Question 3
(33 points) i) A stock is currently priced at 35 USD with 20% volatility and the company will announce its annual report in one period. If the report is positive, the price is expected to increase by one standard deviation. If the report is negative, it is expected to decrease by two standard deviations.
A government discount bond with a face value of 100 maturing in one period has a yield of 4%. Construct the replicating portfolio of a call and the replicating portfolio of a put, both with a strike price of 30, and find the prices of the two options. ii) On 1st January 2012, Unicredit entered a $200 million five-year interest rate fixed-for-floating 3% swap with Parmalat (each year pay fixed, receive 12-month EURIBOR). At the start of the swap EURIBOR was 2%, but one year later interest rates for 4-year swaps are at 4.5%. (a) Show and discuss whether the swap is profitable for the bank or not today. (b) On 1st January 2013, Parmalat asks from Unicredit to terminate the swap.
How much should Uncredited charge to terminate?
(c) Repeat sub-questions
(a) and (b) in the more realistic case of interest rates dropping to 2% instead. iii) A company has 5 mil shares outstanding at a price of 8 GBP. It decides to make a rights issue of one new share for every 7 old shares. The price of the new share is 3 GBP.
(a) Find the ex-rights price of the stock and the value of the right.
(b) Is there an increase in portfolio value for the current shareholders?
Also, what price change are they willing to accept before they become indifferent to having a right?
(c) Show that, for the same number of rights and target amount to be raised, a higher or lower price for the new shares does not make a difference for the shareholders.
(d) What is the effect on shareholder portfolio value if the same amount was to be raised via a cash offer at the same price (3 GBP)? Show numerically
