AQ079-3-2-MFD
Assignment
Page 1 of 3
Answer ALL the questions. Otherwise stated all the prices are in dollars and the interest
rate is continuously compounded.
QUESTION 1 (29 marks)
Suppose you have a long forward contract on a stock that provides a known cash income
b1 , b2 ,...,bn at times 0  t1  t 2  ...  t n  T , respectively. The contract stipulates that you have
to buy the stock at time T at a price K. The current price of the stock is S 0 and the risk-free
interest rate is r. Using no-arbitrage arguments:
(a)
Which is the T-forward price of this stock?
(5 marks)
(b)
How much should you pay for this contract (general case)?
(5 marks)
(c)
How much should you pay for this contract if b1  b2  ...  bn  0 (i.e. in the case of a
non-dividend paying stock)?
(5 marks)
(d)
Consider a 14-month forward contract on a stock with a current price of 45. We assume
that r equals 4% per annum and dividends of 3 per share are expected after three months,
six months, nine months and twelve months.
(9 marks)
(e)
If you sign a free-paid contract of this type, which strike price should be specified in the
contract? If this price is fixed at 30, could you capitalize on this situation? How?
(5 marks)
QUESTION 2 (13 marks)
The price of a European call option with a maturity of ten months a strike price of 27 amounts to
4. The underlying stock price is 23, and a dividend of 0.5 is expected in two months, in five
months and in eight months. The risk-free interest rate is 4% per annum.
(a)
What is the price of a European put option, written on the same stock, that expires in ten
months and has a strike price of 27?
(7 marks)
(b)
If the price of the put in a) is fixed at a value of 10. What opportunities are there for an
arbitrageur?
(6 marks)
Level 2
Asia Pacific University of Technology & Innovation
YYYY
AQ079-3-2-MFD
Assignment
Page 2 of 3
QUESTION 3 (34 marks)
A spread trading strategy involves taking a position in two or more options of the same type. A
bull spread for instance can be created by buying a call option on a stock with a strike price of
K1 and selling a call option on the same stock with the same expiration date and a higher strike
price K2
(a)
What is the payoff function of a bull spread?
(3 marks)
(b)
What is the profit function of a bull spread? Draw a diagram.
(6 marks)
(c)
Do you agree with the following statement: "A bull spread strategy limits the investor's
upside as well as downside risk?" Explain.
(5 marks)
(d)
As a bull spread, a bear spread can be created by buying a call with one strike price K1
and selling a call with another strike price K 2 , but in this case K1  K 2 . Repeat (a) and
(b) for this spread and evaluates the following statement "An investor who enters into a
bull spread is hoping that the stock price will increase. By contrast, an investor who
enters into a bear spread is hoping that the stock price will decline".
(10 marks)
(e)
An investor would like to buy a portfolio consisting of 2 bull spreads and one bear
spread. The calls composing the bull spread have prices equal to C bull1  7.9 , C bull2  3.6
and strike prices K bull1  150 , K bull2  200 whereas the prices and strike prices of the
bear spread amount to C bear1  6.27 , C bear2  6.51 , K bear1  190 and K bear2  165
respectively.
Make a plot of the profit function of the investor by using any suitable graph sheet and
compare it with the profit resulting of an investment of the same amount but in a call
option with a strike price K call  192 . Assume that the interest rate is 4% and the maturity
date of the call options 1 year.
(10 marks)
Level 2
Asia Pacific University of Technology & Innovation
YYYY
AQ079-3-2-MFD
Assignment
Page 3 of 3
QUESTION 4 (24 marks)
A butterfly spread involves positions in options with 3 different strike prices. It is created by

buying a call option with a relatively low strike price, K1 ;

buying a call option with a relatively high strike price, K 3 ; and

selling two call options with a strike price K 2 , halfway between K1 and K 3 .
Suppose a stock is currently worth 61 and an investor feels that a significant price movement in
the next 6 month is unlikely. Suppose that the market prices of six-month calls are as follows:
Strike price
55
60
65
Call price
10
7
5
Assume also that the interest rate is zero for simplicity (this is equivalent to not take into account
the time value of money). If the investor decide to create a butterfly spread by buying one call
with a strike price of 55, buying one call with a strike price of 65 and selling two calls with a
strike price of 60.
(a)
(b)
Level 2
How much money does he need to create this spread?
(11 marks)
Describe graphically the profit of this spread and indicates which scenario is the best for
the investor.
(13 marks)
Asia Pacific University of Technology & Innovation
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