You observe a 50 price for a non-dividend-paying stock. The call option has two years to

mature, the periodically compounded risk-free interest rate is 5%, the exercise price is 50, u =

1.356, and d = 0.744. Assume the call option is European-style.

Required:

a) Compute the probability of an up move based on the risk-neutral probability

(4 marks)

b) Compute the current call option value

(6 marks)

c) Determine the current put option value

(6 marks)

d) Explain four advantages the option valuation method you have used here (4 marks)

QUESTION TWO

a) The current stock price for XYZ ltd is sh. 25. A European call option with an exercise

price of sh. 28 will expire in 160 days. The yield on a 160-day Treasury bill is 5.18%.

The standard deviation of annual returns on XYZS stock is 21%. Compute the premium

for a call option on this stock using Black-Scholes model.

(10 marks)

You may use

c = SN(d1) XN(d2 )erT

d1 =

ln( s X ) + (r + 2 )T

T

a) Assume that the 3.75% US Treasury bond that matures on 15 August 2041 is priced to

yield 5.14% for settlement on 15 October 2014. Coupons are paid semi-annually on 15

February and 15 August. The yield-to-maturity is stated on a street-convention semi

annual bond basis. This settlement date is 61 days into a 184-day coupon period, using

the actual/actual day-count convention. Compute the approximate modified duration and

the approximate Macaulay duration for this Treasury bond assuming a 5 bp change in the

yield-to-maturity.

(10 marks)

QUESTION THREE

a) The Australian dollar is currently worth 0.6100 US dollars and this exchange rate has a

volatility of 12%. The Australian risk-free rate is 7% and the US risk-free rate is 5%.

Compute the value of a 3-month American call option with a strike price of 0.6000 using

a three-step tree.

(9 marks)

b) The Table below provide the results of Simulation of stock price when

= 0.15 and = 0.30 during 1-week periods.Stock price at start of period

Random sample for

Change in stock price during

period

100.00

052

102.45

1.44

108.88

-0.86

105.30

1.46

112.00

-0.69

109.11

-0.74

106.06

0.21

107.30

-1.10

102.69

0.73

106.11

1.16

111.54

2.56

Fill the missing values in the Table.

(11 marks)