2018 BEA602 Assignment 1 [100 marks; 10 percent weighting]
Due Week 8: 12.00pm Wednesday, 12 September, 2018
Question 1 [20 marks]
Cu
ent stock price S is $22. Time to maturity T is six months. Continuously
compounded, risk-free interest rate r is 5 percent per annum. European options
prices are given in the following table:
Strike Price Call Price Put Price
K1=$17.50 $5.00 $0.05
K2=$20.00 $3.00 $0.75
K3=$22.50 $1.75 $1.75
K4=$25.00 $0.75 $3.50
(a) What is the aim of a long (or bottom) straddle strategy? Create a long straddle
y buying a call and put with strike price K3=$22.50 [10 marks]
(b) What is the aim of a short (or top) strangle strategy? Create a short strangle
y writing a call with strike price K3=$22.50 and a put with strike price K2=$20.
[10 marks]
Question 2 [10 marks]
(a) Why is the binomial model a useful technique for approximating options prices
from the Black–Scholes model? [5 marks]
(b) Describe some applications and uses of this model. [5 marks]
Question 3 [20 marks]
Consider the binomial model for an American call and put on a stock whose price
is $60. The exercise price for both the put and the call is $45. The standard
deviation of the stock returns is 30 percent per annum, and the risk-free rate is 5
percent per annum. The options expire in 90 days. The stock will pay a dividend
equal to 3 percent of its value in 50 days.
(a) Draw the three-period stock tree and the co
esponding trees for the call and
the put. [7.5 marks]
(b) Compute the price of these options using the three-period trees. [7.5 marks]
(c) Explain when, if ever, each option should be exercised. [5 marks]
Question 4 [30 marks]
Consider a stock with a price of $120 and a standard deviation of 20 percent. The
stock will pay a dividend of $5 in 40 days and a second dividend of $5 and 130
days. The cu
ent risk-free rate is 5 percent per annum. An American call on this
stock has an exercise price of $150 and expires in 100 days.
What is the price of the American call? Show all calculations.
Question 5 [20 marks]
ABC is cu
ently trading at $78 per share. Your previous calculation of the
historical volatility for ABC indicated an annual standard deviation of return of 27
percent, but examining the implied volatility of several ABC options reveals an
increase in annual volatility to 32 percent.
There are two traded options series that expire in 245 days as show in the
following table:
X = 75 X = 80
Call Put Call Put
DELTA XXXXXXXXXX XXXXXXXXXX
GAMMA XXXXXXXXXX 0.019
The options have $75 and $80 strike prices respectively. The cu
ent 245-day risk-
free interest rate is 4.75 percent per annum, and you hold 2,000 shares of ABC.
Construct a portfolio that is DELTA - and GAMMA- neutral using the call options
written on ABC. Show all calculations.