption? a) At the end of each month, the expected return for the following month is the same over time b) The return observed over a given week can predict the return over the following week c) The standard deviation of underlying asset returns is the same month by month d) The underlying asset price follows a random walk e) None of the above 7. Which of the following statements is true? a) An American Put option should never be exercised prior to expiration b) An American call option on an NDP stock is worth less than the corresponding (i.e., same strike, maturity an underlying) European call c) The amount of dividends paid by the underlying asset during the life of the option is irrelevant in the decision of early exercise for an American Call option d) According to the BSM model, a European put option price may violate put‐call parity e) None of the above is true 8. You are an Australian firm importing goods from Japan and paying in Japanese Yen. To hedge against currency risk you should: a) Buy call options on the Yen denominated in AUD b) Buy call options on the AUD denominated in Yen c) Buy put options on the Yen denominated in AUD d) Write call options on the Yen denominated in AUD e) Do none of the above 12 QUESTION 6 [6 marks] Carefully explain the concept of implied volatility and its importance for option pricing and, more generally, for market participants. Make sure you illustrate the VIX index. 13 Question 7 [9 Marks] A non-dividend-paying stock is currently trading at $32, its volatility is 30%, and the risk-free
rate for all maturities is 5% per annum. Mr Peterman believes the stock is overpriced an
decides to set up a bear spread using European put options with strike prices of $25 and $30
and a maturity of six months.
What must happen to the stock price for Mr Peterman’s strategy to be profitable? (round to 4
digits) 14 QUESTION 8 [15 marks] Costanza Bank, located in Melbourne, Australia, has the following portfolio of over-thecounter European options on the British Pound (symbol £):
Type
Call
Call
Put
Call Position
-1,000
-500
-2,000
-500 Delta of Option
0.50
0.80
-0.40
0.70 Gamma of Option
2.20
0.60
1.30
1.80 Vega of Option
1.80
0.20
0.70
1.40 As hedging instruments the bank is considering traded European options on the £. The spot
FX rate is currently 1.80 Australian Dollars (AUD) for 1 £, with a volatility of 15% p.a. The
risk-free interest rate is 1% in Great Britain and 2.5% in Australia.
Specifically, they are looking at 7-month ATM (i.e., K=1.80 AUD/£) calls.
a. What should the bank do to make the portfolio both gamma neutral and delta neutral?
b. What should the bank do to make the portfolio both vega neutral and delta neutral?
c. Assume the bank decides to set up the delta-gamma neutral position in a. After a month,
the AUD/£ spot FX rate moves to 1.90, while its volatility stays the same. Risk-free rates
of interest also stay the same. The deltas of the over-the counter options change and
become as follows Type
Call
Call
Put
Call Position
-1,000
-500
-2,000
-500 Delta of Option
0.72
0.86
-0.53
0.88 Facing this situation, the bank decides to keep only delta neutrality: what does the bank need
to do in order to accomplish such goal? For all answers show your calculations. 15 16 17 18 END OF EXAMINATION Space for rough work is provided on the next 4 pages. Examiners will NOT take into account anything written on these pages. A formula list begins on page 27. SPACE FOR ROUGH WORK Examiners will NOT take into account anything written on this page. 19 SPACE FOR ROUGH WORK Examiners will NOT take into account anything written on this page. 20 SPACE FOR ROUGH WORK Examiners will NOT take into account anything written on this page. 21 SPACE FOR ROUGH WORK Examiners will NOT take into account anything written on this page. 22 ...

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