BEA602 Derivatives
First and Only Paper
Ordinary Examination
Examiner: Dr Richard Mawulawoe Ahadzie
Time Allowed: TWELVE (12) hours
Instructions:
Place and number ALL your answers in the Microsoft Word file provided, convert your word file into PDF and submit via MyLO when completed. Answer ALL (8) Questions. Be sure to read all instructions and questions carefully before answering. Please cite or write all formulas used, when and where possible. Show all intermediate steps where calculations are involved. This is an open book exam; you must not help or seek Helpance from anybody else. You are not allowed to take the exam as a group or discuss the questions with anyone. You are not allowed to send screenshots of the exam questions during or after the exams to anyone. This is a take home exam.
The use of a standard or financial calculator is allowed for this exam.
Total marks for this paper: 80. This examination accounts for 40 percent of the overall assessment of this unit.
Declaration:
I declare that I recognise that this BEA602 examination is a take-home examination. I understand the University of Tasmania’s policy on Academic Integrity and agree to the terms. I also declare that I have not breached Academic Integrity in this examination.
Breaches of academic integrity such as plagiarism, contract cheating, collusion and so on are counter to the fundamental values of the University. A breach is defined as being when a student:
a) fails to meet the expectations of academic integrity; or
b) seeks to gain, for themselves or for any other person, any academic advantage or advancement to which they or that other person is not entitled; or
c) improperly disadvantages any other member of the University community.
Students engaging in any breach of Academic Integrity may be dealt with under the Student Academic Integrity Ordinance, and this can include the imposition of penalties that range from a deduction/cancellation of marks to exclusion from a unit or the University. Details of penalties that can be imposed are available in that Ordinance.
Submitting this examination through MyLO will be taken as certification that you agree to the terms of Academic Integrity outlined above.
Signed Student: _______________________________
ID Number: _______________________________
Question 1
Mark Gram a third year University of Tasmania student attended a derivatives masterclass this semester. From the class, Mark believes that derivatives always cause significant losses to traders who trade them. Is his believe True or False?
True
False
Cannot be determined with the information given
[2 marks]
Does high volatility in a market lead to more use of financial derivatives? Explain your answer.
[3 marks]
Mike Brooks is an art collector in central Hobart, currently prices of local veterans’ sculptures have skyrocketed. Today, Mike buys a sculpture of the first female lieutenant colonel for $795,500. Last 2-year, he bought the sculpture of the first General for $305,000, which is currently worth $1,250,000 in the spot market. Mike believes that prices will continue to increase and as such has decided to hold the assets and sell later in 5-year time.
Is Mike hedging or speculating? Explain
[2 marks]
Briefly explain how Mike can use derivatives to hedge his exposure, highlight the direct and indirect cost to his strategy.
[3 marks]
[Question 1 =10 marks]
Question 2
To hedge some of the input price risk, a manufacturer can go long position on the futures contract. Is this statement True or False?
True
False
Cannot be determined with the information given
[2 marks]
Explain the effect of volatile interest rates on forward and futures prices, keeping all else constant.
[3 marks]
Suppose an orange farmer and a juicy manufacturer decides to enter a forward contract, the juicy manufacturer goes long to buy some oranges at a fixed price at the end of the year. The farmer goes short to sell some oranges at the end of the year. They agree to trade 1000 ounce of oranges at the forward price of $330 per ounce on the delivery date.
At the delivery date, if the spot price is $300 per ounce, calculate the profit and loss to both the farmer and manufacturer.
[1.5 marks]
Suppose the manufacturer decides to buy a call option instead of the forward contract, the strike price is $270 per ounce, and the premium is $10. What would be the manufacturer profit?
[1.5 marks]
From your solution in question ‘i and ii’, which of the trading strategies is more beneficial to the manufacturer? Explain your answer
[2 marks]
[Question 2 = 10 marks]
Question 3
Suppose you have an insider information that a certain stock price is going to increase for sure with a probability of 65%, assuming it is legal to trade on this information one of the best trading strategies would be to buy the stock on margins or buying a call while simultaneously holding the put. Is this statement True or False?
True
False
Cannot be determined with the information given
[2 marks]
Given that forward contracts have high default risk, list three main reasons any rational trader might prefer to trade a forward contract rather than an identical future contract of same maturity.
[3 marks]
Suppose the current stock price is $35, time to maturity is 0.5 years, risk-free rate is 5% per year, the European call option prices with strike prices K1 = 30 is $2.75 and K2 = 35 is $1.50.
Draw a bearish vertical spread by buying the call option strike prices K2 and selling the call option with strike price K1. Highlight the breakeven points, maximum profit and loss for this payoff diagram.
[3 marks]
Is the above trading strategy profitable to an investor who is optimistic about the underlying stock? Explain.
[2 marks]
[Question 3 = 10 marks]
Question 4
Suppose you hold 0.89 shares of a stock, and you want to hedge your downside risk, this could be achieved by selling a certain portion of money market account units and using the funds to purchases 0.89 additional shares. Is this statement True or False?
True
False
Cannot be determined with the information given
[2 marks]
Briefly discuss the main advantage of exchange-traded contracts to over-the-counter (OTC) contracts.
[3 marks]
Suppose the current stock price is $65, volatility is 30%, risk-free rate is 3% per annum continuously compounded for all maturities, the strike price is $50.
Using the Cox-Ross-Rubinstein approach, determine the price of a derivative whose payoff is given as 2*max[(S_T-K),0] for a three-month time step with an American-style option that expires in six-months using a two-step binomial tree. Where S_T is the stock price. Show all terminate steps.
[4 marks]
Should the American option in c(i) be exercised early? Explain your answer.
[1 mark]
[Question 4 = 10 marks]
Question 5
A derivatives student believes that the risk-neutral valuation technique works well because it assumes all investors are risk-neutral and hence the model fails when investors are not risk neutral. Is this believe True or False?
True
False
Cannot be determined with the information given
[2 marks]
Briefly explain why the hedge ratio is referred to as a Holy Grail in option pricing framework.
[3 marks]
Suppose the current stock price is $70, after six months, it either goes up by the factor U=1.2809 or it goes down by the factor D= 0.6586. The option matures after T=0.5 year, a dollar invested in the money market account earns continuously compounded risk-free rate of 5% per year.
Suppose the option is at-the-money, determine the European call value by using the synthetic single-period binomial approach.
[2.5 marks]
Suppose the market call price is $8. Is there an arbitrage opportunity? Explain how the arbitrage opportunity can be exploited.
[2.5 marks]
[Question 5 = 10 marks]
Question 6
In the Black-Scholes-Merton model, calibration is employed to set the delta and gamma values to zero. Is this statement True or False?
True
False
Cannot be determined with the information given
[2 marks]
Briefly explain the implications of Vega hedging in the Black-Scholes-Merton model framework.
[3 marks]
CSL Ltd’s current stock price is $80, assuming the call option is $15 in-the-money, the time to maturity is 180 days, the historical variance is 0.25 per year and the risk-free rate is 5%.
Using the Black-Scholes-Merton model, determine the call and put option prices.
[2.5 marks]
Determine the new call price if CSL pays a dividend yield of 8% per year. What can you say about the call price in c(i) and c(ii)? Is this consistent with theory?
[2.5 marks]
[Question 6 = 10 marks]
Question 7
Keeping all else constant, the larger a bond’s maturity, the smaller the bond’s duration. Is this statement True or False?
True
False
Cannot be determined with the information given
[2 marks]
Briefly discuss two disadvantages in using duration as a risk measure for changes in the bond price.
[3 marks]
Suppose a coupon paying bond that matures in 4 years, has a coupon rate of 5% percent per year. The bond’s principal is $3,000 and the market price is $1,000.
Using a yield of 0.10 calculate the bond’s duration.
[3 marks]
If the yield increase by 0.0002, use a duration-based formula to predict the change in the bond price.
[2 marks]
[Question 7 = 10 marks]
Question 8
A swap may be created by combining forward rate agreements and zero-coupon bonds in your portfolio. Is this statement True or False?
True
False
Cannot be determined with the information given
[2 marks]
Given swaps are excellent examples of financial engineering and can be profitable, as a rational investor would you enter a swap contract that you do not completely understand. Explain your answer.
[3 marks]
Suppose an American and Australian firms enter into a swap with a three-year term on a principal of $630 million. The spot exchange rate for US is $6.3 per Australian dollar. American raises 100×6.3=$630 million and gives it to Australia, which in turn raises AUD 100 million and gives it to American firm. American firm pays the Australian firm 5 percent per year on AUD 100 million and Australian pays American 8 percent per year on $630 million at the end of each year for three years.
Time to Maturity (in years) US(Domestic) Zero-Coupon Bond Price (USD) Australian (Foreign) Zero-Coupon Bond Price (AUD)
1 B(1)=$0.97 B(1)=$0.92
2 B(2)=$0.79 B(2)=$0.88
3 B(3)=$0.93 B(3)=$0.99
Determine the value of the USD and AUD leg of the cash flows.
[2.5 marks]
Determine the value of the swap of the AUD to the USD.
[2.5 marks]
[Question 8 = 10 marks]
End of Examination
