Reference no: EM13753252
Question 1: The stock price of Big Umbrellas is currently $100. Both call and put options on Big Umbrellas' stock are available for trading on the options market. The stock price is expected to either increase by 10% or decrease by 8% every quarter. The expiry date of the options is in 180 days. The exercise price of both calls and puts is $95. The risk-free rate is 1.5% (per annum).
Assume 360 days in a year and every quarter is 90 days.
(a) Calculate the price of the call option using the binomial option pricing model.
(b) Calculate the price of the put option using the binomial option pricing model.
Question 2: Jane bought a 3 year bond for $1,000. Both the coupon rate of the bond and the yield to maturity at the time of purchase was 8%. Immediately after the purchase, the yield to maturity increased to 10%. Coupons are paid semi-annually.
Calculate the change in the bond's price and explain the impact of the interest rate change on the value of the bond.
Question 3: Collin is a fixed income portfolio manager. His current bond portfolio consists of the following corporate bonds:
|
Corporate Bond
|
Corporate Rate
|
Maturity
|
Convexity
|
Number of Bonds
|
|
A
|
6%
|
6 Months
|
0.50
|
600
|
|
B
|
7%
|
12 Months
|
1.42
|
900
|
|
C
|
8%
|
18 Months
|
3.40
|
800
|
|
D
|
9%
|
24 Months
|
4.46
|
1,000
|
All of Collin's corporate bonds have a face value of $1,000 and pay coupons on a semiannual basis.
Collin is concerned how interest rate changes will affect the value of his portfolio. As part of his research, he has compiled the following information about the term structure of interest rates using government bonds.
|
Maturity
|
Coupon Rate
|
Yield
|
|
6 Months
|
0.0%
|
0.5%
|
|
12 Months
|
0.0%
|
1.0%
|
|
18 Months
|
2.5%
|
1.5%
|
|
24 Months
|
3.0%
|
1.8%
|
All the government bonds have a face value of $1,000 and also pay coupons on a semi-annual basis.
a) Calculate all the implied forward rates beginning after 6 months up till 24 months.
c) Calculate the duration of each of the bonds A, B, C and D. (10 marks)
d) Calculate the value of Collin's bond portfolio using duration only; assuming interest rate has increased by 1.5%.
e) Calculate the value of Collin's bond portfolio after 1 year using both duration and convexity; assuming interest rate has fallen by 1.2%.
Question 4: Amy is the COO of Quantum Industries, a company specialising in next generation quantum computers. Amy is considering a proposal to build a new factory in Brazil. If the new factory is successful, Amy estimates that the company could realise a profit of $100 million. If it fails, the company could make a loss of $75 million. Running through the various scenarios, Amy thinks that there is a 60% chance that the new factory will fail. One of Amy's managers has suggested to Amy that the company build a small pilot factory. If the pilot factory works, then Amy can consider building the full factory.
The pilot factory would cost $10 million to build. Amy thinks that there is a 50-50 chance that the pilot will succeed. If the pilot works, there is a 90% chance that the full factory (if constructed) will also succeed. If the pilot fails, there is only a 20% probability that the full factory will succeed (if constructed).
(a) Illustrate the decision-making process using decision trees and calculate the expected monetary value of building the pilot factory and not building the pilot factory.
(b) If the cost of the pilot factory is increased to $20 million, illustrate whether Amy should build the pilot factory.
|
Comment on cheadle and prendegasts statement
: Comment on Cheadle and Prendegast's statement, as related to your understanding of how they and others in the fight against genocide around the world.
|
|
Using the weighted-average method
: Canler Inc. uses the weighted-average method in its process costing system. The following data concern the operations of the company's first processing department for a recent month. Using the weighted-average method, determine the equivalent units o..
|
|
Discuss either the pro or con of full financial disclosure
: Discuss either the pro or con of full financial disclosure. You must take a position advocating full disclosure and why this is beneficial for the marketplace and the economy or a position arguing that the associated costs of full disclosure outweigh..
|
|
Networking devices for personal computer systems
: Network Inc manufactures networking devices for personal computer systems, using just-in-time methods. After receiving an order for 300 devices, the company bought materials (for cash) costing $14,000 to fill this order. It incurred labor and overhea..
|
|
Illustrate the decision-making process using decision trees
: Illustrate the decision-making process using decision trees and calculate the expected monetary value of building the pilot factory and not building the pilot factory.
|
|
What level of total sales is necessary to achieve break even
: Super Sharp manufactures and sells two products. The first product is a disposable shaving razor blade that lasts about 7 days. The second product is shaving cream. Customers of the first product use one bottle of shaving cream every 28 days.
|
|
Define responsive design
: Define Responsive Design and clarify what techniques can be used to create a responsive design for a web application? Explain what makes jQuery Mobile different from other JavaScript libraries such as jQuery and jQueryUI
|
|
Uncollectible accounts receivable under the allowance method
: OPA provided for uncollectible accounts receivable under the allowance method. Provisions were made monthly at 1% of credit sales, bad debts written off were charged to the allowance account; recoveries of bad debts previously written off were credit..
|
|
Using the high-low method
: Samson owns a machine shop. In reviewing the shop’s utility bills for the past 12 months, he found that the highest bill of $2,800 occurred in July when the machines worked 1,400 machine hours. The lowest utility bill of $2,600 occurred in December w..
|